608 



SCIENCE 



[N. S. Vol. XLI. No. 1060 



Plans have been drawn for the construction 

 of four greenhouses, a heating plant, wells and 

 windmills, and an underground piping system 

 for irrigation purposes, on the new botanical 

 garden for the department of botany of the 

 University of Michigan. The old botanical 

 garden east of the city with the 10,000 trees 

 and shrubs which have been planted there, will 

 be made into a tree and shrub park in about 

 a year. 



Dr. Henry C. Oowles, Dr. G. J. Chamber- 

 lain and Dr. O. W. Caldwell have been pro- 

 moted to fuU professorships of botany at the 

 University of Chicago. 



Dr. Julius Stieglitz, professor of chemistry 

 and director of analytical chemistry in the 

 University of Chicago, has accepted an invi- 

 tation to give courses in chemistry at the Uni- 

 versity of California during the summer term 

 that begins June 21 and closes on August 1. 



Professor Daniel Starch, of the University 

 of Wisconsin, will give courses in educational 

 psychology and educational measurements at 

 the University of Washington, Seattle, dur- 

 ing the coming summer session. 



At the University of Birmingham Dr. 

 Douglas Stanley has been appointed to the 

 chair of therapeutics, and Dr. L. G. Parsons 

 to a newly created lectureship in infant hy- 

 giene and diseases peculiar to children. 



DISCUSSION AND COBBESPONDENCJE 

 THE fundamental EQUATION OF DYNAMICS 



The difference of opinion between Professor 

 Huntington and myseK is probably less than 

 might be inferred from his recent communica- 

 tion.^ I do not object to the use of the equa- 

 tion F/F' = a/a', which indeed is a useful one. 

 But it seems to me misleading to call this the 

 fundamental equation of dynamics, because 

 there is something equally fundamental that 

 is quite independent of this equation — the 

 fact that the mass of a body is one of the 

 factors determining what acceleration it has 

 under the action of a given force. The same 

 fact is expressed by Professor Huntington in 

 the words^ " diilerent bodies require different 



1 Science, February 5, 1915. 



2 These words seem to be a very definite corrobo- 



amounts of force to give them any specified 

 acceleration," which he refers to as " this cen- 

 tral fact of dynamics." My view is that this 

 " central fact " should receive explicit and 

 quantitative^ statement in whatever equation 

 or equations may be adopted for expressing the 

 fundamental law of acceleration. The prin- 

 ciple which such equations must express may 

 be stated in different ways. In the review* 

 which called forth Professor Huntington's 

 comment I expressed the opinion that the 

 method most intelligible to the beginner is to 

 introduce at the outset the body-constant which 

 was called by Newton mass or quantity of 

 matter, and to make the fundamental principle 

 a statement of the way in which the accelera- 

 tion of a body depends quantitatively upon 

 both the applied force and the mass of the body. 

 The principle then takes the following form: 



(a) A force acting upon a body otherwise 

 free would give it, at every instant, an accel- 

 eration proportional directly to the force and 

 inversely to the mass of the body. 



The meaning is perhaps more clearly 

 brought out by writing a definite proportion: 



(J}) Forces F, F', acting upon hodies whose 

 masses are m, m', cause accelerations a, a' 

 such that 



a _ F^ m' 

 a' ~ F' ' In' 



(1) 



It is instructive to consider the following 

 partial statements of the general principle: 



(c) If the same tody is acted upon at differ- 

 ent times hy forces F, F' and if a, a' are the 

 accelerations caused, then 



(2) 



ration of the statement (quoted with disapproval 

 by Professor Huntington) that "an equation 

 whieh results from comparing the effects of dif- 

 ferent forces upon the same tody can not be re- 

 garded as a complete expression of the funda- 

 mental law of motion; it ia equally important to 

 compare the effects of forces acting upon any dif- 

 ferent todies." 



3 The mere qualitative statement above quoted 

 is no more satisfactory than the statement that 

 "different forces acting at different times upon 

 the same body cause different accelerations." 



* Science, December i, 1914. 



