June 26, 1914] 



SCIENCE 



941 



these fundamental assumptions. To define a 

 quantity as a vector, and then conclude that 

 the parallelogram law holds begs the whole 

 question. The logical way to proceed would be 

 to first prove that the quantity is a vector, 

 that is, that the parallelogram law holds and 

 then (advantageously) apply the principles of 

 vector analysis. We can not prove, however, 

 that a force is a vector. We must depend 

 upon experience for our justification in assum- 

 ing a force to be a vector. 



We do not know what a force is. To say 

 that "force is an action" explains nothing, 

 and to define it as a vector begs the whole 

 question. Experience and experience alone 

 can justify us in dealing with forces as vectors 

 of a certain kind. In other words, the " paral- 

 lelogram, law of forces " is nothing more than 

 an assumption and is not a purely " geometric 

 principle." If we assume that a force can be 

 measured by the motion it produces, and if we 

 assume that the effect of each force is inde- 

 pendent of the effect of the other forces acting, 

 then it follows that the parallelogram law holds 

 also for forces, since we know that this law, as 

 a consequence of the principle of independence, 

 does hold for the motions (accelerations) pro- 

 duced. This argument, however, makes two 

 assumptions. Tirst, it assumes that a force 

 can be measured by the acceleration it pro- 

 duces (in its own line of action), and, sec- 

 ondly, it assumes " the principle of independ- 

 ence " for forces. Now these two assumptions 

 are involved in Newton's Second Law of 

 Motion. In other words, the parallelogram law 

 of forces is a consequence of Newton's Second 

 Law of Motion, and, therefore, in its last 

 analysis is an assumption. If, however, the 

 parallelogram law is once assumed for forces, 

 then it can be proved for moments and other 

 (vector) qualities involving force. It is, there- 

 fore, suificient to assume the law to hold for 

 forces. 



It is a question whether we have a right to 

 assume the parallelogram law even for veloc- 

 ities and accelerations without proving it, and 

 to assume it for forces is equivalent, as we 

 have seen, to assuming Newton's Second Law 

 of Motion. 



In my criticism it was stated: 



On page 102 he assumes that a force is propor- 

 tional to the accelerations produced. This as- 

 sumes Newton's Second Law. 



In reply he says: 



This statement is not quite right. The relation 

 between force and acceleration which I have called 

 force-equation is derived on page 106 from the 

 fundamental principle which I have postulated. 

 In this derivation I have made use of the defini- 

 tion of kinetic reaction which is stated and illus- 

 trated on pages 102 to 105, but this is not equiva- 

 lent to assuming a new principle. -' 



This is true as far as it goes, but he fails 

 to add that the form of this " force-equation " 

 depends upon the actual value of this "ki- 

 netic reaction " which he finds as the result 

 of experiments to be equal to the mass times 

 the acceleration produced, that is. 

 Kinetic reaction =z mf. 



He seems to me to be making a " distinction 

 without a difference." At least he is making 

 an assumption here that is equivalent to as- 

 suming Newton's Second Law of Motion. 

 E. W. Eettgee 



Cornell University 



accessory chromosomes of man 

 In reply to Professor T. H. Morgan's state- 

 ment in Science, June 5, 1914, I wish merely 

 to request the reader who may be interested 

 to read my note of May 15^ and my paper, 

 " Accessory Chromosomes in Man," ^ and then 

 Professor Montgomery's paper,^ that he may 

 decide for himself whether Montgomery and 

 I have not agreed in the main regarding the 

 accessory chromosomes of man. This was the 

 only point at issue in my former communica- 

 tion, which was meant not as a " complaint," 

 but as a correction to a misleading inference. 

 As to the material on which Montgomery 

 and I came to different conclusions regarding 

 a second pairing of the ordinary chromosomes. 

 Professor Morgan is mistaken in stating that 



1 Science. 



2 Biol. Bull, XXX., 4; September, 1910. 



3 Jour. Acad. Nat. Sci. PMla., XV., second series, 

 1912. 



