Hobbes, Galileo, and the Physics of Simple Circular Motions

in Hobbes Studies

Hobbes tried to develop a strict version of the mechanical philosophy, in which all physical phenomena were explained only in terms of bodies in motion, and the only forces allowed were forces of collision or impact. This ambition puts Hobbes into a select group of original thinkers, alongside Galileo, Isaac Beeckman, and Descartes. No other early modern thinkers developed a strict version of the mechanical philosophy (not even Newton who allowed forces of attraction and repulsion operating at a distance). Natural philosophies relying solely on bodies in motion require a concept of inertial motion. Beeckman and Descartes assumed rectilinear motions were rectilinear, but Galileo adopted a theory which has been referred to as circular inertia. Hobbes’s natural philosophy depended to a large extent on what he called “simple circular motions.” In this paper, I argue that Hobbes’s simple circular motions derived from Galileo’s belief in circular inertia. The paper opens with a section outlining Galileo’s concept, the following section shows how Hobbes’s physics depended upon circular motions, which are held to continue indefinitely. A third section shows the difficulty Hobbes had in maintaining a strictly mechanistic philosophy, and the conclusion offers some speculations as to why Galileo’s circular inertia was never entertained as a serious rival to rectilinear inertia, except by Hobbes.

Abstract

Hobbes tried to develop a strict version of the mechanical philosophy, in which all physical phenomena were explained only in terms of bodies in motion, and the only forces allowed were forces of collision or impact. This ambition puts Hobbes into a select group of original thinkers, alongside Galileo, Isaac Beeckman, and Descartes. No other early modern thinkers developed a strict version of the mechanical philosophy (not even Newton who allowed forces of attraction and repulsion operating at a distance). Natural philosophies relying solely on bodies in motion require a concept of inertial motion. Beeckman and Descartes assumed rectilinear motions were rectilinear, but Galileo adopted a theory which has been referred to as circular inertia. Hobbes’s natural philosophy depended to a large extent on what he called “simple circular motions.” In this paper, I argue that Hobbes’s simple circular motions derived from Galileo’s belief in circular inertia. The paper opens with a section outlining Galileo’s concept, the following section shows how Hobbes’s physics depended upon circular motions, which are held to continue indefinitely. A third section shows the difficulty Hobbes had in maintaining a strictly mechanistic philosophy, and the conclusion offers some speculations as to why Galileo’s circular inertia was never entertained as a serious rival to rectilinear inertia, except by Hobbes.

Hobbes’s natural philosophy was one of only four strict versions of the mechanical philosophy. He was in good company, with Galileo, Isaac Beeckman, and of course, René Descartes. The four versions of the mechanical philosophy developed by these thinkers (admittedly only partially developed in Galileo’s case) were strict in the sense that they explained all physical phenomena in terms only of inert matter in motion. For these four thinkers, any unexplained principles of activity in matter, whether originating from scholastic notions of substantial forms, or from supposed occult qualities, seminal principles, active principles, or any similarly mysterious notions, had to be excluded from natural philosophy. Hobbes stated it clearly:

… as for those that say anything may be moved or produced by itself, by species, by its own power, by substantial forms, by incorporeal substances, by instinct, by anti-peristasis, by antipathy, sympathy, occult quality, and other empty words of schoolmen, their saying so is to no purpose.1

The proud boast of each of these thinkers was that such unexplained conceptions were completely unnecessary, since everything could be explained merely by the impacts and collisions, frictions, combinations, and separations, of the perpetually moving, but otherwise inert, particles of matter which were held to constitute all things.2 Although prevailing historiography in the history of science tends to suggest that all the mechanical philosophers were alike in this regard, this is not true. Virtually every other “mechanical philosopher” (unless of course he, or very occasionally she, was a follower of Descartes) still clung to some residual notions from earlier natural philosophies, and supposed that there must be in-built principles of activity in bodies to account for all their interactions with other bodies. Even Isaac Newton, to mention one very prominent example, insisted that

Particles have not only a Vis inertiae [force of inertia], accompanied with such passive Laws of Motion as naturally result from that Force, but also that they are moved by certain active Principles, such as is that of Gravity, and that which causes Fermentation, and the Cohesion of Bodies.3

So, Hobbes was a member of a select group, and should be recognised as one of only four thinkers who developed a system of natural philosophy which can be said to be kinematic in so far as it invoked only motions of bodies in its explanations. These kinematic systems allowed forces of impact or collision, but rejected all occult notions of forces, such as attraction and repulsion, and can be said to be different, therefore, from more dynamic versions of the mechanical philosophy (such as Newton’s), which allowed occult, or unexplained, forces.

In order for a purely kinematic system to work, it had to be based on some kind of inertial principle. According to Aristotle, everything that moves has to be kept in motion by something acting as a mover, and motion ceases when the mover ceases to act (the scholastics even had a Latin dictum to sum this up: omne quod movetur ab alio movetur).4 Galileo and Beeckman seem to have been the first to realise the possibilities for improving our understanding of the physical world if it is assumed that, contrary to the Aristotelian dictum, a body once set in motion will continue to move indefinitely unless something intervenes to stop it. Galileo was led to believe that it was perfectly circular motion that would continue indefinitely, while Isaac Beeckman assumed that only rectilinear motion could continue as long as it was undisturbed. Beeckman’s assumption was taken up by Descartes and developed into the most influential version of kinematic philosophy—Cartesianism.5 Galileo’s assumption that circular motion was inertial, although seemingly paradoxical for us, was taken up by Thomas Hobbes and became a mainstay of the physics he developed in De corpore and other writings.

The Galilean antecedents of Hobbes’s natural philosophy account for the emphasis in his mature works, upon what he calls “simple circular motions.” The aim of this paper is to consider the concept of “simple circular motion” and how it serves Hobbes’s purposes. The concept is certainly fundamental to his physics, and yet it has scarcely been addressed by most Hobbes commentators.6 I want to begin by filling in the Galilean background, so that we can understand why Hobbes was so impressed with the idea of circular inertia and chose to develop that in preference to the Cartesian alternative. Before going any further, however, it is perhaps worth dismissing the only other possible source for Hobbes’s obsession with circular motions. Theories about the power of circular motions in mechanics and in physics more generally had comparatively recently become available with the first publication in Latin (in 1517) of the pseudo-Aristotelian Mechanical Problems. The Aristotelian author of this work declared that the various mechanical questions discussed in this work were “not altogether identical with physical problems” but not “entirely separate from them” either, but “the original cause of all such phenomena is the circle.”7 Throughout the work, accordingly, the author keeps returning to the properties of circles to solve his problems.8 The similarities with Hobbes (and with Galileo) are only superficial however. Circles figure in this Ancient work as the shape indicated by movements of the end of a lever, or by the tipping of an unbalanced steelyard, or by other movements made during the operation of the six simple machines. The explanations are couched much more in terms of statics than in the kinematics which Galileo will develop and which Hobbes will take up. If we add to this the fact that Hobbes was no great admirer of Aristotle, it seems unlikely that he would have been inspired to base his new physics on principles borrowed from a source which, like all his contemporaries, he would have regarded as authentically authored by the founder of the Lyceum.

By contrast, Hobbes’s admiration for Galileo is very well known. Furthermore, Hobbes recognised that Galileo’s great achievement was in pointing the way to a kinematic natural philosophy, a philosophy based on motion:

Galileus in our time… was the first that opened to us the gate of natural philosophy universal, which is the knowledge of the nature of motion. So that neither can the age of natural philosophy be reckoned higher than to him.9

The famous Florentine can be seen, therefore, as the most likely source of inspiration, and even a source of motivation, for Hobbes; and this is easily confirmed by studying the details of their respective natural philosophies. We should begin, therefore, by considering the role of circular movements in Galileo’s philosophy.

Galileo and “Circular Inertia”

The crucial aspect of Galileo’s physics, which was to become fundamental to Hobbes, was the concept which is more often than not referred to by Galileo scholars as “circular inertia”, but which might just as well be called “perpetual circular motion.”10 Galileo seems to have persuaded himself, and tried to persuade his readers, that once a body was set in circular motion it would continue to move this way for ever—unless something intervened to change the situation. It is not possible to say with any certainty how Galileo came up with this radical departure from Aristotelian physics. It is possible that he was first excited by the fact that the new explanation for the tides, proposed by his friend Paolo Sarpi, enabled him to dismiss (so he believed) the occult influence of the Moon.11 This new theory explained the tides solely as a result of the daily rotation of the Earth on its axis, as proposed by Copernicus, and the proposed annual revolution around the Sun.12 But this now committed Galileo to Copernicanism, and that required some explanation as to why the Earth was perpetually moving (an explanation which Copernicus himself had never provided). It may be that Galileo then decided to cut the Gordian knot and make the circular motion of the Earth natural to it—generalising from this would lead him to suggest circular motion was natural to all bodies. These speculations are at least consistent with what we know of Galileo’s early career, with his extreme anti-occultism, and with his evident excitement about, commitment to, and blindness to the shortcomings of, the tidal theory.13

Be that as it may, the clearest statements of circular inertia appear in the Dialogue on the Two Chief World Systems (1632). Consider, for example, the protracted discussion, on the Second Day, between Salviati and Simplicio about the behaviour of a perfectly spherical and smooth ball on a hard, highly-polished and perfectly smooth surface. The two characters readily agree that if the surface is sloping the ball will either descend down the slope with increasing speed, or, if forcibly pushed upwards, will move up the slope with continually decreasing speed. But what happens, Salviati asks, in the case of a ball set in motion on a perfectly horizontal plane? To his surprise, Simplicio finds himself declaring that the ball must continue to move at the same speed, there being no reason why it should speed up or slow down, and that it will continue to so move for as long as the plane extends. Here is the relevant part of the discussion:

Salviati: Now tell me what would happen to the same movable body placed upon a surface with no slope upward or downward.

