September 10, 1915] 



SCIENCE 



341 



bodies B and C and that forces equal to F, ap- 

 plied to B and 0, cause accelerations a', a". 

 We recognize the truth of the following state- 

 ments about the values of a' and a" : 



Both a' and a" are greater than a. 



If one of the accelerations a', a" is less than 

 2a the other is greater than 2a. 



If a' and a" are equal, each is equal to 2a. 



The accelerations satisfy the equation 1/a' 

 -{-l/a"=l/a. (This of course includes the 

 three preceding statements.) 



These statements are consequences of H. ; 

 but the reason we recognize this is because we 

 recognize that A contains more matter than 

 either B or 0, and that the sum of the quan- 

 tities of matter of B and is equal to that of 

 A. That is, in interpreting H. we regard 

 mass as a measure of quantity of matter. 



As another illustration, let A and B be any 

 two distinct bodies such that when equal forces 

 are applied to them the acceleration of A is 

 less than that of B. Proposition II. tells 

 us that the mass of A is greater than that of 

 B; but is there any reason for saying that A 

 contains more matter than 5? There is this 

 reason: We know that, by removing from A 

 some quantity of matter, there will remain a 

 body A' such that, if equal forces be applied to 

 A' and B, their accelerations will be equal; or 

 by adding to B some quantity of matter there 

 will be produced a body B' such that, if equal 

 forces be applied to A and B', their accelera- 

 tions will be equal. Moreover, we know that 

 the matter which must be taken from A to pro- 

 duce A', and that which must be added to B 

 to produce B', have equal masses m as tested 

 by II.; and that if the accelerations of A 

 and B due to equal forces F are a' and a" , a 

 body of mass m acted upon by a force F would 

 have an acceleration a such that 1/a = 1/a' — 

 1/a". These facts are all recognized as 

 consequences of H. because we regard mass 

 as therein used to be a measure of quantity 

 of matter; they would not follow if our notion 

 of mass were derived wholly from proposition 

 n. itself. 



The significance of mass in the second law 

 of motion is sometimes stated in the following 

 form: 



III. The forces required to give equal ac- 

 celerations to different todies are proportional 

 to their masses. 



It is easy to cite illustrative cases showing 

 that in applying this proposition also we in- 

 terpret mass as a measure of the matter of 

 which bodies are composed. Thus the state- 

 ment that " body A has three times the mass 

 of body B " means more than that " body A 

 requires three times as much force as body B 

 to give it a specified acceleration"; it means 

 that the material contained in body A might 

 be made into three bodies, each of which would 

 require the same force as body B to give it a 

 specified acceleration. 



It is of course true that an important part 

 of the import of propositions H. and IH. 

 consists in giving precision to the definition of 

 mass. But the illustrations which have been 

 given show that the preliminary definition of 

 mass as quantity of matter is not without 

 important meaning, and serves a useful pur- 

 pose in explaining the significance of mass in. 

 the laws of motion. 



L. M. HosKiNs 



Stanford Universitt, 

 August 5, 1915 



IS SIVAPITHEOUS PILGMM AN ANCESTOR OF MAN? 



In the " Records of the Geological Survey 

 of India " for February, 1915, Dr. Guy E. Pil- 

 grim has described the fossil anthropoids of 

 India, including several new forms of great 

 interest from the Lower, Middle and Upper 

 Siwaliks. Through the kindness of Dr. Pil- 

 grim the American Museum of Natural His- 

 tory has received casts of his types and prin- 

 cipal specimens of Siwalik anthropoids, con- 

 sisting of fragments of jaws and isolated 

 molars. These casts, together with Dr. Pil- 

 grim's excellent illustrations, have enabled the 

 writer to make a critical comparison of the 

 extinct Indian anthropoids with the existing 

 anthropoids and with recent and extinct races 

 of man. 



Pilgrim describes several new species of 

 Dryopithecus, a genus characteristic of the 

 Upper Miocene of Europe. Its known range 

 is thus extended to the Upper Miocene of 



