THE THEORY OP GRAVITATION. 151 



XVIII. 



These synthetic demonstrations of laws of falling bodies by the intro- 

 duction of mechanism whose existence is only surmised, may perhaps 

 be less philosophical than analytic demonstrations which are based 

 entirely upon observed phenomena. Still it must be recalled that in 

 cases where direct observation has been difficult and inexact, error has 

 frequently attended deductions of this latter kind. At all events the 

 former kind of demonstration is much more philosophical than a gra- 

 tuitous hypothesis, which is, nevertheless, the means of invention 

 employed by Galileo; and its results are quite as well established as are 

 the laws of Galileo since they are proved by exactly the same meaus, 

 that is by the sensible accord of their consequences with the phenomena. 

 Nothing else than this is claimed by Galileo himself and his principal 

 successors. 



XIX. 



But the atomists would have encountered one very serious objection, 

 to which they were necessarily exposed in common with all physicists 

 who undertake an explanation of gravitation. For by having thickness 

 a roof receives not a whit more of hail, or a shield of arrows; whereas, 

 remaining otherwise unchanged, the weight of all bodies is augmented 

 in direct proportion of their thickness. Conversely when one removes 

 a heavy body from a shop or dwelling, or reduces it to sheets exposed 

 without protection to material influences (the rain, for example) it 

 receives more than when protected or concentrated so as to present a 

 small surface. But it has never been found by merchants and artisans, 

 who are continually in the habit of weighing, that bodies appear heavier 

 in open air than when under cover, and gold-beaters have never per- 

 ceived that the weight of the metal augments in proportion to the 

 increase of its surface. 



In a word, if the collision of atoms is the cause of heaviness, the 

 weight of bodies ought to be proportional to their surface (or rather to 

 their horizontal projection). How, then, does it happen that the weight 

 is proportional to the mass? 



Do the gravitational atoms then act across the thickest and most 

 compact envelopes of all substances as fully as through the air? And 



responding spaces will be proportional to the squares of the whole times, and the 

 sums of the (equally numerous) small spaces — that is to say, the whole distance 

 traversed— will also he proportional to the squares of the whole times. 



Remark: The assumption with which I started, and which is tacitly made in the 

 other. demonstrations of this law, is a sort of license equivalent to supposing that 

 the parts of the times and spaces are infinitely small, and is less conceivable than 

 one is accustomed to suppose. It is an inevitable inconvenience of the common 

 hypothesis of the continuity of the action of gravitation. But this inconvenience 

 is not encountered when we substitute the hypothesis of discontinuity. I mean to 

 say that there arises no contradiction when the time increments are taken equal to 

 the intervals between the blows of the gravitational agency. 



