148 THE THEORY OF GRAVITATION". 



as the square of the distance. For the sake of brevity the mechanical 

 cause may be left out of consideration in the discussion. 



As these philosophers would have foreseen many difficulties in rigor- 

 ously testing every consequence to see if it coincided exactly with 

 observation, and would therefore have refrained from embarking upon 

 so serious a task before perceiving that the deductions accorded in gross 

 with the results of experience, I presume they would not seriously have 

 applied geometry and computation to this gravitation without having 

 first determined by simple reasonings what, approximately, would be 

 the effects flowing from it, and seeing that these conjectures accorded 

 roughly with the real constitution of the universe ' I believe I do no 

 violence to probabilities in presuming that the ancient philosophers 

 would have been acquainted with some such reasonings. Having fewer 

 matters than we to distract their attention, they were able to make very 

 exact deductions in subjects requiring nothing but meditation. With 

 reference to the acquired knowledge which would be needed in such 

 reasonings, it will be recalled that the theory of conic sections had 

 been discovered and cultivated before the birth of Epicurus, that 

 Archimedes had made great advance in the doctrine of centers of 

 gravity, and that the ancient geometers, and especially the last named, 

 employed approximations with great ingenuity when they were unable 

 to attain to rigorous precision. 



XIV. 



Encouraged by these first successes and animated by the grandeur of 

 the enterprise it is highly improbable that these ardent and subtile 

 geometers 2 would have stopped here. They would doubtless have 

 invented for the purpose some means for passing from the ratio of sensi- 

 ble quantities to that of their imperceptible elements, and conversely 

 from elementary quantities to their summation, at least for the simple 

 case required when one wishes to avoid the numerical computation of 

 the small anomalies of the movements of the celestial bodies. 



1 1 had intended to insert here some preliminary observations which the atoniists 

 would probably have made. I had collected them in part from various researches 

 (or incidental points) made by good geometers who have undertaken to illustrate to 

 readers but little advanced in mathematics some of the truths of physical astronomy. 

 The remainder were from notes of lectures which I have myself given upon these 

 matters. But I have omitted this digression on account of its length. Perhaps 1 

 may be permitted to remark that these elementary tests may be rendered very con- 

 vincing, although some of them presuppose so little knowledge of geometry that 

 they may even be stated without reference to figures. 



2 It should be borne in mind that we are not here speaking of the Epicureans as 

 some have really, been — that is to say of a nature decidedly lazy and consequently 

 ignorant of astronomy and physics — but of philosophers simply, Epicureans as 

 respecting the fundamental propositions of physics only, but resembling rather their 

 contemporaries of other sects in general enlightenment and taste for research. Such 

 a supposed character for these philosophers is by no means forced, since the physical 

 and speculative dogmas of Epicurus did not necessarily entail his moral precepts and 

 practices. 



