July 7, 1916] 



SCIENCE 



19 



At the last meeting of the corporation of 

 the Massachusetts Institute of Technology 

 promotions and appointments were made to the 

 instructing staff as follows : From assistant to 

 associate professor Daniel E. Comstock (theo- 

 retical physics), George L. Homer (topograph- 

 ical surveying), C. L. E. Moore (mathematics), 

 Ellwood B. Spear (inorganic chemistry), Wil- 

 liam E. Wickenden (electrical engineering). 

 Instructors were promoted to assistant profess- 

 orships as follows : James M. Barker (struc- 

 tural engineering), Ralph G. Hudson and 

 Waldo V. Lyon (electrical engineering), Earl 

 B. Millard (theoretical chemistry). Dr. Fred- 

 erick G. Keyes was appointed associate pro- 

 fessor of physico-chemical research. 



DISCUSSION AND CORRESPONDENCE 



SOME FUNDAMENTAL DIFFICULTIES OF 

 MECHANICS 



A long and interesting exchange of views 

 on the fundamental equation of mechanics, 

 which has taken place in the columns of Sci- 

 ence, has led me to review some old notes in 

 that connection. It has seemed to me that the 

 question may be viewed from two different 

 points, that of the systematizer and that of 

 the teacher. The former desires an equation, 

 fundamental in that from it he can develop 

 the science most easily. The latter must con- 

 sider as the fundamental principles those which 

 appeal most directly and forcibly to the stu- 

 dent, which enable the student to progress most 

 easily, with rapidity and security. By the 

 student I mean the average student, who has 

 much experience of a mechanical nature, but 

 is unaccustomed to logic and cares little about 

 unity. 



To the teacher of mechanics students in 

 masses, that is, to nearly every mechanics or 

 physics teacher, even in college and technical 

 school, the first-named viewpoint is unimpor- 

 tant as compared with the second. His busi- 

 ness is to diagnose the student's difficulties, 

 and then to obviate or remove them. Some of 

 these difficulties are inherent in the laws of 

 mind and matter. 



Any teacher will admit that to the average 

 student the descriptive, phenomenological, atti- 



tude toward mechanics is quite too rarefied, 

 too impersonal. Professor C. B. Mann has 

 well said: 



To a beginner pushes and pulls are the real 

 forces. 



The beginner can imagine himself pushing 

 or pulling, exerting an effort and taking an 

 interest. Descriptively, it has been questioned 

 whether the concept of force is of much value 

 in mechanics; but the sense and memory of 

 effort give the student his starting point, and 

 the teacher must begin kinetics with force as 

 well as with acceleration and mass. 



When we exert effort we observe we either 

 change the motion of bodies, or change the 

 relative positions of bodies or of their parts, 

 hence the forms of bodies. During such 

 changes of position or form, more or less tem- 

 porary changes of motion occur. 



Hence we all quite unnecessarily infer that 

 when the motions of bodies are changed, or 

 their relative positions, or their forms, there 

 must be something going on analogous to an 

 effort; this we call force, and we say that the 

 above effects of effort are the effects of force. 



Moreover, we observe that while the changes 

 of relative position or form of bodies due to 

 our effort may persist after we have ceased to 

 exert effort, on the contrary the motion which 

 has been produced by an effort does not con- 

 tinue, it always diminishes and finally ceases. 

 We note that the effort needed for the produc- 

 tion or increase of motion depends on the 

 contact of the body acted on with other things, 

 as soil, pavement, ice ; water, if floating ; oil, if 

 lubricated; air, if swinging suspended; and 

 also on the form of the body, flat or jagged or 

 round. In some cases the production of mo- 

 tion is harder, in others easier, the duration of 

 the motions is shorter or longer, but sooner or 

 later the motions end in rest. If we want a 

 thing to keep going we have to keep pushing or 

 pulling; and this without exception in all our 

 bodily experience. 



Hence we hastily but naturally conclude that 

 rest is the natural state of all bodies, and that 

 for the maintenance of even constant motion 

 continuous effort, or force, is necessary. 



It has been pointed out that the scholastic 