Simplicio: Here I must think a moment about my reply. There being no downward slope, there can be no natural tendency toward motion; and there being no upward slope there can be no resistance to being moved, so there would be an indifference between the propensity and the resistance to motion. Therefore it seems to me that it ought naturally to remain stable…

Salviati: I believe it would do so if one set the ball down firmly. But what would happen if it were given an impetus in any direction?

Simplicio: It must follow that it would move in that direction.

Salviati: But with what sort of movement? One continually accelerated, as on the downward plane, or increasingly retarded as an on the upward one?

Simplicio: I cannot see any cause for acceleration or deceleration, there being no slope upward or downward.

Salviati: Exactly so, but if there is no cause for the ball’s retardation, there ought to be still less for its coming to rest; so how far would you have the ball continue to move?

Simplicio: As far as the extension of the surface continued without rising or falling.

Salviati: Then if such a space were unbounded, the motion on it would likewise be boundless? That is perpetual?

Simplicio: It seems so to me…14

But, Salviati then asks what would count as an example of a perfectly horizontal plane on the Earth? It is of course a plane which maintains a constant distance from the centre of the Earth. Galileo provides the example of the surface of the sea when it is perfectly calm:

Salviati: Then a ship, when it moves over a calm sea, is one of these movables which courses over a surface that is tilted neither up nor down, and if all external and accidental obstacles were removed, it would thus be disposed to move incessantly and uniformly from an impulse once received?

Simplicio: It seems that it ought to be.15

So, the hard, highly polished and perfectly smooth horizontal plane, envisaged earlier in the discussion, would in fact be a sphere (or we could reduce it to a circular track) concentric with, and surrounding, the Earth.

The point of all this, then, is to persuade his readers that once something is set in motion in a circle around the Earth, it will persist in this state for ever. We can see this privileging of circular motion again in Galileo’s famous, or notorious, “cosmogonical fancy”.16 Galileo suggests that God might have created the Sun first, and then created each of the planets at a unique place in space, from which he successively released them. Releasing Mercury first, God allowed it to fall, accelerating all the while, to a particular distance from the Sun, whereupon he deflected its motion into a circle around the Sun. This is repeated for each planet, but each is allowed to fall through a successively diminishing distance, and so each planet ends up moving in its final circular orbit slower than the planet before (and of course has a greater circumference to travel to complete an orbit). The important thing to note is that once the planet is deflected into circular motion around the Sun its speed no longer increases (nor does it slow down). Galileo takes it for granted that this is just like the case of the ball rolling on a horizontal plane around the Earth—there is no reason why the ball, or the planet, should accelerate or decelerate:

We may say with Plato that at the beginning He [God] gave it a straight and accelerated motion; and later, when it had arrived at that degree of velocity, converted its straight motion into circular motion whose speed thereafter was naturally uniform.17

For Galileo, then, circular motion is natural and perpetual. When something is moving uniformly in a circle, we do not need to seek for a continually acting cause which is keeping it in motion. It is only accelerating or decelerating motions that need to be explained in terms of causes. A major point of Galileo’s example of the ball on a horizontal plane is that, once it is set in motion, the ball continues to move because there is no reason why it should speed up or slow down. It is undeniable, of course, that the horizontal plane has to be defined in terms of a central point of gravitational attraction. Galileo could not escape from this recalcitrant fact, but he could claim to have made the centre of gravity irrelevant to his discussion, and to his explanation of the perpetual movement of the sphere. The sphere moved the way it did precisely because the force of gravity was no longer affecting it. Consequently, the movement of the sphere did not depend on any mysterious force, but merely on the fact that it was set in motion at some point by a mover, and thereafter continued to move at the same speed because there were no causes operating on it to change its motion. In modern terms it is a kinematic account, not a dynamic one.18

Of course, a modern reader might object that Galileo had not really removed gravity (how could he?), but merely countered its effects by means of the supposed indefinitely extended horizontal plane. As Alexandre Koyré pointed out, for bodies to move perpetually and with uniform motions, Galileo “needed to have them supported by imaginary planes, so as thereby to counteract the unavoidable action of gravity.”19 But Galileo’s thinking long preceded the establishment of Newton’s third law of motion (that action and reaction are equal and opposite), and it seems perfectly clear that Galileo regarded the horizontal planes he called upon to be required only by the nature of his illustrative examples (as in the case of a ship “when it moves over a calm sea… and if all external and accidental obstacles were removed, it would thus be disposed to move incessantly and uniformly from an impulse once received”20). The “cosmogonical fancy”, after all, did not require the presence of physical planes, and in his Mechanics of 1601 Galileo had simply insisted “That heavy bodies, all external and adventitious impediments being removed, can be moved in the plane of the horizon by any minimum force.”21 It was the “plane of the horizon” in the abstract that was crucial for Galileo, not any physical plane.

Here, then, we have Galileo’s solution to the problem that had been bequeathed to his followers by Nicholas Copernicus. Copernicus had never tried to explain what it was that kept the Earth in motion. Galileo’s solution proposed that the perpetual motion of the Earth did not need a perpetual moving force (thereby rejecting the scholastic adage omne quod movetur ab alio movetur) but simply moved in a circle because it was its nature to do so. For Galileo, then, circular motion is declared to be the only real natural motion:

There is no doubt that to maintain the optimum placement and perfect order of the parts of the universe as to local situation, nothing will do but circular motion or rest.22

Accordingly, the straight motions, up or down, which Aristotle declared to be natural below the Moon, are not natural at all:

What is thus said of earth may be said as reasonably of fire and of the greater part of the air, to which elements the Peripatetics are forced to assign as an intrinsic and natural motion one with which they were never moved and never will be, and to abolish from nature that motion with which they move, have moved, and are to be moved perpetually. I say this because they assign an upward motion to air and fire, which is a motion that never belongs to the said elements, but only to some of their particles—and even then only to restore them to perfect arrangement when they are out of their natural places.23

It is important to note, however, that Galileo does not merely use his supposedly natural circular motions to explain the perpetual motions of the Earth and the other planets. Circular motions play a much wider role in his physics. As we’ve already seen, he uses the rotation of the Earth on its axis and its revolution about the Sun to explain why the tides occur. This is a fundamentally important aspect of Galileo’s physics—because it takes a phenomenon which has previously been explained in terms of the occult influence of the Moon, and which Galileo can now explain by recourse only to the motion of the Earth. Kinematics replaces occultism.

On the Second Day, in the Dialogue, Galileo even tries to suggest that the supposed acceleration due to gravity of falling bodies (another prominent unexplained notion in contemporary natural philosophy) is in fact an illusion resulting from the rotation of the Earth and the fact that a falling body moves (naturally) on a circular trajectory. As Salviati is made to say of a body falling from the top of a tower: “the body really moves in nothing other than a simple circular motion, just as when it rested on the tower it moved with a simple circular motion” (because the tower stands on the rotating Earth).24 In spite of appearances, “the true and real motion of the stone is never accelerated at all, but is always equable and uniform.” And consequently, “we need not look for any other causes of acceleration or any other motions, for the moving body, whether remaining on the tower or falling, moves always in the same manner; that is, circularly, with the same rapidity, and with the same uniformity.”25 Again, the kinematics of simple circular motion displaces an occult notion—acceleration due to gravity.

Galileo’s diagrammatic illustration (Figure 1) helps us to understand this remarkable claim. The circular line bi represents the surface of the Earth. The line cd represents the circle swept out by the top of the tower as it is carried along by the rotating Earth. The line marking out a semicircle from C through I to A shows the track followed by the falling body, moving with its own natural circular motion. The point A is the centre of the Earth, but the falling body is not held to be approaching it as a culminating point of its travel—much less because it is drawn to that point by some occult force—in principle the falling body would continue past A and return circularly to C, because natural circular motion is perpetual, but of course its journey is actually curtailed by the surface of the Earth at I.26 So, the body falls from the top of the tower at C and strikes the ground at the foot of the tower, but by that time the foot of the tower has been carried by the rotating Earth to I. Between bc (the starting position of the tower), and id, Galileo has marked equally-spaced successive positions of the tower at F, G, H, and L. We can see by eye that the points along the line of the tower marked out by the semicircular line cia, which are the successive positions of the falling body are not equally spaced but show a clear increase. Accordingly, to an observer watching the falling body, the body would seem to be accelerating as it fell down through the height of the tower, but in fact it is not accelerating at all, merely following its natural circular path with uniform motion.

