December 24, 1915] 



SCIENCE 



907 



poundala X seconds = pounds X feet per second ; 

 1 poundala 1/32.2 pound force; 



pounds X seconds = slugs X feet per second; 1 

 slug ^32.2 pounds; 



pounds X timals = pounds X feet per second; 1 

 timal = 1/32.2 second; 



pounds X seconds = pounds X gravitals per sec- 

 ond; 1 gravital = 32.2 feet. 



The timal and gravital are just as ridiculous 

 or semi-ridiculous as the pouudal or slug, and 

 no more so. Neither one of them has any rea- 

 son for existence except the pleasing allitera- 

 tion, copied from the C.G.S. system, " imit 

 force acting on unit mass causes unit accelera- 

 tion." I see no reason why we should use this 

 principle when it leads to no useful result, but 

 does lead to the worse than useless ones of 

 wasting the time of the student and confusing 

 his mind. If it is such a good thing, why has 

 it not yet been grafted on the metric system? 

 Why do we not have kilogrammal as a unit 

 of force and kiloslug as a unit of quantity of 

 matter ? 



Is there any reason why in the English sys- 

 tem we should not adhere to the good old prin- 

 ciple. Unit force (pound) acting on unit mass 

 (1 pound) gives it an acceleration of 32.1'740 

 feet per second? 



Professors Franklin and MacWutt, Septem- 

 ber 24: 



Let us retain as tbe fundamental meaning of 

 the word mass the result of weighing on a bal- 

 ance scale. . . . Use a balance on a batch of sugar 

 and you get always and everywhere the same nu- 

 merical result. . . . We respect the experience of 

 two thousand years in that we base our definition 

 of mass on the use of the balance. 



I have no objection to the physicists' using 

 the word mass in this sense, but they should 

 not try to prevent their students from using 

 the word weight in the same sense; and I do 

 object to their telling their students that the 

 unit of force is a poundal, when all the rest of 

 the world says it is a pound. 



Professor "Wilson, October 15 : 



To obtain valuable training in kinetics a knowl- 

 edge of the differential and integral calculus, in- 

 cluding the simpler differential equations, is neces- 

 sary .... We therefore have the fundamental 

 equation of kinetics in the form d/dt (.mv) ^^gf. 



The calculus is not at all necessary when we 

 are dealing with uniformly accelerated motion, 

 and valuable training in kinetics was obtained 

 in the study of the early editions of Weisbach, 

 in which calculus was not used. In fact when 

 the problem involves acceleration not con- 

 stant, but varying according to some assumed 

 law a graphical or arithmetical solution of it 

 will be more useful training than its solution 

 by the calculus. Let Professor Wilson give tQ 

 his students the boat problem with frictional 

 resistance added and find what resiilts they get 

 by applying his differential formula to it. 

 The problem is : A boat with its load, the total 

 weighing 1,000 pounds, is towed in still water 

 with a constant force of 1 pound. The fric- 

 tional resistance is 0.2i;2 pounds, v being 

 speed in ft. per sec, and the force available for 

 acceleration is (1 — v-) pounds. What speed 

 will the boat have at the end of 1, 2, 3 and 4 

 minutes; how far will it travel each minute 

 and how long time will it take to bring it to a 

 speed of 0.999 of the theoretical maximum at 

 which the acceleration is zero? 



It is of course true that weight is not a definite 

 constant thing from place to place. 



It is a constant thing if weight is defined, 

 as is customary in commerce, as the quantity 

 of matter in pounds determined by weighing 

 it on an even balance. 



. . . proceed to Newton's law that the rate of 

 change of momentum is equal to the force. Here 

 however we have an equation that is no longer 

 homogeneous either in the mass or in the force. 



This is a new kind of language to me. I 

 confess my ignorance of the meaning of the 

 phrase " homogeneous either in the mass or in 

 the force." Whatever it may mean it surely 

 has no place on " elementary " mechanics. 



The equation ma = f, or any equation involving 

 accelerations leads to the ridiculously needless con- 

 cepts of transverse and longitudinal (and an infin- 

 ity of oblique) masses. 



Here again Professor Wilson is too deep for 

 me. I have used the equation ma = f for 

 forty years (imderstanding that m means the 

 quotient w/g) and never have been led to any 

 such concepts. I thank Professor Wilson for 

 the expression "ridiculously needless con- 



