Mat 27, 1910] 



SCIENCE 



821 



Newton any suggestion of such a definition. 

 Galileo, according to the extract quoted, said 

 that " the properties of accelerated motion are 

 defined, without consideration of their causes, 

 in such a way that the momentum (of the 

 body)' increases uniformly from the initial 

 condition of rest in simple proportionality to 

 the time," but this is a very different thing 

 from a denial that force causes motion, or 

 from an assertion that force is the rate of 

 change of momentum. 



Newton's second law of motion, according 

 to one of the translations, is : " If a body be 

 acted on by several forces it will obey each as 

 though the others did not exist, and this 

 whether the body be at rest or in motion." 

 It would be difficult to explain this law if we 

 substitute for the word " forces " the words 

 " rates of change of momentum," especially if 

 the body is at rest and therefore has no mo- 

 mentum. 



Referring to the example of the action of 

 force given in my former letter in Science, a 

 stone is suspended from a projecting shelf by 

 an elastic cord. The earth's gravitation acta 

 on the stone. There is a tension and an elas- 

 tic resistance in the cord. The word force is 

 used as a generic term to include all those 

 varieties of force that are designated by the 

 words gravitation, tension, resistance, stress, 

 etc. As long as the cord sustains the stone 

 these several forces act, but as there is no 

 motion there is no momentum, nor rate of 

 change of momentum, which Professor Crew 

 says force " is." 



Let the cord break. We now have motion, 

 which is change of position during time; 

 velocity, ds/dt; momentum and constant ac- 

 celeration; all so long as the stone is falling 

 freely, and we may write the equations: 

 FT = MV; F = MV/T; F = MA; V = 2S/T. 



Before the cord breaks we have two elemen- 

 tary concepts to deal with, matter and force. 

 After the cord breaks, and while the stone is 

 falling, we have two other elementary con- 

 cepts, space and time, and a few complex con- 

 cepts : velocity, T = 28 /T or ds/dt, momen- 

 tum, y^/gy^Y, and acceleration, (7,— FJ/T. 

 It is only by a somewhat complex mathemat- 



ical deduction that we arrive at the " pure con- 

 cept of the intellect, but a precious concept,"" 

 F = (ilf 7, — MY^ -=- T, which Professor Crew 

 says is a " perfectly correct, competent and 

 complete description of force." A boy twelve- 

 years old easily grasps the concept that the 

 force acting on the stone is the pull that tends 

 to break the cord, and while he does not 

 know what force is except by its effects, he 

 easily conceives that it is the cause of mo- 

 tion when the cord breaks; it takes a meta- 

 physician to arrive at the definition that 

 force is the time rate of the change of mo- 

 mentum. 



Let us return to the equations. In order to 

 make them true we must choose certain units 

 for each quantity. Some writers on physics 

 say that the unit of mass is 1 lb. and that the- 

 unit of force is a poundal. Others say that 

 the unit of mass is 32.2 lb. and the unit of 

 force 1 lb.; still others that the unit of weight, 

 (quantity of matter, 17) is 1 lb. and that M 

 is merely an expression to signify Yf /g. One- 

 book on high-school physics defines mass as 

 the quantity of matter, and gives its unit as 

 1 lb., and also gives the unit of weight (re- 

 sultant of the attraction of gravitation) as 

 1 lb., and later gives the equation T7 = Mg, 

 which is wrong if the definitions of the units 

 are right, for in that case 17 = Mg becomes 

 1 = 1 X 32.2. In the G.G.S. system there is 

 no such trouble, for in it there are four dif- 

 ferent units to represent the four elementary- 

 quantities, viz. : dyne, gramme, centimeter, sec- 

 ond. It is only when we try to graft the so- 

 called absolute system on the English system, 

 with its pound representing both quantity of 

 matter and force, and invent new terms, such 

 as the poundal and the gee-pound, to get over 

 the difficulty which exists in the minds of the- 

 metaphysical physicists (but not in the minds 

 of engineers, to whom il/=17/5'), that eon- 

 fusion begins. 



The equation ¥ = (MY ^ — MY ^ ^T may 

 be interpreted as follows : When a force ¥' 

 acts during a time T" on a body which is free- 

 to move, and whose mass (17/^) is M, and 

 gives the body an increase of velocity from 

 7, to 7„ during that time, then if the units; 