Figure 1

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Figure 1

Galileo’s attempt to use simple circular motion to dismiss the concept of acceleration due to gravity. Dialogue, Second Day. A body falling from the top of a tower C, on the rotating Earth, will not fall straight down but will fall in the circular path cia (where A is the centre of the Earth), with unifom (non-accelerating) motion. To an observer, the succesive positions of the falling body against the wall of the tower (shown successively at F, G, H, L, and D) will give the (false) impression of accelerated motion.

Citation: Hobbes Studies 29, 1 (2016) ; 10.1163/18750257-02901002

An obvious way to test the validity of this claim would be to provide a thorough mathematical analysis, showing that the successive positions of the falling body did conform to a supposed uniform circular movement. Galileo certainly did not do that in the Dialogue, and indeed he was clearly aware that this theory seemed to contradict his discovery that descending bodies follow a parabolic path (even so, he still insisted that “if the line described by a falling body is not exactly this, it is very near to it”).27 Nevertheless, in spite of the obvious difficulties with this theory, he included it in the Dialogue. It was just too good an example of how a supposedly occult notion, like gravitational attraction, might be dismissed and replaced by “simple circular motions.”

Galileo’s theory of “circular inertia” and his speculations about perpetual “simple circular motions” were evidently crucial factors in the new physics which he hoped to develop. In spite of the difficulties confronting these speculations, Galileo clung to them because they seemed to him to hold great promise for excluding occult qualities and other unexplained factors from natural philosophy, and for enabling him to produce a purely kinematic system.

Furthermore, it is also clear that Galileo was not alone in thinking that simple circular motions were the key to a kinematic philosophy. Thomas Hobbes, seeking to develop his own system of new philosophy, distinct from that of his detested rival Descartes, as we shall now see, adopted Galileo’s concept of circular inertia, and his notion of “simple circular motions”, and made them fundamental features of his physics. Hobbes implicitly believed Galileo when he wrote that circular motion “once acquired, it will continue perpetually with uniform circular motion.”28

Hobbes and Simple Circular Motion

Let us begin with a brief look at Hobbes’s physics before he saw how he could adapt and exploit Galileo’s concept of simple circular motion. In the Anti-White the starting point for Hobbes’s physics seems to be the Sun, which is seen as the driver which keeps everything else moving. He provides an explanation of sunlight, for example, by assuming that the Sun is continually pulsating, repeatedly expanding and contracting. It is the spherical expansion outwards of the surface of the Sun which gives rise to an expanding outward sphere of light, successively transmitted through the surrounding medium. At this point in his career, Hobbes evidently does not regard it necessary to provide an explanation for this perpetual movement of the Sun. He only provides a rationally based account as to why it must be pulsating in and out. It cannot perpetually expand, he pointed out, because “if it could, it would be completely diffused”. Therefore, its expansion must be countered by a period of contraction. “There must always be in the Sun a systole and diastole, or a contraction and dilation, alternately.”29 The sun is held to have a pulsific faculty, in just the same way as the heart in the physiological systems of Galen and William Harvey (the words “systole” and “diastole” being the precise terms used by medical writers to refer to the contraction and expansion of the heart). Indeed, perhaps Hobbes was taking too literally William Harvey’s trope, in the Preface to his De motu cordis, that the Sun “might well be designated the heart of the world.”30 Hobbes proceeded to use the inherent motion of the Sun to explain the motion of the Earth:

It is agreed that there is present in the Sun a certain motion which dilates it in every direction and by which the Sun illuminates everything situated around it. That motion, combined with another motion, the rotary one [established by Galileo’s observations of sunspots], will compel the air or ether next to [the Sun] to take on a circular action…31

But Hobbes’s determination to reject all occult and unexplained notions from natural philosophy soon became as strong as that of Galileo and Descartes (perhaps stimulated by the fact that Descartes could boast of having eschewed all unexplained phenomena). Like them, he began to understand the importance of a fully kinematic system—a system where all physical phenomena could be explained solely in terms of bodies in motion. Given the bitter rivalry between Hobbes and Descartes, it is hardly surprising that Hobbes should turn to the work of Galileo to help him to develop his own system. Accordingly, it was not long before Hobbes replaced his pulsing, animated Sun with something more in keeping with a strictly mechanical philosophy, namely, a Sun which performed a perpetual simple circular motion of the kind we have seen invoked by Galileo.

The key to a more mechanistic philosophy for Hobbes was what he referred to as motus cribrationis—the motion of a sieve.32 We have to imagine the Sun moving the way a sieve is moved in the hands of a farmer, or the way the shallow pan is moved by a gold prospector panning for gold in a river. Typically, the sieve or pan will be moved with a small gyratory motion about a fixed point. If the Sun is held to be moving this way, then pulses of light are still sent out from the Sun, but not all at once around its whole surface, as was supposed in the pulsation theory, but successively as each part of the circumference pushes outward during the Sun’s sieve-like gyration (compare Figure 2 with Figure 3).33

Figure 2

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Figure 2

The Sun dilates and contracts about a fixed centre C, generating pulses of light (shown as arrows) as it dilates, simultaneously on all sides.

Citation: Hobbes Studies 29, 1 (2016) ; 10.1163/18750257-02901002

Figure 3

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Figure 3

Here we see the Sun in three successive positions (shown by a solid, a dashed, and a dotted line respectively) as its centre moves in a small circle around the point D. The points A, B, and C show the successive positions of the centre of the Sun as it gyrates. Pulses of light are given off in a correspondingly successive fashion, as consecutive parts of the Sun’s surface move outward. The gyration of the Sun is so rapid that the staccato nature of the light pulses is indiscernible.

Citation: Hobbes Studies 29, 1 (2016) ; 10.1163/18750257-02901002

This sieve-like motion of the Sun has taken over from its supposed systole and diastole in the strange Latin poem “On the Motions of the Sun, Aether and Earth…”34 As in the Anti-White, the rotation of the Sun upon its axis is asserted on the evidence of “the spots which the optic tube has long enabled us to see in the body of the Sun” (ex maculis quas dudum in corpore Solis/Exhibuit nobis tubus opticus aspiciendas); and this rotation is said to be transferred to the surrounding aether so that eventually

This aethereal motion will make its way right to the Planets, and sweep them along with it, and among them the Earth’s globe afloat in the aether (Motus hic aethereus, secum rapietque Planetas,/Inter eosque globum Tellurisin Aethere nantem).

The motion of the aether, set up by the rotation of the Sun on its axis, seems to account for the orbital motions of the planets, sweeping them along:

mobile Ether touches the moving Sun everywhere, Ether must go round in contact with the moving Sun, and the Ether that is in contact with this Ether takes on a similar motion, as does the Ether next to this. Starting from there, this ethereal motion will make its way right to the Planets… (Mobilis atque Aether motum Solem undique tangat,/Aethera contiguum moto cum Sole necesse est/Circumagi, atque Aether tangens hunc Aethera, motum/Concipitsimilem, similemque huic proximus Aether./Unde propagates procedet adusque Planetas…).35

But Hobbes wants to account for both diurnal rotation and annual revolution of the Earth. Consequently, the Sun also must have two different kinds of motion:

But this rotation of the Sun on its axis is not enough in itself to impart to the Earth those twin movements whose names are annual and diurnal. For if one may invoke a cause from an effect, one may only invoke a sufficient cause. So if the Earth is provided with a double motion (almost all astronomers now say so), it is reasonable for its mover to be presented with a double motion too. So in addition to the movement by which it is rotated on its axis, a second motion should be allotted to the Sun, by which all of it is carried round into a ring. Further, this movement is more expedient for moving the fluid breezes from the Sun’s body. By rotating his sieve in this way while he is busy cleansing his wheat, a farmer shakes out the chaff and any light matter, and propels it round every way to the edges of his sieve (Solis at haec proprio super axe rotation sola/Non satis est dandis Telluri motibus illis/Binis, Annuus atque Diurnus qui vocitantur./Nam si ex effectu liceat causam indigitare,/Indigitare tamen nisi causam sufficientem/Non licet. Ergo si Tellus sit duplice motu/Praedita (et Astronomi nunc omnes pene, fatentur)/Motorem illius pariter donarier aequum est/Duplice motu. Igitur Soli est alter tribuendus/(Praeter motum que proprio super axe rotatur)/Motus, quo circumlatus sit totus in orbem. Adde quod hic motus conducibilis magis est, qui/Aurus summoveat fluidas a corpore Solis./Sic Cribro circumlato, purgare Colonus/Dum triticum satagit, paleas, & quod leve cunque est/Excutit, adque oras Cribri circum undique pellit.).36

Although it is by no means clear how the second motion of the Sun can cause the diurnal rotation of the Earth, it is obvious that Hobbes is claiming that both the rotation and the revolution of the Earth are communicated to it by the rotation of the Sun on its axis and by the revolution of the Sun in a tiny orbit around a central point—just as a sieve is swirled in the hands of a farmer.

