July 29, 1910] 



SCIENCE 



145. 



uralness, common usefulness, of the gravi- 

 tation units, the pound-force, as a unit, 

 being thoroughly familiar to us from 

 childhood, because of our acquaintance 

 with spring balances graduated in this 

 unit. 



-But can we get rid of all our verbal diffi- 

 culties by keeping to the gravitation units ? 

 What shape does our acceleration equa- 

 tion, which I have written / = m X «, take 

 in this ease? I ask this question, even on 

 paper, with a feeling of trepidation, an 

 uncomfortable sense that some engineer is 

 reaching out for his club while I write the 

 words. Let me hasten to put W for the 

 number of pounds of matter in the body 

 dealt with, F for the number of pounds of 

 accelerating force applied to it, g for the 

 gravity constant 32.2, A for the accelera- 

 tion in feet per second per second. I thus 

 get F = W/gXA. 



But we like to give names to things 

 which we use often, and the quotient W/g 

 is such a thing. What shall we call it? 

 I will here take as my guide for the mo- 

 ment Professor William Kent and will 

 quote from an article by him which ap- 

 peared in Science December 24, 1909, 

 under the title, ' ' The Teaching of Elemen- 

 tary Dynamics in the High School." 



"Mass. — It is convenient to call the 

 quantity M =^ W/g by a name, and the 

 name 'mass' has been given to it, although 

 this name is perhaps unfortunate, since the 

 word mass is also used in other senses. 

 Thus it is commonly used to mean an in- 

 definite quantity of matter, as a lump or 

 portion. It is also used by many text- 

 book writers in the sense in which we have 

 used the word weight, for a definite quan- 

 tity of matter stated in pounds, and these 

 writers try to restrict the word weight to 

 mean only the force with which the earth 

 attracts matter. (Do not tell the student 

 that, 'the engineer's unit of mass is 32.2 



pounds.' The engineer has no such unit.. 

 When he weighs a quantity of matter he 

 records the result as a weight, and his unit 

 is a pound. ) ' ' 



I think I see the point which Professor 

 Kent wishes to make in the warning con- 

 tained in his parenthesis. To be accurate 

 we must say, The unit of mass, according 

 to the engineer, is the mass of 32.2 pounds- 

 of matter. But even this morsel is a bit 

 difficult of assimilation. 



I do not propose to criticize Professor 

 Kent's syllabus — as intended for the use of' 

 engineering students. His ideas are of 

 course perfectly clear and consistent, his. 

 words also. His general method of pre- 

 senting the subject of elementary dynamics- 

 I find rather wearisome to read, not be- 

 cause it is so "heretical" from my point of' 

 view, but because it is so much like my- 

 own. 



I like to teach, so far as I can succeed in 

 teaching, these simple elements of dynam- 

 ics ; but when I think of the capacities and 

 needs of the high-school pupil and remem- 

 ber that he will very likely not be an engi- 

 neer, I can not feel that Professor Kent's, 

 syllabus would make the subject anything 

 less than formidable to him. If we enter- 

 upon the definite quantitative treatment 

 of Newton's second law, of the formula 

 / = mXa, we must use the unfamiliar- 

 and academic, though logically simple, 

 poundal or dyne, or we must, turning to 

 gravitation units, meet the difficulty which 

 Professor Kent recognizes in the passage 

 on mass which I have quoted. In fact, the 

 school teacher, not knowing what partic- 

 ular system of units the unknown future 

 examiner of his pupils will prefer, must,, 

 in order to be sure, train them in both 

 systems, or, .rather, in four systems, the 

 absolute and also the gravitation metric; 

 units, the absolute and also the gravitation 

 English units. 



