Abstract
Kepler never called his three planetary laws ‘laws’, discussed them as a coherent group, stated them to be three or put them in the order that has become canonical today. When and by whom his insights were conceptualised in their modern form is an open question. Previous conjectures point to the astronomical literature of the later 18th century. By contrast, this short article tries to show that the conceptualisation of Kepler’s laws took place in the late 17th and early 18th centuries. This process was furthered by the growing popularity of the notion of ‘laws of nature’ as an epistemic category at the time. It involved Newton and Leibniz as well as the earliest authors of textbooks of Newtonian astronomy and physics.
Kepler’s three laws can be found stated in his œuvre at various places, in different forms and in varying degrees of clarity and explicitness.
1
However, nowhere are they called laws, discussed as a coherent group, stated to be three or put in the order that has since become canonical. This raises the question of how exactly they came to be perceived as Kepler’s first, second and third law. The part of the problem concerning the ordering was already stated in 1990 by the late Owen Gingerich, who first found the three laws in their modern form in Jérôme Lalande’s Abrégé d’astronomie (Amsterdam, 1774). As Gingerich puts it: Now Kepler never considered them in one place nor did he number them, so it is something of a mystery as to when this ordering took place. Lalande implied that the threefold numbering was already in use, so I wonder if it was introduced by LaCaille. Since, of the two, Lalande was the more original, perhaps he invented the 1-2-3 order without claiming credit.
2
A few years later, Curtis Wilson, who was apparently unaware of Gingerich’s contribution, thought to have found out who first called Kepler’s findings ‘laws’ and fixed their number at three: Voltaire in his Élémens de la philosophie de Neuton (Amsterdam, 1738) and Robert Small in An account of the astronomical discoveries of Kepler (London, 1804) respectively. 3
In fact, none of the four early modern authors just mentioned played a major role in the establishment of Kepler’s laws in their present form. Lacaille, Voltaire and Small made no substantial contribution at all 4 and while Lalande’s Abrégé is indeed the first place known to me where the three laws are called thus and presented as a group of three items numbered according to their modern order, 5 Lalande himself contributed at best the number ‘3.’ before the third law, as will become clear.
Since Gingerich’s and Wilson’s contributions, the Digital Revolution has opened up a wealth of previously inaccessible early modern sources and made it correspondingly easier to answer questions such as the present one. In this note, I try to provide a fuller and more correct account of how the three laws were singled out as particularly important from the plethora of insights and ideas to be found in Kepler’s writings, came to be called ‘laws’ and were put in their present order. In doing so, I start from an important prerequisite for the entire development, namely the concept of ‘laws of nature’ and its history (1). The rest of the account (2–5) is arranged according to the protagonists involved.
The conceptualisation of mathematically describable regularities in the course of nature as ‘laws of nature’ was a protracted and complex development. 6 Already in antiquity, such regularities were discovered and formulated, while ‘law of nature’ and similar terms were applied to quite different phenomena. A number of ancient authors, such as Archimedes, the author of the pseudo-Aristotelian Mechanics or Ptolemy, reduced natural processes, conditions and phenomena to mathematical terms but did not call the results of their efforts ‘laws’. When Archimedes formulated the principle named after him, he simply wrote:
When bodies specifically lighter than a fluid are put into the fluid, they will be submerged to such a degree that the weight of such a quantity of the fluid as is equal to the submerged part equals the weight of the entire body.
7
On the other hand, authors like Plato, Lucretius or Pliny the Elder happily used the expressions ‘law(s) of nature’ (νόμος τῆς φύσεως, ‘leges naturae’) or ‘contracts of nature’ (‘foedera naturae’) to indicate, not laws of nature in the modern sense, but regularities in nature in a broader sense or supposedly natural conditions in human life. Lucretius, for one, wrote as follows about the decay of things over time: Finally, do you not see that even rocks are defeated by time, that high towers collapse and stones become brittle, that the temples and statues of the gods are wearing down and show cracks, and that not even their holy power can extend the boundaries set by fate and strive against the contracts of nature?
8
During the Middle Ages and the Renaissance, the expression ‘law of nature’ was not used for formulations that would be labelled as such today either, as far as can be said at present. It was not until the second third of the 17th century that this situation began to change. Galilei called his law of free fall not a ‘law’, but at least a ‘rule’ (‘regola’) in his Discorsi (Leiden, 1638).
9
More importantly, Descartes, whose corpuscular and mechanist view of the physical world was influenced by Lucretius and ancient atomism in general,
10
wrote about ‘laws / rules of nature’ (‘loix / regles de la Nature’, ‘leges / regulae Naturae’) in Le monde (composed around 1630, first printed Paris, 1664) and Principia philosophica (Amsterdam, 1644). At the beginning of both works, he identified three such laws – presented in different order and slightly different form – that regarded the tendency of a body to maintain its condition as long as it was not exposed to external influences, its tendency to move in a straight line, and the behaviour of two colliding bodies.