It is perhaps worth noting that the basic idea of the Sun’s motion being responsible for moving the other planets had already been suggested by Galileo. In his Letter to the Grand Duchess Christina of 1615, after reminding his readers that he had established the rotation of the Sun on its axis in his Letters on Sunspots (1613), Galileo went on to say:

I do not think it would be far from correct philosophizing to say that, in so far as it is the greatest minister of nature and, in a way, the heart and soul of the world, it transmits to the surrounding bodies not only light but also (by turning on itself) motion; thus, just as all motion of an animal’s limbs would cease if the motion of its heart were to cease, in the same way if the Sun’s rotation stopped then all planetary revolutions would also stop.37

Hobbes’s poem on the motion of the Sun was probably written after his return to England in 1651, when he once again became part of the household of the Earl of Devonshire, for whom the poem was written. By the time the De corpore appeared, in 1655, Hobbes was fully committed to his motus cribrationis. As he then insisted,

This [motion] as it is the most simple, so it is the most frequent of all circular movements; being the same which is used by all men when they turn anything round with their arms, as they do in grinding or sifting.38

No longer confined only to the Sun, these sieve-like motions are invoked everywhere. These sieving motions are simple circular motions, and once set-up are held, in accordance with the Galilean assumption, to continue forever. Although there is nothing in the De corpore to say how these motions begin, it is safe to assume that, as in the Cartesian system, they were an aspect of the creation. So, the motion of the Sun is no longer occult, but entirely kinematic. Moreover, these bodies moving with simple circular motion are capable of passing on these motions to surrounding bodies. Hobbes did not seem to have the same concern as Descartes that the amount of motion in the world system should be fixed, so that as one body newly began to move, another comparable moving body must cease from movement. For Hobbes, the simple circular motions seemed to be able to spread from one body to another in a completely dizzying way.

The details of how simple circular motion can be spread to surrounding bodies, which can in their turn pass the motions on further, are given in Chapter 21 of the De corpore. Sections 3 to 11 of that chapter provide what might be seen as Hobbes’s laws of motion. We learn, for example, that the parts of a medium surrounding a moving body “will be carried about with the same motion and velocity”, and that “homogenous bodies are congregated, and heterogeneous dissipated by simple motion in a medium where they naturally float.”39 The movements of the medium caused by a body moving with simple circular motion will cause another body in the medium to move with simple circular movement, and so simple circular motion begets simple circular motion.40

The discussions which are intended to justify Hobbes’s claims are a strange mixture of physical and geometrical arguments. A physical claim, such as that in which we are told one body moving with simple circular motion will cause another body to move in the same way, is provided with an elaborate geometrical account which concludes with these words:

Wherefore the sphere efg is moved with simple circular motion; which was to be demonstrated.41

The argument seems to work in essentially the same way as a geometrical demonstration in astronomy. According to Aristotle, a full explanation of a physical phenomenon required an exposition involving causes, including an understanding of the necessary connection between the supposed cause and its effect. In physics the causal account in question might be expected to focus on efficient causation, but with regard to astronomy this wasn’t possible. Explanation in astronomy, therefore, depended on an understanding of formal causes. The cause of an eclipse could be readily understood by considering the arrangement in space of the Sun, Earth and Moon. Similarly, the motion of a planet could be understood in terms of the combined motions of an epicycle, carrying the planet, and a deferent carrying the epicycle.42

Hobbes’s “properties” of simple circular motion are either simply stated or are demonstrated by recourse to geometrical constructions—there is little or no attempt to show how simple circular motions are transmitted physically. But this seems to be a deliberate stratagem on Hobbes’s part. In the penultimate paragraph of the De corpore Hobbes insists that “all the theorems” of the “first, second, and third parts” of this work “are rightly demonstrated”, but the fourth part, the physics, “depends upon hypotheses; which unless we know them to be true, it is impossible for us to demonstrate that those causes, which I have here explicated, are the true causes…” The essentially geometrical account of the properties of the simple circular motions in Part iii are rightly demonstrated, Hobbes wants to insist. But he cannot, for example, demonstrate that the Sun really moves with a simple circular motion—which is a fundamental claim of his physics.43

In the second chapter of Part iv, on “Physics, or the Phenomena of Nature”, we are introduced to six suppositions which are necessary for understanding natural phenomena. The third of these is “that in the Sun and the rest of the planets there is and always has been a simple circular motion.” Hobbes might have said (in keeping with the claims of Chapter 21) that the planets derived their simple circular motions from the original simple circular motion in the Sun, but he perhaps wanted to avoid the suggestion, associated with his own earlier work and with other more occult systems, that the Sun was the driving force in the universe.44 Be that as it may, the principal role of the Sun is soon acknowledged:

Now as I have demonstrated the simple annual motion of the Earth from the supposition of simple motion in the Sun; so from the supposition of simple motion in the Earth may be demonstrated the monthly simple motion of the Moon… the demonstration will be the same, and therefore need not be repeated.45

Simple circular motions feature prominently throughout the concluding chapters of De corpore. They are invoked to account for astronomical details of the planetary system, the tides, light, heat and colour, coldness and hardness, and finally gravity and magnetism. Although the sieve-like motion of the Sun is not mentioned explicitly it is implicit in section 2 of Chapter 27, for example, where we read:

The body of the Sun doth by its simple circular motion thrust away the ambient ethereal substance sometimes one way sometimes another…46

After 1655 Hobbes remained entirely committed to this same system of mechanical philosophy. In his Dialogus physicus de natura aeris (Physical Dialogue of the Nature of the Air, 1661), for example, Hobbes provides a non-vacuist account of what is going on in the chamber of the air-pump by moving rapidly from the simple circular motion of the Earth, which is said to be “congenital to its nature”, to the claim that the atmosphere also has a simple circular motion congenital to its nature.47 This circular motion of the air is made very strong and rapid by the action of pumping the air-pump and this brings about all the phenomena observed in the pump which have been misinterpreted as due to vacuum, or as Hobbes wrote:

Both these fantasies, the gravity of the air as well as the elastic force or spring of the air, were dreams.

Indeed, Hobbes even goes so far as to say that the fellows of the Royal Society have

found a machine that can excite the motion of the air so much that… the hypotheses of Hobbes, which indeed were probable enough before hand, may by this be rendered more probable.48

Similarly, in the Decameron Physiologicum of 1678, Hobbes’s physical explanations still start from the motus cribrationis of the Sun even though he no longer uses that phrase. Perhaps feeling that the meaning of this phrase was insufficiently clear, Hobbes now provides a diagram and a description in geometrical terms:

  • Take into your hand any streight Line, (as in this Figure [Figure 4]) the Line lam, which we suppose to be the diameter of the Sun’s Body; and moving it parallelly, with the ends in the Circumference, so as that the end M may withal describe a small Circle, as Ma. It is manifest that all the other points of the same Line lm will by the same Motion, at the same time, describe equal Circles to it. Likewise if you take in your hand any two Diameters fastened together, the same Parallel-motion of the line lm, shall cause all the points of the other Diameter to make equal Circles to the same Ma.49

Figure 4

Download Figure

Figure 4

Hobbes defines his simple circular motion here, not by analogy with a sieve, but by describing the movement of the diameter of the Sun lam as remaining parallel to itself, as its ends are made to move in small circles (shown at point M and labelled as a).

Citation: Hobbes Studies 29, 1 (2016) ; 10.1163/18750257-02901002

Surprisingly, Hobbes does not refer to the authority of Galileo for this kind of motion, but to Copernicus:

  • …I like your Argument the better, because it is drawn from Copernicus his foundation. I mean the compounded Motion of Straight and Circular.

  • I think I shall not offer you many demonstrations of Physical conclusions that are not derived from the Motions supposed or proved by Copernicus. For those Conclusions in Natural Philosophy I most suspect of falshood, which require most variety of Suppositions for their demonstrations.50

Presumably there is some rhetorical purpose behind this, which we can no longer recover. Although he did not compound straight and circular motions in the way Hobbes suggests, Copernicus could legitimately be invoked as a foundational thinker for the new philosophies. The rhetorical implication would seem to be that nobody now doubts the motions of rotation and revolution “supposed or proved by Copernicus,” and so it is safe for Hobbes to base his “demonstrations” upon them. To base his demonstrations overtly upon Galileo’s ideas would be to introduce an extra layer of “suppositions”, so Hobbes refers only to the foundational Copernican movements, while really he is talking about Galileo’s and his own perpetual “simple circular motions.” Hobbes must have been all too aware that Galilean circular inertia had not been embraced by any other thinker, perhaps accordingly he chose not to explicitly invoke Galileo’s authority.

