424 



SCIENCE 



[N. S. Vol. XLI. No. 1055 



Oliver H. Arnold, while the funds for equip- 

 ment have been subscribed. 



Professor Thomas S. Fiske has been desig- 

 nated as administrative head of the Columbia 

 University department of mathematics for 

 two years beginning July 1, in the place of 

 Professor Cassius J. Keyser, who retires at 

 his own request. 



Mr. Morris M. Wells, of the University of 

 Ulinois, has been appointed instructor in the 

 department of zoology in the University of 

 Chicago. 



The Benjamin Peirce instructorships in 

 mathematics at Harvard University, the terms 

 of whose establishment were recently an- 

 nounced in Science, have now been filled for 

 the year 1915-16 by the appointment of Dr. 

 Edward Kircher and Dr. George A. PfeifEer. 



DISCUSSION AND COSMESPONDENCE 



THE FUNDAMENTAL EQUATION OF MECHANICS 



To THE Editor of Science : Professor Hunt- 

 ington's letter in Science of Eebruary 5 is an 

 important contribution to the subject of the 

 teaching of elementary dynamics, but the fact 

 that he and Professor Hoskins are not in 

 agreement on " the question whether F ==■ ma 

 or F/F' = A/A' is the better form in which 

 to introduce the fundamental equation of 

 mechanics " shows that something remains to 

 be said on the subject. In my opinion neither 

 of these equations ought to be considered as 

 fundamental, for both are derived from more 

 elementary equations. 



Professor Huntington objects to F = ma for 

 certain reasons. He might have made other 

 objections to it : for example, the equation is 

 not true in the ordinary English system (foot- 

 pound-second) until it is hybridized by valuing 

 either F or m in some other unit than pounds 

 (poundal or gee-pound) or a in " gravitals " 

 (instead of feet) per second per second (1 

 gravital = 32.1Y4 feet),^ or else the letter m is 



1 The writer invented the ' ' gravital ' ' and also 

 the "timal" (=1/32.2 of a second) over 20 years 

 ago as antidotes to the ' ' poundal, ' ' merely to serve 

 as ' ' horrible examples ' ' of what might be done in 

 the way of introducing still further confusion into 

 our systems of units. He also invented the 



explained as not being quantity of matter in 

 pounds, but only the quotient or ratio W/g. 

 Neither is it true in the metric kilogram-meter- 

 seeond system. (I do not think the metric 

 people have yet tried to introduce a "kilo- 

 grammal " or a " gee-kilogram.") It is of 

 course true in the dyne-centimeter-gramme- 

 second system, but this system is only used in 

 higher physical theory, and it should not be 

 inflicted on young students. The equation 

 F^ma is, however, a handy equation to work 

 with when it is understood that m is merely 

 a conventional symbol for W/g. 



The equation F/F' ^A/A' may be useful 

 for some purposes, but I agree with Professor 

 Hoskins in not accepting it as fundamental or 

 as the best equation to be used as an introduc- 

 tion of the subject. Each of the equations 

 being open to objection, I wish that both Pro- 

 fessor Hoskins and Professor Huntington 

 would consider the following treatment of the 

 subject, and let me know what objections 

 there are to it. 



Quoting Professor Huntington's words : 

 " The first serious problem which confronts 

 the teacher of dynamics is the problem of 

 making the student understand the effect 

 which a force produces when it acts on a mate- 

 rial particle " (I would substitute the word 

 "body" for material particle). 



Let us start with the student just out of 

 the grammar school, who has never studied 

 physics, but who understands the simplest 

 forms of algebraic equations, and how to 

 make a^'F/m, out of F^ma. He already 

 knows the ordinary meaning of the words time, 

 space, force, matter (or stuff, solid, liquid or 

 gas) . He may be told that the word " body " 

 means a piece or chunk of stuff, and that 

 velocity is just another name for speed. He 

 knows that force may be measured by a spring 

 balance, and that the quantity of matter in a 

 body may be determined by weighing it on 

 grocer's even-balance scale or on a platform 



"massal"^ 32.2 pounds, but that has got into 

 some test-books disguised under the names of 

 "gee-pound," slug, and "engineers unit of 

 mass." The latter term is especially objection- 

 able, for it has never been used by engineers. 



