702 



SCIENCE 



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



(mass) then its normal weight is one pound 

 (force) (galley 35). 



(A) The normal weight, W^, of a body is its 

 weight in vacuo, at sea level in latitude 45°. 



(i) A " set of standard weights " is a set of 

 metal pieces each of which is marked with its 

 normal weight. 



(/) The process of weighing a body on an 

 equal arm balance, against a set of standard 

 weights, gives the normal weight of the body. 



Qc) The process of weighing a body on a 

 spring halance, on the other hand, gives the 

 local weight of the body. 



(0 To graduate the scale of a spring bal- 

 ance find the local weight of a set of standard 

 weights as just explained (by computation 

 from the value of g at the locality in ques- 

 tion) and then suspend the pieces successively 

 on the spring, and mark on the scale the de- 

 flection caused by the local weight of each 

 piece (galley 34). 



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

 push or a pull. 



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

 mental equation. 



(o) If in the fundamental equation F/W = 

 A/g we substitute the equation for mass, 

 m^c{W/g), where c is the numerical factor 

 depending on the choice of units, we have 

 cF =^mA. Any system of units which makes 

 c = 1 in this equation is called an absolute 

 system of units. 



(p) The equation F = mA will give incor- 

 rect results if the forces and masses are given 

 in any but absolute units. In particular it 

 should never be used in the ordinary problems 

 of engineering. 



(q) On account of the special character of 

 this equation F^mA it is unfortunate that 

 it should be so often taken as the fundamental 

 equation of dynamics instead of the general 

 equation F/W=::A/g from which it is de- 

 rived (galley 41). 



Comments on the above Extracts 

 (a) For " length, time, angle and force," we 

 would better read " space, time, matter and 

 force." Mechanics is the science of the ac- 

 tion of force upon matter. Matter is that 



upon which force acts, and it is just as impor- 

 tant as force in most engineering problems. 

 Matter occupies space, therefore space is one 

 of the four elementary concepts of mechanics. 

 Length is merely the linear measurement of 

 space in one direction, and therefore it should 

 be placed in the list of derived quantities, 

 with area and volume. Angle should also be 

 placed in the list of derived quantities; it is 

 the difference in direction of two lines that 

 meet in a point, or the difference in position 

 of a line that is rotated a certain distance 

 about one of its ends. 



(h, c) If " the quantity called mass " is the 

 quantity of matter in a body, then this state- 

 ment is incorrect. The quantity of matter in 

 a body is of the utmost importance to the 

 engineer, independent of the force of gravity 

 acting upon it, if the body is to be moved hori- 

 zontally, or rotated, or accelerated, or if he or 

 his client has to pay for it. 



(d, e) Here are two definitions of " mass " 

 which are inconsistent. If mass is the quan- 

 tity of matter, why should it be " thought of, 

 roughly " ? Why is it not defined with pre- 

 cision as the quantity of matter as determined 

 accurately by weighing it on an even balance 

 scale and compared with the standard pound 

 (or kilogram) ? 



The second definition is the ratio W/g, or a 

 quantity proportional to this ratio. 



The fact is that the word "mass," as ap- 

 plied to matter, is used in three different 

 senses : 



1. As synonymous with "portion," "piece" 

 or " lump " of matter, as in the expression 

 "this mass weighs ten pounds," the words 

 " weighs ten pounds " referring to the quan- 

 tity of matter as determined by weighing. 



2. As synonymous with the word " weight " 

 (quantity of matter), as the word weight is 

 universally used in ordinary language, and 

 nine times out of ten by the engineer, who 

 rarely uses the word "mass" in this sense. 

 Example : " This lump has a mass of ten 

 pounds." 



3. As synonymous with the ratio W/g, 

 where either W is the weight (quantity of 

 matter) and g is 32.1Y4, the acceleration due 



