Mat 5, 1911] 



SCIENCE 



ro3 



to gravity at the sea level at latitude 45°, or 

 W is the force with which gravity attracts the 

 body at any given place and g is the accelera- 

 tion due to gravity at that place. The quan- 

 tity or ratio W/g is constant in either case. 

 In this the mass of the ten-pound lump is 

 10/32.174, and since it is a ratio it has no 

 unit. The statement that " the engineers' 

 unit of mass is 32.2 pounds," found in some 

 books on physics, is incorrect. The engineer 

 has no such unit. 



Giving the name " mass " to the ratio W/g 

 was perhaps unfortunate, but it can not now 

 be helped, since it is universally used in this 

 sense in the engineering text-books of the past 

 sixty years or more. It is a handy term, and 

 the use of the single letter M instead of the 

 fraction W/g often simplifies calculations. It 

 is hard enough to get rid of a bad term, for 

 example, "poundal," which has been in the 

 high-school books on physics for the past 

 thirty years in spite of the numerous attacks 

 upon it. It is not likely that we can get rid 

 of the term mass, M, in the sense of W/g 

 unless some one invents another and a better 

 name for it. 



Of course confusion results from the three 

 different meanings given to the same word 

 " mass," but the confusion arises chiefly from 

 its use in the second sense given above, as 

 synonymous with weight (quantity of mat- 

 ter). It is so used in all the books on physics, 

 but as already stated, is rarely so used by 

 engineers. It would tend to diminish the 

 confusion if the books on physics mentioned 

 that in engineering " mass " means the ratio 

 W/g, and not the quantity of matter in 

 pounds, thus preparing students for what they 

 will afterwards learn in their engineering 

 studies. 



(/) " The weight, W, of a body, at a given 

 place, is the force that causes it to fall if un- 

 supported." 



The word " weight " is used in two senses : 

 (1) in the sense given in the above definition, 

 which is that of the text-books on physics, 

 and (2) in the sense of quantity of matter as 

 determined by the common method of weigh- 

 ing it. In this sense it is used universally in 



ordinary literature and in commercial trans- 

 actions, and nine times out of ten by engi- 

 neers, in all calculations in which quantity of 

 matter is involved. 



In this sense W is a constant quantity; in 

 the first sense it is inconstant, varying with 

 the latitude and with the elevation above the 

 sea level. 



In the second sense, quantity of matter, the 

 word weight was used long before Newton's 

 time. It is thus used in the clause of the 

 constitution of the United States that author- 

 izes congress to fix the standard of weights 

 and measures, in acts of congress establishing 

 the Bureau of Weights and Measures, and in 

 acts of the British parliament. It is thus 

 used in the King James version of the English 

 Bible : " And they shall eat bread by weight " 

 (Ezek. 4: 16). It is not conceivable that this 

 meaning of the word " weight " can ever go 

 out of use. It is in the language of the people 

 and it is there to stay. 



The beginning of confusion in the minds of 

 students as to the meaning of the words 

 " weight " and " mass " results from the fact 

 that the high-school text-books use the word 

 mass for what is commonly called weight, and 

 attempt to restrict the word weight to mean 

 only the force with which a body is attracted 

 by gravity at a given place. 



(g, h) " If the mass of a body is one pound 

 (mass) then its normal weight is one pound 

 (force)." 



By mass we here understand quantity of 

 matter, and not the ratio W/g given in defini- 

 tion (e). 



The " normal weight " (this appears to be a 

 new and useless term, and therefore unde- 

 sirable) is the force with which a body is at- 

 tracted to the earth by gravity at latitude 45°. 



If the sentence (g) were made to read: " If 

 the weight of a body is one pound, then the 

 force with which gravity attracts it at the sea 

 level in latitude 45° is one pound," it would 

 be strictly accurate, in harmony with the 

 every-day use of the language, and would 

 avoid the confusion arising from the use of 

 the word " mass." The meaning of the word 

 "weight" in this sentence is not ambiguous 



