December 24, 1915] 



SCIENCE 



901 



(6) that the distance or space traversed varies 

 as the force, as the square of the time, and 

 inversely as the quantity of matter. It equals 

 half the product of the velocity and the time. 

 Expressed in algebraic form: 

 Velocity, feet per second, 



V = 



Distance, feet, 



FTg 



w ■ 



(J 1 FPg 



S = 



VT 

 2 ■ 



(1) 



(2) 



(3) 



The value of g in these equations is always 

 32.1740 when W is the quantity of matter in 

 pounds, as determined by weighing it on an 

 even balance scale, F is in standard pounds of 

 force (1 pound of force being the force with 

 which a pound of matter is attracted to the 

 earth at the standard locality, a place where 

 the " acceleration due to gravity " is 32.1740 

 feet per second per second), and V is meas- 

 ured in feet per second. (In the metric sys- 

 tem, if F and W are in grammes and V in 

 centimeters per second, g = 980.665.) 

 Transposing (1), 



FT = 



WV 



or if 



K = 



W 



FT = MV. 



(4) 



From (3), 



Impulse = Momentum. 

 T = 2S/V; 



substituting this value of T in (4) 



2 FS/V = MV; 

 whence 



FS = i Mr'. (5) 



In (4) let 



Work done = Kinetic energy. 

 V/T = A, 

 acceleration, then 



A — M/F. 

 Whence 



F=zMA. 

 Force = M times acceleration. 



Falling Bodies. — At or near 45 deg. latitude 

 at the sea level F^W, then from (1) we have 



V = gT. If T = l second 7 = 32.1740 feet 

 per second. At other locations, F = W X 

 (9i/g), or Wg/32.1740, where g^ is the accelera- 

 tion due to gravity at the given location. In 

 equation (1) V = FTg/W, taking F=W, 

 substituting for T its value 2S/V, and for 8 

 the letter ff, for height of fall, we obtain 



r' = 2 gB; F= V2 gS. 



(7) 



The expression Wgjg may be called the 

 " local weight." It equals the gravitational 

 attraction, measured in standard pounds of 

 force, upon W pounds of matter. It is the 

 weight that is indicated on a spring balance 

 calibrated for the standard locality, so that it 

 will measure standard pounds of matter at 

 45° at the sea level and standard pounds of 

 force at any locality whatever. 



Professor Hoskins, April 23: 



. . . introduce at the outset the body-constant 

 which was called by Newton mass or quantity of 

 matter . . . the acceleration of a body depends 

 quantitatively upon both the applied force and 

 the mass of the body . . . and the still more con- 

 cise form A = F/m results if units are so chosen 

 that unit force acting upon unit mass causes unit 

 acceleration. 



There is no objection to these statements if 

 it is clearly understood what is meant by the 

 terms unit force and unit mass, but Professor 

 Hoskins might have gone further and shown 

 that this form of equation results if F is in 

 dynes and m in grams or if F is in poundals 

 and m in pounds, or if F is in pounds and m 

 in slugs, but that is not true if F and m are 

 both in pounds. It is true, however, if it is 

 understood that F is standard pounds of force 

 and that m is merely a symbol for the ratio W 

 pounds of matter divided by 32.1740. 



Standard weight defined as the force required to 

 give the body the acceleration 32.1740 ft. per sec. 

 It is important to make clear the fact that the 

 quantity called standard weight is in reality the 

 measure of a body constant and is quite inde- 

 pendent of gravity in spite of the fact that it is 

 given a name which is almost always associated 

 with gravity. 



Professor Hoskins and I are here in exact 

 agreement, but I am not sure that he is aware 