Hobbes and Unexplained (Occult) Motions

Unfortunately for the cogency of Hobbes’s system, there are a number of places in his mature writings where he seems to forget the importance of upholding a system which rejects all unexplained principles, and explains everything only in terms of inert matter in inertial motion. It is difficult to know what to make of these lapses. They could simply be lapses into loose talk, where Hobbes knows what he means and forgets that his readers might not know. We have already seen an example that might fit into this category, in the Physical Dialogue of the Nature of the Air, where he wrote that the Earth and its atmosphere had a simple circular motion “congenital to its nature.” It may well be that this was just a loose way of saying, as he did in Part iv of the De corpore, “that in the Sun and the rest of the planets there is and always has been a simple circular motion.”51 In the De corpore, the implication is no more a betrayal of strict mechanical principles than was Descartes’s assumption that the world system was set moving at the Creation by God. So, it is possible that when Hobbes said simple circular motion was congenital to the nature of the Earth, and the atmosphere, he simply meant that they have always moved that way, ever since the Creation.

Be that as it may, there are other places where Hobbes genuinely seems to forget the power of inertial kinematics, and simply relies on unexplained principles of movement. Consider, for example, Hobbes’s account of magnetism. Magnetic attraction is explained in terms of “reciprocal motion, or motion of the parts forwards and backwards.”52 This motion of the parts of the magnet will be communicated by the air to a nearby piece of iron, Hobbes writes,

and consequently that there will be in all the parts of the iron the same reciprocations or motions forwards and backwards. And from hence also it will follow, that the intermediate air between the stone and the iron will, by little and little, be thrust away; and the air being thrust away, the bodies of the loadstone and the iron will necessarily come together.53

This looks like an attempt to provide a mechanical explanation for that most occult of objects, the magnet, except for one important detail: where do the reciprocal motions of the parts of a magnet originate? Forgetting circular motions, Hobbes sees these backwards and forwards movements as being similar to the frictional movements which have to be performed upon a piece of jet before it becomes an electrical attractant. In the case of a magnet, however, rubbing backwards and forwards is not necessary. Consequently, Hobbes casually states, a magnet must have an “internal principle of motion peculiar to itself.”54 Hobbes really does seem to have forgotten himself here, accepting that some phenomena, such as magnetism, simply are occult. A strange lapse, given that it is at the end of this same discussion that he provides the dismissal, which we have already seen, of those who invoke occult principles:

… as for those that say anything may be moved or produced by itself, by species, by its own power, by substantial forms, by incorporeal substances, by instinct, by anti-peristasis, by antipathy, sympathy, occult quality, and other empty words of schoolmen, their saying so is to no purpose.55

Perhaps such lapses are the result of the inordinately long period, with long interruptions, over which the De corpore was written. Marin Mersenne referred to Hobbes’s De motu, loco, et tempore in 1644, which clearly was a working title for Hobbes’s natural philosophy, but it wasn’t until 1655 that the De corpore, having passed through many different drafts or partial drafts, was finally published.56 Furthermore, during this period Cartesianism became the single most influential alternative to scholastic Aristotelianism. Accordingly, rectilinear inertia became an increasingly familiar concept among natural philosophers. Even Hobbes used it in the De corpore, though he did not link it to, much less discuss its incompatibility with, circular inertia.57 It is possible, however, that the contemporary emphasis upon Cartesian rectilinear inertia led him to present his own Galileo-inspired view in a rather low-key way. After all, Galileo’s own discussion of circular inertia in his Dialogue had never caught on, and by 1655 was perhaps already forgotten, or remained unnoticed, by every natural philosopher except Hobbes. Whatever the reason, Hobbes knew better than to reject Cartesian rectilinear inertia, and never tried to present an explicit defence of circular inertia as superior to, and a substitute for, Cartesian inertia. Like Galileo’s own theory, therefore, the inertial nature of Hobbes’s simple circular motions became easy to overlook.

Furthermore, his glib statement in the Physical Dialogue of the Nature of the Air that the movements of the Earth and the atmosphere were in each case “congenital to its nature,” proved to be a damaging mistake. Robert Boyle made much of it in his An Examen of Mr T. Hobbes his Dialogus physicus de natura äeris (1662). Boyle took for granted that Hobbes was an atheist and took great delight in pointing out that if Hobbes could claim the particles of bodies are innately moving, then he should ask himself

…whether or no Gassendus, and those other Atomists that admit Creation, may not hence countenance their grand supposition of the congenite motion of Atoms, which granted, would destroy the best part of Mr Hobbs’s philosophy.58

Similarly, missing the inertial nature of “simple circular motion,” Boyle defended his own notion of particles with “ingenite motion” in the same terms:

Those, likewise, that fancie a Spring properly so called in particular Aerial Corpuscles, will hence perhaps take occasion to think they may suppose an ingenite motion fit for their turn, as well as he an ingenite motus circularis simplex…59

Subsequently, Boyle compares Hobbes’s view unfavourably with the Cartesian inertial view:

…the Cartesians will think it at least as allowable for them to suppose the Motion he will not grant in their Materia subtilis, as for Mr Hobbs to assume it in his Particulae terreae; especially since he seems to make each such Atom put into and kept in a regular motion; whereas they assume but the having of one general impulse given to the whole mass of Matter…60

He also points out that Hobbes’s motus circularis simplex cannot be “made out” by any “Example or Experiment,”61 and the theory likewise seems dubious:

Nor is it manifest why, because the Terrestrial Globe moves in a vast Circle about the Sun, each particular Atom of it must describe a small Circle in the Air about I know not what Centre.62

Similarly, Hobbes’s self-moving particles (as Boyle sees them) contradict one of Hobbes’s self-professed mechanical principles:

How well likewise his Hypothesis will agree with his Fundamental Doctrine, that Nihil movetur nisi a corpore contiguo & moto [Nothing is moved but by a contiguous body that is in motion], I leave him to consider.63

We should bear in mind, of course, that Boyle was engaged in polemic. He may well have been fully aware that Hobbes claimed to have developed a strictly mechanical system (using Galilean circular inertia), but it suited him to present Hobbes as someone who invoked unexplained activity in matter as much as did Gassendi or Boyle himself. But it seems to me perfectly possible that Boyle genuinely did not know of the Galilean antecedents of Hobbes’s simple circular motions, and would not have been aware of the foreshadowing of the principle of inertia in the works of Galileo. Inertia, for Boyle, would have been seen as a Cartesian, and rectilinear, affair.

Be that as it may, it is surprising, nevertheless, that Hobbes had made it so easy for Boyle to present his philosophy in the way that he did; reducing Hobbes’s would-be strict mechanical philosophy to a philosophy which assumed unexplained principles of activity in matter. Earlier in the Dialogus de natura aeris, Hobbes had insisted “that there can be nothing that can impart motion to itself, or diminish it.”64 Moreover, he had taken Descartes to task for introducing uncaused motions into his physics:

For that hypothesis itself, in which is supposed a motion of subtle matter, very swift yet without a cause… is scarcely that of a sane man.65

And yet, shortly after this he has his interlocutors, A and B, refer to “that motion that Hobbes calls simple circular” as “congenital” to the Earth and “congenital” to “many earthy particles… interspersed in the air.”66

If there is any possibility of defending such inconsistencies, it might be found in Hobbes’s self-professed nescience about physics. Although Hobbes was willing to make dogmatic claims about his mathematical proofs, or about rational arguments based on clearly defined terms (following such arguments in the Decameron physiologicum, for example, one of the interlocutors repeatedly says, “All this is certain”, or “It is certain”),67 he felt it was not possible to be dogmatic in physics. It is possible to claim that simple circular motion begets simple circular motion, provided we agree to accept the principle that

If in a fluid medium a spherical body be moved with simple circular motion, and in the same medium there float another sphere whose matter is not fluid, this sphere also shall be moved with simple circular motion.68

But it is not possible to say with certainty that the Sun, Earth, or anything else, really does move with simple circular motion—this is something we can only suppose hypothetically. As Hobbes wrote at the end of De corpore,

In the first, second, and third parts, where the principles of ratiocination consist of our own understanding, that is to say, in the legitimate use of such words as we ourselves constitute, all the theorems, if I be not deceived, are rightly demonstrated. The fourth part depends upon hypotheses; which unless we know them to be true, it is impossible for us to demonstrate that those causes, which I have here explicated, are the true causes of the things whose productions I have derived from them.69

It is possible that Hobbes might have seen his own deviation from strict mechanical principles as justifiable on these nescient grounds, but if so, it could hardly be said to be a persuasive defence. Talk of congenital motion simply seems, as Boyle pointed out, to contradict Hobbes’s premise that motion of a body can only be initiated (in the period after the Creation) by the impact of another moving body. Hobbes seems to have betrayed his own principles in the Dialogus de natura aeris, and thereby to reveal himself to be an inconsistent and unconvincing natural philosopher.