11
Like Galilei’s ‘regola’, Descartes’ ‘laws’ or ‘rules’ were concerned with basic physical phenomena, although unlike Galilei,
12
he made no attempt at formulating them in mathematical terms. By way of illustration, the first law from Le monde and the second from the Principia philosophica may be quoted: But I do not wish to delay any longer in telling you by what means Nature alone will be able to unravel the confusion of the Chaos of which I have spoken, and what are the laws that God has imposed upon her. . . . The first is: That each part of matter in and of itself always continues to be in the same state, as long as the encounter of others does not force it to change it.
13
The second law of nature is as follows: that each part of matter, considered separately, never tends to move continuously along any curved lines but only along straight ones . . .
14
In the late 1660s, Descartes’ laws inspired a lively debate on the phenomenon of motion and in particular of collision among the fellows of the recently founded Royal Society. 15 Three fellows, John Wallis, Christopher Wren and Christiaan Huygens, were asked to publish their thoughts on the matter in the Philosophical transactions. Complying with this request in three short Latin contributions, 16 all of them presented the regularities suggested by them with the help of mathematical formulas and diagrams, and all of them called these regularities ‘laws’. Wallis’ contribution, for example, is titled ‘A Summary Account given by Dr. John Wallis, of the General Laws of Motion’ and concludes: ‘And these are, according to my opinion, the general laws of motion, to be applied to specific cases by means of calculation’. 17 The simultaneous use of mathematical presentation and legal terminology by three prominent virtuosi on the same subject appears to have been an important step towards establishing mathematical laws of nature as a more widely accepted concept. Over the following decades, this concept gradually became standard.
2. We are now better positioned to understand why Kepler refrained from referring to his three laws by that name. As his dates of birth and death (1571–1630) indicate, he lived a few decades too early to witness the emergence of the modern concept and terminology of ‘laws of nature’. Although it would of course not have been completely impossible for him to call his three laws ‘leges naturae’, this would not have been an obvious possibility but rather a bold conceptual innovation in his day. It is therefore not surprising that Kepler did not take this step. 18 Nor did anybody else call his astronomical findings ‘laws’ during his lifetime or for some decades after his death, although each law was known and used individually by several astronomers, as shown by J.L. Russell. 19 A fortiori, Kepler’s three laws were not understood as a coherent group or put in their present order.
3. Towards the end of the 17th century, Descartes’, Wallis’, Wren’s and Huygens’ way of talking of ‘laws’ was prominently adopted in Newton’s Principia mathematica (London, 1687). Although Newton was slow to describe Kepler’s insights in such terms, 20 he made a vital contribution to the development under consideration in two other respects: first, his mechanical interpretation of Kepler’s findings transformed them from astronomical statements about the solar system into universally valid statements of classical mechanics and ultimately of physics, the discipline based on natural laws par excellence. 21 Second, Newton, harking back to Descartes, who had placed his three laws of motion at the beginning of the Principia philosophica, introduced the Principia mathematica by ‘AXIOMS OR LAWS OF MOTION’ (‘AXIOMATA SIVE LEGES MOTUS’, 12–13) set in monumental capital letters. 22 These – the laws of inertia, of acceleration and of action and reaction – were not only mathematical laws of nature prominently placed: they were laws of motion, they were three, and their order was fixed by a numeration. In other words, they provided an obvious model for the precise way in which Kepler’s laws were conceptualised.
4. The ‘AXIOMATA SIVE LEGES MOTUS’ figure prominently in an anonymous review of the Principia mathematica in the Acta eruditorum (1688, 303–15, p. 305), where they are not only succinctly paraphrased but also introduced by the sentence ‘The axioms contain the following laws of motion’ (‘Axiomata has leges motus continent’). This review was read by Leibniz, to whom it gave a first idea of the contents of the Principia mathematica. Proof of Leibniz’s encounter with the Principia mathematica through this review can be found in his ‘Tentamen de motuum coelestium causis’ (Acta eruditorum, 1689, 82–96), in which he attempts a physical explanation of Kepler’s findings. 23 In § 20 on p. 92, he writes about the inverse-square law of gravitation, derived by him, with the help of his calculus, from the elliptical shape of the planet’s orbit in the previous paragraph:
I see that this theorem has already been known then [during the composition of the Principia mathematica] to the highly renowned Isaac Newton as well, as becomes clear from the Acta’s review, even though I cannot judge from this review how he came up with it.
