704 



SCIENCE 



[N. S. Vol. XXXIII. No. 853 



or doubtful. It means both tliat the quantity 

 of matter will balance the standard pound on 

 an equal arm balance, and that the force 

 which gravity exerts on it at latitude 45° is 

 one pound, as indicated by a properly gradu- 

 ated spring balance. 



{i, j) If for the words " normal weight " in 

 these two sentences we use simply the word 

 weight, it will express the idea accurately, 

 whether the word means quantity of matter or 

 the force with which gravity would act on the 

 body at latitude 45°. The two meanings are 

 synonymous and the two quantities identical. 

 The measure of the quantity of matter in a 

 body is the measure of the force with which 

 gravity attracts it at latitude 45°. 



(fc) The process of weighing a body on a 

 spring balance, on the other hand, gives the 

 " local weight " of a body. The term " local 

 weight " also appears to be new, but as it 

 strictly expresses the idea of the attraction of 

 gravitation on a body at a given locality, and 

 there is no other short term that so clearly 

 expresses it, it may be considered unobjection- 

 able. The words " gravity of a body " might 

 properly be used to express the idea, if text- 

 book writers would agree to it, for its value 

 would vary in the same proportion as the 

 earth's gravitational force varies, with the 

 locality. 



The sentence (Ic), however, is true only if 

 the spring balance has been graduated with 

 standard weights at latitude 45°. If gradu- 

 ated with standard weights at the locality 

 (other than lat. 45°) where the weighing is 

 done, it will give the " normal weight," or 

 quantity of matter, just as an even balance 

 would do. 



(0 This sentence is not clear. A spring 

 balance graduated, say, at latitude 30°, by 

 hanging on it successively the standard 

 weights, 1, 2, 3, 4, etc., pounds, and marking 

 the deflection shown by each, will show at 

 latitude 30° the weight (quantity of matter) 

 of bodies weighed on it, but if it is desired 

 that the balance should indicate " local 

 weight," then the standard weights hung on 

 it should be increased in the proportion that 

 the attraction of gravitation is less at latitude 



30° than at latitude 45°, or in the ratio 

 32.174-^32.131, or 1/1.0013. If 1.0013 

 pounds is hung on the scale it will indicate 

 1 pound, and 1 pound hung on it will indicate 

 0.9987 pound, the " local weight " of 1 pound 

 of matter at latitude 30°. Spring balances, 

 however, are never used for weighing as accu- 

 rately as 1.3 parts in 1,000, since for such 

 weighing a microscope would be needed to 

 read the deflections. " Local weight " is 

 rarely needed in engineering problems, and if 

 it should be needed it is determined not by 

 weighing on a spring balance hut by multi- 

 plying the weight (quantity of matter) by the 

 ratio of the value of g at the location to 

 32.174. 



(m) " Force may be thought of, roughly, as 

 anything of the nature of a push or a pull." 

 Why " roughly " ? The definition of force as 

 a push or a pull is as precise as language can 

 make it. 



(n) " F/W == A/g is taken as the funda- 

 mental equation." This is only one form of 

 the fundamental equation. The fundamental 

 fact in dynamics is that if a force F is ex- 

 erted constantly for a time T upon a body free 

 to move, whose weight is W, giving it a 

 velocity V (starting from rest when F^O) 

 at the end of the time T, then the following 

 equation is true (in the foot-pound-second 

 system of units) : 



FT={W/g)Y, 



or, li A = V/T then Fg == WA, from which 

 the equation F/W = A/g is derived; also if 

 M=W/g, then FT = MV and F = MA. 



(o) "If in the fundamental equation 

 F/Yf =. A/g we substitute the expression for 

 mass, m^ciW/g), where c is the numerical 

 factor depending on the choice of units, we 

 have cF = mA. Any system of units which 

 make c ^ 1 in this equation is called an abso- 

 lute system of units." 



The value of c in the foot-pound-second 

 system is given as 32.174, and in the dyne- 

 gramme-second system as 1. In the foot- 

 pound system m = 32.174:W/g. 



This is out of harmony with the engineer- 

 ing text-books and with engineering literature 