But at least Hobbes learned his lesson from Boyle’s critique, and in his subsequent natural philosophical works he never again referred to simple circular motion as “congenital.” Hobbes takes more care in his later writings in natural philosophy to be much more strictly mechanical. In the Decameron physiologicum (1678), for example, he even manages to provide a mechanical account of magnetism. He announces his anti-occult approach at the outset of the discussion:

  • I come now to hear what Natural Causes you can assign of the vertues of the Magnet; and first, why it draws Iron to it, and only Iron.

  • You know I have no other cause to assign but some local Motion, and that I never approved of any argument drawn from Sympathy, Influence, Substantial Forms, or Incorporeal Effluvia. For I am not, nor am accounted by my Antagonists for a Witch.70

As promised, B gives an account of magnetic “attraction” which involves simple circular motions in the particles of the magnet, the iron, and the air in between; these motions are “supposed” by B, but given what has gone before, the implication is that these motions are not “congenital” but are either the result of the Creation, or are generated by the (created) motions of the Sun.71

Conclusion

It seems clear, then, that Hobbes, like Galileo, Beeckman, and Descartes, set out to develop an entirely kinematic system of natural philosophy—a system in which the concept of force was eschewed (except of course for the entirely kinematic force of impact or force of collision), and in which all explanations were couched only in terms of bodies in motion.

Although at the beginning of his career as a speculative natural philosopher Hobbes entertained the essentially occult idea that the Sun could drive the world system by virtue of its inherent pulsific faculty, Hobbes quickly dropped this in favour of his kinematic account. It is possible that Hobbes recognised the importance of this as a result of his knowledge of Descartes’s system, but his own version of kinematic natural philosophy derived from Galileo’s system rather than from Descartes’s, and relied upon the assumption that circular (as opposed to rectilinear) motion was inertial and would continue indefinitely if nothing intervened.

Furthermore, as far as I am aware, Hobbes was the only historical thinker who seems to have taken Galileo’s simple circular motions—his “circular inertia”— seriously. There is nothing comparable to Hobbes’s kinematic system of philosophy to be found in the works of any of Galileo’s Italian followers, or anywhere else. The temptation, of course, is simply to say that none of Galileo’s other followers were foolish enough to think it would work—only Hobbes was sufficiently lacking in critical philosophical faculties to be taken in by Galileo’s belief in “circular inertia” as opposed to the rectilinear inertia which we all know to be true. But to talk this way is to allow ourselves to be blinded by what we know. Contemporaries of Galileo, and even of Hobbes, could not have been as sure as we are that “circular inertia” is a misconceived idea. On the contrary, the idea might well have seemed to them to be every bit as plausible as rectilinear inertia. Certainly, it seemed more than plausible to Galileo—and to Hobbes.

We need to ask ourselves, therefore, why Galileo’s theory was not more influential than it was. After all, Galileo was almost universally admired among contemporary natural philosophers, and Hobbes himself was by no means the fool that John Wallis and others tried to suggest he was. We could, therefore, take the fact that Hobbes tried to extend Galileo’s speculations to develop a kinematic system of natural philosophy to rival Descartes’s, as an indication that others might reasonably have been expected to do so too. But if nobody did do so, and it very much looks that way, it seems important to ask why they did not.

This is perhaps a matter for future research, but let me just conclude by offering my own preliminary thoughts on this matter. It seems to me that it is fair to say that Galileo, Beeckman, Descartes, and Hobbes were the only original thinkers who tried to develop a completely kinematic system of natural philosophy. The lynch-pin for Galileo and Hobbes was perpetual circular motion, for Descartes (following Beeckman) it was perpetual rectilinear motion. No other would-be original system-builder, from Gilles Personne de Roberval, Thomas White, Kenelm Digby, Pierre Gassendi, and beyond, up to and including Newton, seemed to realise the power of a genuinely kinematic philosophy, and accordingly allowed various unexplained occult notions into their systems. But, this should not surprise us; after all, there was no prior demand in the seventeenth century for a non-occult, or a strictly mechanical system.72 What was required, what was looked for, was a philosophical system of comparable encyclopaedic scope to scholastic Aristotelianism; a system which could be substituted for scholasticism in the universities throughout Europe, and which was capable of providing answers to any and all questions about the natural world. Galileo announced in his Siderius Nuncius of 1610 that he was writing a System of the World, but he was unable to complete it.73 Beeckman never published anything, and Hobbes and Gassendi both took too long to put their natural philosophies into print.74 It was Descartes, in 1644, who was the first to provide a complete, fully-worked out system, capable of replacing Aristotle tout à fait. By the time Hobbes’s system appeared, in 1655, Cartesianism was already attracting the attention of natural philosophers throughout Europe—even those who were not persuaded by Cartesianism found themselves having to address it. For the most part, those who were not persuaded found it impossible to believe in a system in which matter was held to be completely passive and inert, and turned instead to theories of matter with in-built principles of activity.75 If readers recognised that Hobbes’s De corpore was a strict mechanical philosophy, in which bodies were held to be passive and capable of acting only by impact upon other bodies, they would be unlikely to see it as an improvement on Cartesianism (the De corpore was by no means as well worked-out as the Principia philosophiae).76 But if, like Boyle, they failed to understand the inertial nature of simple circular motion, and saw it merely as another kind of “congenite” activity in matter, they would surely have found it less plausible than other systems which depended on self-active matter, such as those developed by thinkers with a profound knowledge of chemical phenomena.77 If we add to these natural philosophical considerations the various factors stemming from Hobbes’s reputation as the author of Leviathan, with dangerous and unpalatable political and religious views, it is hardly surprising that his new system of physics, for all its Galilean pedigree, failed to win adherents.

1 Thomas Hobbes, The English Works of Thomas Hobbes, collected and edited by Sir William Molesworth, 12 vols (London: John Bohn, 1839), abbreviated as ew, vol. I; this quotation at Part iv, Ch. 30, § 15, p 531.

2 This is not strictly true for Galileo, who did not properly develop an atomist, or corpuscularist, physics, although he did tinker with atomist ideas; see Pietro Redondi, Galileo eretico (Torino: Einaudi, 1983) and A. Mark Smith, “Galileo’s Theory of Indivisibles: Revolution or Compromise?”, Journal for the History of Ideas, 37 (1976), pp. 571–588. Even so, his physics of matter in motion conformed at a macro-level with the micro-physics of the other three; see John Henry, “Galileo and the Scientific Revolution: The Importance of His Kinematics”, Galilaeana, 8 (2011), pp. 3–36. On Descartes’ natural philosophy, see Stephen Gaukroger, Descartes’ System of Natural Philosophy (Cambridge: Cambridge University Press, 2002). Beeckman is less well-known and had no influence, except (crucially) upon Descartes; see Klaas van Berkel, Isaac Beeckman on Matter and Motion: Mechanical Philosophy in the Making (Baltimore: Johns Hopkins University Press, 2013).

3 Isaac Newton, Opticks… Based on the Fourth Edition, London 1730 (New York: Dover, 1979), p. 401. For fuller discussion of occult qualities in early modern natural philosophy, see John Henry, “Occult Qualities and the Experimental Philosophy: Active Principles in pre-Newtonian Matter Theory”, History of Science, 24 (1986), pp. 335–381 and Alan Gabbey et al. “New Doctrines of Body and Its Powers, Place and Space”, in Garber, D. and Ayers, M. (eds), The Cambridge History of Seventeenth-Century Philosophy (Cambridge: Cambridge University Press, 1998), pp. 553–623.

4 James A. Weisheipl, “The Principle Omne quod movetur ab alio movetur in Medieval Physics”, Isis, 56 (1965), pp. 26–45.

5 On Beeckman see van Berkel, Isaac Beeckman. Descartes defended rectilinear motion by invoking the immutability of God; see Gary Hatfield, “Force (God) in Descartes’ Physics,” Studies in History and Philosophy of Science, 10 (1979), pp. 113–40 and Daniel Garber, Descartes’ Metaphysical Physics (Chicago: University of Chicago Press, 1992). Galileo’s use of “circular inertia” is less well studied—indeed some Galileo scholars have tried to rescue him from the idea and to claim that he really believed in rectilinear inertia; see, for example, Stillman Drake, Galileo: Pioneer Scientist (Toronto: University of Toronto Press, 1990), p. 229. For a discussion of circular inertia in Galileo see Alexandre Koyré, Galileo Studies (Hassocks: Harvester Press, 1978), pp. 154–175.

6 The major exception is Frithiof Brandt, Thomas Hobbes’ Mechanical Conception of Nature (Copenhagen and London: Levin & Munksgaard, 1928), but little has been said about Hobbes’s use of simple circular motions since then. The only discussion I am aware of is the very brief Samuel Mintz, “Galileo, Hobbes, and the Circle of Perfection,” Isis, 43 (1952), pp. 98–100.

7 Aristotle, Mechanical Problems, in Aristotle, Minor Works, translated by W. S. Hett (Cambridge, Mass.: Harvard University Press, 1936), p. 331.