24
Under these circumstances, it seems to be no coincidence that the very same article also contains a crucial step towards the conceptualisation of Kepler’s laws. On its opening page, Leibniz states the following about Kepler: So he found out that any given primary planet [that is, a planet as opposed to a moon] follows an elliptical orbit, in one of whose foci there is the sun, and observes such a law of motion that by the lines drawn from the sun to the planet areas are always cut off which are proportional to the respective timespans. The same man realised that several planets of the same solar system have orbital periods which relate as the 1.5th powers of their mean distances from the sun; indeed, he would have cheered greatly had he known—as was admirably noted by Cassini—that also the satellites of Jupiter and Saturnus obey the same laws with regard to their planets as the planets with regard to the sun.
25
Here, Kepler’s laws are apparently called ‘leges’ for the very first time (the second is even called a ‘lex motus’, exactly as Newton’s three laws). Moreover, all three laws are mentioned in one place and in their modern order. That they belong together as a group is underlined once more on the next page (p. 83), where they are collectively called ‘laws’ again: ‘But I have often marveled that Descartes did not even try to provide reasons for the celestial laws found out by Kepler . . .’ 26 All that is missing in Leibniz’s article is their explicit numbering.
5. While the ‘Tentamen’ represented a decisive step forward in the conceptualisation of Kepler’s laws, this journal article was not a fitting medium for spreading their new understanding, since its technicality restricted its readership to a handful of experts. In terms of dissemination, one should rather look towards more popular text genres. If one does so, one makes a find in the very genre in which Gingerich had already searched – the astronomical textbook, to be more precise, its Newtonian variety. In fact, the notions expressed in Leibniz’s article were taken over into the two earliest textbooks of Newtonian astronomy and celestial mechanics, David Gregory’s Astronomiae physicae et geometricae elementa (Oxford, 1702) and John Keill’s Introductio ad veram astronomiam seu lectiones astronomicae (Oxford, 1718). 27
Gregory cites Leibniz’s phrase ‘legum coelestium a Keplero inventarum rationes reddere’ (see Note 26) on p. 99 of his Elementa, marking it as an exact quote by printing it in italics. On p. 212, one finds the first two laws in their modern order within one sentence. On p. 85, Gregory has all three laws in one place, albeit in the order 3 – 1 – 2. Speaking about Kepler’s role in the history of astronomy, he rhetorically asks: For what greater or more divine thing could have happened to a human being in this field than to determine most precisely the relations between the orbits of the planets through harmonic speculation, than to first discover the truest way—that is, the elliptical one—of the planets around the sun and finally than to specify the truest manner in which a planet goes along on this path, namely so that it moves over areas proportional to the times, if a straight line is drawn towards the centre of the sun, which is placed in a focus of the ellipse?
28
In Keill’s Introductio, the three laws are even found together and in the present order on p. 363, prominently placed at the very beginning of lesson XXIV: Kepler was the first to prove that the planets are carried, not in circular, but in elliptical orbits and that they move around the sun, which is placed in one of the two foci of the ellipse, in such a way that a line drawn from a planet to the centre of the sun always sweeps over such areas of the ellipse as are proportionate to the timespans in which they are covered. This divine . . . discovery . . . must be adopted all the more because with its help Mr Newton laid open . . . the universal laws of motion. Kepler also proved from the movements observed that in all planets the orbital periods relate as the 1.5th powers of their distances [from the sun] . . .
29
The second law is called a ‘lex’ soon after (p. 364). As in Leibniz’s article, the only thing missing in Keill’s Latin is an explicit numeration. This, however, was made good for in a French translation published in 1746, 30 where on p. 480 the first two laws are numbered as they are today, making it easy for the reader to find out the number of the third for himself.
Gregory’s work was moderately successful, 31 Keill’s very much so: it went through at least fifteen editions in four languages and remained in print for three quarters of a century. 32 It is thus reasonable to assume that Keill in particular was instrumental in spreading the idea of Kepler’s three laws. If Lalande was really the first to explicitly number the third law I cannot tell, but this point is obviously of subordinate importance.
In sum, it should have become clear that the conceptualisation of Kepler’s three laws began considerably earlier than hitherto presumed – not in the vernacular astronomical literature of the late 18th and early 19th centuries, but in the Latin one of the decades around 1700. Moreover, it was neither a punctual nor a chance event but a process that followed a comprehensible logic. It was suggested by the designation of mathematical regularities in nature as ‘laws’ that became common in the course of the 17th century and prompted by the model of Newton’s own three laws of motion. After Leibniz had for the first time presented Kepler’s insights in a manner that comes close to their modern understanding, his view of things was soon disseminated to a wider audience in the Newtonian textbook tradition.
