May 5, 1911] 



SCIENCE 



107 



different values according to which system of 

 units is used, there being six systems, kilo- 

 gram-centiirieter, pound-foot, dyne-centimeter, 

 poundal-foot, G„-kilogram-centimeter and g„- 

 pound-foot, that in the first system the value 

 of c is 980.665; in the second, 32.174; and in 

 the other four systems 1, but that the last 

 three are only in the text-books (and students 

 must study them and pass examinations on 

 them) and are never used in practise. He is 

 also told that the engineer has a different unit 

 of mass from the physicist, 32.2 pounds, which 

 is not true. 



When the student gets into practical engi- 

 neering studies he is told to forget all he 

 learned about the " concept of mass " and that 

 he need think of the word " mass " only as a 

 short term to use instead of the ratio W/g, 

 =,M, without any coefScient, c, that weight, 

 W, has the same meaning that it has in com- 

 merce, quantity of matter, and that g in that 

 ratio is always the constant, 32.2, or, to be 

 more precise, 32.174. What then is the use of 

 confusing the young student with so many 

 notions of the " concept of mass " when he 

 has to unlearn them later? 



The Definitions that should he in the Text- 

 books 



Criticisms of the definitions of mechanical 

 units given in the report of the committee 

 will fail of their proper effect unless other defi- 

 nitions are offered which the committee may 

 possibly consider when the report is revised 

 for final publication. The following defini- 

 tions are offered for such consideration as 

 they may deserve. 



Weight, W. (1) Quantity of matter in a 

 body, as weighed anywhere on an even balance 

 scale with standard weights. (2) The force 

 with which the earth's gravitation attracts a 

 body at the sea level in latitude 45° (or at any 

 place where the acceleration due to gravity is 

 32.174 feet per second per second). 



Unit of Weight. The pound, the quantity 

 of matter in the standard piece of metal pre- 

 served in the bureau of standards in London. 



Force. That which causes or tends to cause 

 or to change motion. A push or a pull. 



The Unit of Force. The pound ; the attrac- 

 tion of the earth's gravitation on a pound of 

 matter at the sea level at latitude 45°. 



The weight of a body, W, is both the num- 

 ber of pounds of matter it contains and the 

 number of pounds of force with which it is 

 attracted to the earth at latitude 45°. The 

 two numbers are exactly the same and there- 

 fore it is unimportant which definition is 

 used in connection with the solving of prob- 

 lems. 



Local weight, W^, the force with which the 

 earth's gravity attracts a body at any given 

 place, measured in units of force. It may be 

 determined by weighing it accurately on a 

 spring balance which has been graduated at 

 latitude 45°, with standard weights, or, more 

 easily, by computation, multiplying the 

 weight, W, by the ratio of the value of g at the 

 given locality to 32.174. W^ varies with the 

 location of a body. The difference between 

 the weight of a body and the " local weight " 

 at latitude 30° is (32.174/32.131) — 1, or 

 0.0013 of a pound, for each pound. The dif- 

 ference, 13 pounds in 10,000, is so small that 

 it need not be taken into account in any ordi- 

 nary engineering calculation; in fact, the 

 " local weight " is practically never used in 

 engineering problems. When it is needed it 

 is found by computation from the value of g 

 at the given locality. 



Mass, M. (1) W/g, the ratio of the quantity 

 of matter in a body (or of the attraction of 

 the earth's gravity upon it at latitude 45°) 

 to the acceleration due to gravity at latitude 

 45° (32.174 feet per second per second). This 

 is the meaning of the word " mass " when it is 

 used in engineering problems. (2) The quan- 

 tity of matter in a body, identical with W (1) 

 above, what is called weight ordinarily in 

 commerce and in literature. This is the defi- 

 nition used in many text-books on physics, in 

 which " weight " is restricted to mean what is 

 defined as " local weight " above. 



In answer to an objection that may be 

 raised to the double definition of W, (1) and 

 (2), that the same word, in science, ought not 

 to be used to express two ideas that are so dif- 