8 Aristotle, Mechanical Problems, p. 333. The influence of the Mechanical Questions on Descartes has recently been explored by Helen Hattab, “From Mechanics to Mechanism: The Quaestiones Mechanicae and Descartes’ Physics,” in Peter R. Anstey and John A. Schuster (eds), The Science of Nature in the Seventeenth Century: Patterns of Change in Early Modern Natural Philosophy (Dordrecht: Springer, 2005), pp. 99–129.

9 Hobbes, De corpore, The Author’s Epistle Dedicatory, in ew, vol. I, p. viii.

10 Some scholars object to the phrase “circular inertia” on the grounds that it is a contradiction in terms, since inertia refers to rectilinear motion. But, we are considering a period before “inertia” was deemed to refer only to rectilinear motions, and so we can, perhaps, be allowed to use the term to refer to any kind of motion that is held to continue indefinitely, without any action being required to perpetuate it.

11 Ron Naylor, “Paolo Sarpi and the First Copernican Tidal Theory,” British Journal for the History of Science, 47 (2014), pp. 661–675.

12 The combination of the daily and annual motions was envisaged as creating a sudden change in the relative motion of the surface of the Earth as seen from the Sun. This sudden change of motion was held to account for the tides in the same way that a sudden change of motion of a barge carrying drinking water across the Venice lagoon would result in dramatic sloshing of the water in the barge. See Galileo Galilei, Dialogue Concerning the Two Chief World Systems, translated by Stillman Drake (New York: Modern Library, 2001), Fourth Day, pp. 493–4; and for explication: E. J. Aiton, “Galileo’s Theory of the Tides,” Annals of Science, 10 (1954), pp. 44–57 and Ron Naylor, “Galileo’s Tidal Theory,” Isis, 98 (2007), pp. 1–22.

13 The flaws in the tidal theory are discussed in the articles by Aiton and Naylor (see previous footnote).

14 Galilei, Dialogue, Second Day, p. 171.

15 Galilei, Dialogue, Second Day, p. 172.

16 Galilei, Dialogue, First Day, pp. 32–3.

17 Galilei, Dialogue, First Day, p. 23, see also p. 32.

18 For a fuller discussion, showing just how determinedly Galileo tried to exclude gravitational attraction from any consideration, see John Henry, “Galileo and the Scientific revolution.”

19 Koyré, Galileo Studies, p. 239.

20 Galilei, Dialogue, p. 172; see also Stillman Drake, “The Concept of Inertia,” in Stillman Drake, Essays on Galileo and the History and Philosophy of Science, Volume 2 ( Toronto: University of Toronto Press, 1999), p. 143.

21 Quoted from Drake, Galileo: Pioneer Scientist, p. 108.

22 Galilei, Dialogue, First Day, p. 51.

23 Galilei, Dialogue, First Day, p. 52.

24 Galilei, Dialogue, Second Day, p. 193.

25 Galilei, Dialogue, Second Day, p. 193.

26 The logic of Galileo’s theory demands this perpetual circular motion, but Galileo himself fudged the issue by claiming to a correspondent that he believed all descent ended at the centre of the Earth. For fuller discussion see John Henry “Galileo and the Scientific Revolution: The Importance of His Kinematics”, Galilaeana, 8 (2011), pp. 3–36, p. 30.

27 Galilei, Dialogue, Second Day, p. 194.

28 Galilei, Dialogue, First Day, p. 32.

29 Thomas Hobbes, Thomas White’s De Mundo Examined, translated by Harold Whitmore Jones (London: Bradford University Press/Crosby Lockwood Staples, 1976), p. 101.

30 William Harvey, Exercitatio anatomica de motu cordis et sanguinis in animalibus (Frankfurt: 1628), translated by G. Whitteridge in W. Harvey, An Anatomical Disputation Concerning the Movement of the Heart and Blood in Living Creatures (Oxford: Blackwell Scientific Publications, 1976), p. 76. It is perhaps worth noting that Harvey may well have been an extra source of inspiration to Hobbes with regard to the importance of circularity in the natural world. See Walter Pagel, William Harvey’s Biological Ideas: Selected Aspects and Historical Background (Basel and New York: Karger, 1967), pp. 89–124.

31 Hobbes, Thomas White’s De Mundo, p. 209.

32 Hobbes first uses motus cribrationis in the Latin Optical Manuscript, written after 1641, probably in 1646, where it is an addition to the pulsating motion of the Sun. Subsequently, the pulsating motion is dropped altogether. See Brandt, Thomas Hobbes’ Mechanical Conception, pp. 198–203.

33 The pulsific theory has the advantage of being three-dimensional: the pulsating Sun would send light out spherically. The sieve-like motion of the Sun would only send out pulses of light in the plane of the motion. But Descartes’s vortex system suffered from a similar problem—the vortex acted in a plane and could not, for example, account for the spherical shape of the planets, much less allow for spherical diffusion of light from the Sun. I am very grateful to my graduate student Xiaona Wang for her help in preparing the diagrams.

34 Thomas Hobbes, De Motibus Solis, Aetheris & Telluris, in Thomas Hobbes, Critique du De Mundo de Thomas White, edited by Jean Jacquot and Harold Whitmore (Jones Paris: Librairie Vrin, 1973), pp. 441–447. “On the Motions of the Sun, Aether and Earth; but especially a hypothetical Cause for the greater Number of Days in the Northern Hemisphere than in the Southern.” Written for William Cavendish, Third Earl of Devonshire, the date of composition is unknown but I am assuming here that it pre-dates De corpore.

35 Hobbes, De Motibus Solis, Aetheris & Telluris, p. 443. I am very grateful to my colleague John M. Forrester for his invaluable help in translating Hobbes’s Latin verse.

36 Hobbes, De Motibus Solis, Aetheris & Telluris, pp. 443–444.

37 I have used the translation in Maurice A. Finocchiaro, The Galileo Affair: A Documentary History ( Berkeley: University of California Press, 1989), p. 116. Johannes Kepler had suggested the Sun’s rotation enabled it to sweep the planets around in their orbits in his Astronomia nova (Prague, 1609).

38 Hobbes, De Corpore, ew, vol I, Part iii, Ch. 21, § 2, p. 320.

39 Hobbes, De Corpore, ew, vol I, Part iii, Ch. 21, § 4, p. 322, and § 5, p. 324.

40 Hobbes, De Corpore, ew, vol I, Part iii, Ch. 21, §§ 10 and 11, pp. 329–32.

41 Hobbes, De Corpore, ew, vol I, Part iii, Ch. 21, p. 330.

42 On formal causes in astronomy, see, for example, Nicholas Jardine, “Epistemology of the Sciences”, in C. B. Schmitt and Quentin Skinner (eds), The Cambridge History of Renaissance Philosophy (Cambridge: Cambridge University Press, 1990).

43 Hobbes, De Corpore, ew, vol I, Part iv, Ch. 30, § 15, p. 531. For a discussion of Hobbes’s non-dogmatic scepticism with regard to physical hypotheses, see Noel Malcolm, “Hobbes and Roberval”, in Aspects of Hobbes (Oxford: Clarendon Press, 2002), pp. 156–99 and Brandt, Thomas Hobbes’s Mechanical Conception, pp. 196–98.

44 Hobbes, De Corpore, ew, vol I, Part iv, Ch. 26, § 5, p. 427. The Sun as a driving force in the solar system appears in Johannes Kepler’s Astronomia nova (Prague, 1609), where the link between the Sun and planets is held to be a strange combination of magnetism and light, and is distinctly occult. Sir Kenelm Digby, Two Treatises. In the one of which the nature of bodies; in the other the nature of mans soule is looked into… (Paris, 1644) also relies upon the Sun as an unexplained source of “universal action”, ultimately responsible in an occult way for many Earthly phenomena. The same is true of Gilles Personne de Roberval, Aristarchi Samii de mundi systemate, partibus et motibus eiusdem (Paris, 1644).

45 Hobbes, De Corpore, ew, vol I, Part iv, Ch. 26, § 6, p. 429.

46 Hobbes, De Corpore, ew, vol I, Part iv, Ch. 27, § 2, p. 448.

47 Thomas Hobbes, Dialogus physicus de natura aeris (London, 1661) in Steven Shapin and Simon Schaffer, Leviathan and the Air-Pump: Hobbes, Boyle, and the Experimental Life (Princeton: Princeton University Press, 1985), Appendix, pp. 361–391.

48 Hobbes, Dialogus physicus, pp. 377, 379.

49 Thomas Hobbes, Decameron Physiologicum; or, Ten Dialogues of Natural Philosophy, ew, Vol. vii, Chapter iv, pp 69–177: p. 97.

