616 



SCIENCE 



[N. S. Vol. LI. No. 1329 



These remarks are interesting, but not alto- 

 gether to the point. Those modern apologists 

 do not actually quote Aristotle, nor do they 

 base their reasoning on -what Aristotle actu- 

 ally said. 



Aristotle discusses falling bodies in six or 

 more different parts of his " Physica " and 

 "De Ccelo." 



1. He considers'' a body falling through 

 media of different densities — air, water and 

 media indefinitely rare. Then he considers 

 also bodies of different weights falling through 

 the same medium. Endeavoring to disprove 

 the existence of a vacuum, Aristotle says : 



That which ig heavier . . ., other things being 

 equal, moves faster through the same space, and 

 indeed faster according to the ratio of the magni- 

 tudes of the things, so that this must happen also 

 through a vacuum. But this is impossible; for 

 why should it move faster? In a plenum this is 

 necessarily true, because the larger moves more 

 rapidly by its power of greater penetration. 



Thus, according to this Aristotelian passage, 

 not only do the larger bodies move faster 

 through a medium, but they would move 

 faster even through a vacuum, if such existed. 



2. Aristotle asserts^ that each of the bodies 

 constituting the universe was originally at 

 rest (as taught by Anaxagoras), that each 

 was heavy or light and had power to move. 



, For suppose A without weight, but B possessing 

 weight; and let A pass over a space CD, but B in 

 the same time passes over a space CE — for that 

 which has weight will be carried through the larger 

 space. If now the heavy body be divided in the 

 proportion that space CE bears to CD, . . . and 

 if the whole is carried through the whole space CE, 

 then it must be that a part in the same time would 

 be carried through CD. Consequently the body 

 without weight and the one possessing weight pasj 

 over the same distance, which is impossible. 



Here Aristotle's law is applied to bodies 

 initially at rest. 



5 "Physica," Book IV., cap. 8. We are using 

 Oarl Prantl's " Aristoteles ' Werke. Griechisch und 

 Deutseh," Bd. I., Leipzig, 1854, pp. 187-191. 



e"De Ccelo," Book III., cap. 2; Prantl, Vol. 2, 

 pp. 203-205. 



3. Aristotle argues' that " if there were an 

 unlimited increase in the weight, there would 

 be also an unlimited increase in velocity." 

 The volume of a falling body is specially con- 

 sidered in " De Ca3lo," Book IV., cap. 1 :* 



4. In "De Coelo," Book I., cap 6,» we find: 



If such and such a weight is moved so and so 

 far in such and such a time, then some larger 

 weight will be moved through the same distance 

 in still shorter time, shorter in the inverse ratio 

 of the weights. ... A limited weight can pass over 

 any limited line in a limited time. 



5. In "De Ccelo," Book IV., cap. 2," Aris- 

 totle argues, likewise, that the more fire will 

 proportionally move upward with greater 

 speed and the less fire with less speed, and 

 similarly for the downward motion of more 

 gold or more lead. Here, as in most other 

 passages, the shapes of the moving bodies are 

 not considered. 



The above shows that Aristotle considered 

 his law applicable when the motion took place 

 from rest as in (2), when there was no upper 

 limit to the weight that the moving body may 

 have as in (3), when the time of motion may 

 be reduced or increased as in (4), and when 

 the moving bodies are different weights of 

 any metal, like gold or lead, as in (5). No 

 restriction is placed by Aristotle to the com- 

 bination of some or all of these four condi- 

 tions in one and the same motion. To our 

 surprise, he was willing to apply his law even 

 to motion in a vacuum (were a vacuum 

 possible) as is seen in (1). It appears there- 

 fore that Aristotle allowed his law a general- 

 ity of application which certainly did include 

 the special conditions imder which Galileo 

 performed his experiment of dropping a one- 

 pound shot and a hundred-pound shot through 

 the air from the leaning tower. 



Florian Cajori 



TJNIVEHSITY op CALirORNIA 



T'De Coalo," Book I., cap. 8; Prantl, Vol. 2, 

 p. 65. 



That body is heavier than another which, in an 

 equal bulk, moves downward quicker. 



8 Prantl, Vol. 2, p. 243. 



» Prantl, Vol. 2, p. 47. 



10 Prantl, Vol. 2, p. 249. 



