December 24, 1915] 



SCIENCE 



903 



equation becomes 7 = 32.1740 FT/W. Re- 

 move the restriction that the body starts from 

 rest, and let it have at a given instant a veloc- 

 ity Tj and at the end of the time T a velocity 

 F,. Let V^V, — Fj, then the equation ap- 

 plies equally well to this case, if we define F 

 as the increase of velocity during T seconds. 



Now remove the restrictions that the body 

 is not retarded by friction and that the force 

 is constant. The velocity then will not vary 

 directly as the time, but in some other way, 

 which can be expressed graphically by plotting 

 velocities or distances against time. The 

 problem is now not one of uniformly accele- 

 rated motion and it belongs to another chapter 

 of the discussion, but we can still use the same 

 formula if we differentiate it, assuming that 

 for a differential of the time the force and the 

 quantity of matter are constant. We then have 

 dv = 32.1740 F/Yf dt or dv/dt =■ 32.1740 F/W. 

 This is a formula for the general case, but it 

 is not fundamental; it is derived from the 

 fundamental equation V^FTg/W after 

 dividing both sides of the equation by T. The 

 notion of instantaneous rate of change of 

 velocity, i. e., acceleration, is not introduced 

 until we give the name acceleration to the 

 quantity dv/dt (or V/T if the acceleration is 

 constant), and the term mass does not appear 

 nntil we give the name mass to the quotient 

 W/g and thus derive A = F/M, or F = MA, 

 a most useful equation when we define M as 

 W/g, but it is derived and not fundamental. 



Professor Fulcher, April 30: 



Gravitational foree overcome — weight raised. 



Elastic force overcome — spring stretched. 



Trictional force overcome — sled dragged. 



A pound weight (lb. wt.) is the force required 

 to lift 3.55 eu. in. of iron. 



I approve of Professor Pulcher's method of 

 progressing from matters of every-day experi- 

 ence, and it is the method I use, as shown in 

 my article in Science, December 24, 1909. I 

 am glad to see that he uses the words " weight 

 raised" instead of "mass raised," for the 

 words are in harmony with the young student's 

 understanding of the word weight. I should 

 prefer, however, to say elastic resistance and 

 frictional resistance, instead of elastic force 



and frictional force. The use of " pound 

 weight (lb. wt.) " instead of the term " pound 

 force " I consider objectionable. The word 

 weight is now used correctly and generally in 

 common language with two meanings, (1) 

 quantity of matter (determined by weighing 

 it on an even balance or by multiplying its 

 volume by its specific gravity), and (2) the 

 force with which the earth's gravity attracts 

 that matter ; while the words " pound weight " 

 have a specific meaning, viz., a piece of metal 

 marked 1 lb., used in weighing. Neither 

 "weight" nor "pound weight" are properly 

 applied to the horizontal force required to drag 

 a sled or to a vertical force of 1 lb., as meas- 

 ured on a spring balance, exerted (vainly) to 

 lift a 2 lb. weight. 



Before we can determine the effect of a constant 

 unbalanced foree in changing the motion of a 

 body, we must study some simple types of mo- 

 tion: (1) uniform; (2) constantly changing 

 speed; (3) parabolic motion; (4) uniform cir- 

 cular motion; (5) motion due to a constant gravi- 

 tational force. 



I would teach (1) very briefly and postpone 

 (2), (3) and (4) until after (5) had been 

 studied experimentally with Atwood's ma- 

 chine, and until after the problem of a heavy 

 boat in still water, pulled with a very small 

 force, say 1 lb. on a 1,000-lb. boat for 4 seconds 

 (frictional resistance neglected) had been 

 studied, deriving the general equation of con- 

 stant acceleration (2) from the experimental 

 data. 



Gravitational Units. — I would drop this term 

 and substitute two others, (1) English units: 

 pound, foot, second, (2) metric units, kilo- 

 gram (or gram) meter (or centimeter), second. 

 These units are absolute if W is defined as 

 quantity of matter obtained by weighing on 

 an even balance scale and g is 32.1740 ft. per 

 sec. =■ 980.665 cm. per sec. 



Absolute Units. — ^I would drop this term, 

 also the poundal, and substitute O.G.S. 

 (centimeter-gram-second) . 



Alexander McAdie, April 30 : 



Now what is the difficulty with the C.G.S. sys-. 

 tern? 