50 Hobbes, Decameron Physiologicum,ew, vol. vii, Ch. iv, pp. 98–99.

51 Hobbes, De Corpore, ew, vol I, Part iv, Ch. 26, § 5, p. 427.

52 Hobbes, De Corpore,ew, vol I , Part iv, Ch. 30, § 15, p. 526.

53 Hobbes, De Corpore,ew, vol I, Part iv, Ch. 30, § 15, p. 528.

54 Hobbes, De Corpore,ew, vol I, Part iv, Ch. 30, § 15, p. 526.

55 Hobbes, De Corpore,ew, vol I, Part iv, Ch. 30, § 15, p. 531.

56 Marin Mersenne was a self-appointed “intelligencer,” who encouraged natural philosophers he admired, and promoted their work to others. See Roger Moreau, Marin Mersenne et la naissance de l’esprit scientifique (Perros Guirec: éditions Anagrammes, 2012). On his links to Hobbes, see Malcolm “A Summary Biography” in Aspects of Hobbes, especially pp. 17–22. See also Brandt, Thomas Hobbes’ Mechanical Conception, pp. 166–200.

57 Hobbes seems to invoke rectilinear inertia in De corpore, ew, vol I, Part ii, Ch. 8, § 19, p. 115, although he does not explicitly say the continuing motion will be rectilinear. At Part ii, Ch. 9, § 7, p. 125, he repeats the point and takes the opportunity to criticise Descartes: “There is one that has written that things moved are more resisted by things at rest, than by things contrarily moved; for this reason, that he conceived motion not to be so contrary to motion as rest.” Hobbes insists the opposite is true. The criticism of Descartes suggests Hobbes is using the Cartesian principle of inertia here, not the Galilean principle. This is confirmed in the account of gravity at Part iv, Ch. 30, § 4, p. 512, where the inertial motion being invoked is clearly rectilinear.

58 Robert Boyle, An Examen of Mr T. Hobbes his Dialogus physicus de natura äeris, in R. Boyle, The Works, vol. iii, The Usefulness of Natural Philosophy and sequels to Spring of the Air, 1662–63, edited by Michael Hunter and Edward B. Davis ( London: Pickering and Chatto, 1999) vol. iii, pp. 109–188, p. 134.

59 Boyle, An Examen of Mr T. Hobbes, p. 134.

60 Boyle, An Examen of Mr T. Hobbes, p. 134.

61 Boyle, An Examen of Mr T. Hobbes, p. 133.

62 Boyle, An Examen of Mr T. Hobbes, p. 134.

63 Boyle, An Examen of Mr T. Hobbes, p. 134.

64 Hobbes, Dialogus Physicus, p. 355.

65 Hobbes, Dialogus Physicus, p. 359.

66 Hobbes, Dialogus Physicus, p. 361.

67 Hobbes, Decameron Physiologicum, ew, vol. vii, pp. 98 and 112.

68 Hobbes, De Corpore, ew, vol. I, Part iii, Ch. 21, § 10, p. 329.

69 See Hobbes, De Corpore,ew, vol. I, Part iv, Ch.30, § 15, p. 531. For fuller discussion, see Brandt, Thomas Hobbes’ Mechanical Conception, pp. 195–200, and pp. 217–248; and Malcolm, Aspects of Hobbes, pp. 156–99.

70 Hobbes, Decameron Physiologicum, ew, vol. vii, Chapter ix, p. 155.

71 Hobbes, Decameron Physiologicum, pp. 156–57. The explanation is hardly convincing, but it is evidently trying to confine itself to mechanical principles (subsequent to the initiating of motions by God).

72 For fuller discussion of this point, see Henry, “Occult Qualities and the Experimental Philosophy” and Henry, “The Origins of the Experimental Method—Mathematics or Magic?” in Hubertus Busche, Stefan Heßbrüggen-Walter (eds), Departure for Modern Europe: Philosophy between 1400 and 1700. A Handbook of Early Modern Philosophy (Hamburg: Felix Meiner, 2011), pp. 702–714.

73 Galileo Galilei, Discoveries and Opinions of Galileo, edited and translated by Stillman Drake (New York: Random House, 1957), pp. 43, 45, and 58.

74 Gassendi’s philosophy did not become well known until after his death (1655), with the publication of his Opera omnia (Lyon, 1658). And, of course, Hobbes did not publish his natural philosophy until 1655: Elementorum philosophi sectio prima De corpore (London, 1655).

75 Prevailing historiography makes it look as though strict versions of the mechanical philosophy, specially Cartesianism, swept the board, but this has been shown to be not the case in Britain, and further scholarship may show a similar picture across the Continent. On Britain, see Henry “Occult Qualities and the Experimental Philosophy” and Henry “The Reception of Cartesianism”, in Peter Anstey (ed.), The Oxford Handbook of British Philosophy in the Seventeenth Century (Oxford: Oxford University Press, 2013), pp. 116–143.

76 For an indication of the power and sophistication of the Cartesian system, see John Schuster, Descartes Agonistes: Physico-Mathematics, Method and Corpuscular-Mechanism, 1618–33 ( Dordrecht: Springer, 2013).

77 On the role of chemical knowledge and chemical approaches to natural philosophy in the early modern period, see William Newman, Atoms and Alchemy: Chymistry and the Experimental Origins of the Scientific Revolution (Chicago: University of Chicago Press, 2006) and Lawrence M. Principe (ed.), Chymists and Chymistry: Studies in the History of Alchemy and Early Modern Chemistry (Sagamore Beach, ma: Watson Publishing International llc, 2007).

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Hobbes, Galileo, and the Physics of Simple Circular Motions

in Hobbes Studies

Sections

References

3

Isaac NewtonOpticks… Based on the Fourth Edition London 1730 (New York: Dover1979) p. 401. For fuller discussion of occult qualities in early modern natural philosophy see John Henry “Occult Qualities and the Experimental Philosophy: Active Principles in pre-Newtonian Matter Theory” History of Science 24 (1986) pp. 335–381 and Alan Gabbey et al. “New Doctrines of Body and Its Powers Place and Space” in Garber D. and Ayers M. (eds) The Cambridge History of Seventeenth-Century Philosophy (Cambridge: Cambridge University Press 1998) pp. 553–623.

8

AristotleMechanical Problems p. 333. The influence of the Mechanical Questions on Descartes has recently been explored by Helen Hattab “From Mechanics to Mechanism: The Quaestiones Mechanicae and Descartes’ Physics” in Peter R. Anstey and John A. Schuster (eds) The Science of Nature in the Seventeenth Century: Patterns of Change in Early Modern Natural Philosophy (Dordrecht: Springer 2005) pp. 99–129.

11

Ron Naylor“Paolo Sarpi and the First Copernican Tidal Theory,” British Journal for the History of Science47 (2014) pp. 661–675.

19

KoyréGalileo Studies p. 239.

20

GalileiDialogue p. 172; see also Stillman Drake “The Concept of Inertia” in Stillman Drake Essays on Galileo and the History and Philosophy of Science Volume 2 ( Toronto: University of Toronto Press 1999) p. 143.

21

Quoted from DrakeGalileo: Pioneer Scientist p. 108.

31

HobbesThomas White’s De Mundo p. 209.

35

HobbesDe Motibus Solis Aetheris & Telluris p. 443. I am very grateful to my colleague John M. Forrester for his invaluable help in translating Hobbes’s Latin verse.

36

HobbesDe Motibus Solis Aetheris & Telluris pp. 443–444.

48

HobbesDialogus physicus pp. 377 379.

59

BoyleAn Examen of Mr T. Hobbes p. 134.

60

BoyleAn Examen of Mr T. Hobbes p. 134.

61

BoyleAn Examen of Mr T. Hobbes p. 133.

62

BoyleAn Examen of Mr T. Hobbes p. 134.

63

BoyleAn Examen of Mr T. Hobbes p. 134.

64

HobbesDialogus Physicus p. 355.

65

HobbesDialogus Physicus p. 359.

66

HobbesDialogus Physicus p. 361.

71

HobbesDecameron Physiologicum pp. 156–57. The explanation is hardly convincing but it is evidently trying to confine itself to mechanical principles (subsequent to the initiating of motions by God).

Figures

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    Galileo’s attempt to use simple circular motion to dismiss the concept of acceleration due to gravity. Dialogue, Second Day. A body falling from the top of a tower C, on the rotating Earth, will not fall straight down but will fall in the circular path cia (where A is the centre of the Earth), with unifom (non-accelerating) motion. To an observer, the succesive positions of the falling body against the wall of the tower (shown successively at F, G, H, L, and D) will give the (false) impression of accelerated motion.

  • View in gallery

    The Sun dilates and contracts about a fixed centre C, generating pulses of light (shown as arrows) as it dilates, simultaneously on all sides.

  • View in gallery

    Here we see the Sun in three successive positions (shown by a solid, a dashed, and a dotted line respectively) as its centre moves in a small circle around the point D. The points A, B, and C show the successive positions of the centre of the Sun as it gyrates. Pulses of light are given off in a correspondingly successive fashion, as consecutive parts of the Sun’s surface move outward. The gyration of the Sun is so rapid that the staccato nature of the light pulses is indiscernible.

  • View in gallery

    Hobbes defines his simple circular motion here, not by analogy with a sieve, but by describing the movement of the diameter of the Sun lam as remaining parallel to itself, as its ends are made to move in small circles (shown at point M and labelled as a).

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