706 



SCIENCE 



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



gineering." Using the formula F/W =■ A/g 

 we have F = A W/g. Since g is to be taken 

 for latitude 30° its value is 32.131. We then 

 have F = 1/1 X 100,000 X 32.131/32.174 X 

 1/32.131 = 3,108.1 pounds. 



K the engineer had used the more precise 

 value of g at latitude 45° he would have ob- 

 tained the same result as the mathematician. 

 He would not consider that the value of g at 

 latitude 30° entered into the problem at all. 

 In the mathematician's solution it enters 

 twice, in numerator and denominator, and 

 therefore cancels out. 



The only cases in which the engineer ever 

 needs to consider the value of g at latitudes 

 other than 45° are those of precise calcula- 

 tions in which the force of gravity at a par- 

 ticular place enters into the problem, as in the 

 case of the velocity of falling bodies, the power 

 of falling water, the value of the mechanical 

 equivalent of heat, etc. Thus the mechanical 

 equivalent of heat is 777.52 foot pounds, or 

 the work of lifting 1 pound 777.52 feet high, 

 at latitude 45°. The figure obtained by ex- 

 periments made in raising weights at a lower 

 latitude would be greater in the proportion 

 that the attraction of gravity is less. Steam 

 at a temperature of 327.8° F. has a pressure 

 of 100 pounds per square inch above vacuum 

 if the pressure is measured by its lifting a 

 weight (piece of metal) at latitude 45°. It 

 would raise a heavier weight, in the ratio 

 32.174/32.131, at latitude 30°, and a lever 

 safety valve would have to be loaded with a 

 larger weight at latitude 30° than at latitude 

 45° to resist the pressure. A bar of metal 

 tested on a lever testing machine at latitude 

 45° and showing an ultimate resistance of 

 32,131 pounds would show 32,174 pounds if 

 tested at latitude 30°, since at latitude 30° 

 the poise on the lever would be attracted less^- 

 by gravity than at latitude 45°, and it wohIS 

 have to be moved farther out on the scale 

 beam to balance the ultimate load applied to 

 the test piece. 

 Note on "The Concept of Mass" (Galley 35). 



It is not clear just what the report means 

 by the word " mass." It is defined in one 

 paragraph as " the ratio W/g, or a quantity 



proportional to this ratio, m^ciW/g), W 

 here being a force and not a quantity of mat- 

 ter," but a little later appears the expression 

 " the mass of the body measured in units of 

 mass," indicating that by mass is meant quan- 

 tity of matter. 



A great deal of mental energy has been 

 wasted by teachers and text-book writers in 

 trying to give high school and college students 

 a " concept of mass," and more trouble is yet 

 in store for teachers and students if future 

 text-books adopt the language of this report 

 concerning the " concept." 



A boy before he goes to the high school has 

 a perfectly clear idea of matter and of weight. 

 He knows that matter is weighed by the grocer 

 on even-arm balances and platform scales, and 

 he has seen meat weighed on spring balances. 

 He knows that in order to answer the question 

 " How much sugar is in that package ? " the 

 weight of the package is obtained by weighing 

 it with a balance, using pieces of metal called 

 weights, or by putting it on a spring balance 

 and noting the indication. He knows that 

 the weight of a pound of lead is 1 pound, 

 whether it is weighed in London or in Pan- 

 ama, and that it is bought and sold as a 

 pound everywhere that English weights are 

 used. He has never heard the word " mass " 

 except in its common meaning, of something 

 like " bulk," or as a general term of indefinite 

 quantity, as in the expression in the preface 

 of the report, " lost sight of in a mass of 

 details." When he begins to study physics, 

 however, he has to learn that what he thinks 

 he knows about weight is all wrong, that the 

 weight of a thing is not constant, but variable, 

 varying with the latitude and elevation above 

 sea level; that it is not the measure of quan- 

 tity of matter, but only of the force with 

 which the earth's gravity attracts matter ; that 

 the word " mass " should be used where he 

 formerly used " weight " ; and that he must 

 get a " concept " of mass diilerent from the 

 concept of weight. Later he learns that mass 

 is also c{W/g), the ratio of the force with 

 which gravity attracts matter at a given place 

 to the acceleration due to gravity at that 

 place, multiplied by a coefficient, c, which has 



