926 



SCIENCE 



[N. S. Vol. XLIII. No. 1122 



undoubtedly solve actual problems with ac- 

 cordant results. If this is true it is evident 

 that the disagreement is largely a matter of 

 words rather than of principles, and that if 

 all understood one another a large part of the 

 apparent disagreement would vanish. Most of 

 us find it diificult to give the same careful con- 

 sideration to propositions advanced by others 

 that we expect them to give to our own. The 

 habitual use of a certain routine tends to give 

 the mind a " permanent set " which makes it 

 difficult to appreciate the fact that equal famil- 

 iarity might prove another routine to be 

 equally effective. One who is strenuously op- 

 posed to a particular method will find it a 

 useful exercise to adopt that method tempo- 

 rarily and apply it to actual problems in suffi- 

 cient number and variety to make him thor- 

 oughly familiar with it. 



1 have not the slightest doubt that the rou- 

 tine favored by Mr. Kenf^ can be used effec- 

 tively in teaching students to state correctly 

 the solutions of problems in uniformly accel- 

 erated motion. Neither have I any doubt that 

 the method outlined by me^ can be used with 

 equal effect. In the explanation of the funda- 

 mental equation the two methods are in fact 

 identical, except as regards the matter of the 

 choice of units. Mr. Kent apparently believes 

 that the adoption of a particular set of units^ 

 is essential to the success of his method, while 

 I believe it to be important to emphasize the 



1. Science, December 24, 1915. 



2 Science, April 23, 1915, p. 609. 



'Mr. Kent refers to the "good old principle, 

 Unit force (pound) acting on unit mass (1 pound) 

 gives it an acceleration of 32.1740 feet per sec- 

 ond. " As a matter of fact the antiquity of this 

 "principle" is considerably less than that of the 

 poundal (it was only in 1901 that the value 

 32.1740 feet per second per second was adopted 

 by the International Conference of Weights and 

 Measures as the most probable value of g at sea- 

 level in latitude 45°) ; moreover it may be doubted 

 whether this unit force has ever been employed 

 practically. The really "good old" unit force is 

 the weight of a pound mass (or kilogram mass) 

 wherever the observer happens to be; this is still, 

 and doubtless will continue to be, the unit em- 

 ployed in most practical applications. 



fact that the choice of units is arbitrary and 

 that Mr. Kent's units are no more easily under- 

 stood than other systems which are in common 

 use. To define units so that unit force would 

 give unit quantity of matter an acceleration of 

 1 foot per second per second seems to me to be 

 as simple and as easily understood as the defi- 

 nition unit force is the force which would give 

 unit quantity of matter an acceleration of 

 S2.nif0 feet per second per second. The two 

 definitions are based upon the same funda- 

 mental principle, and it would seem that a very 

 effective method of helping the student to 

 grasp the real significance of this principle is 

 to give him plenty of practise in applying both 

 definitions and in reducing forces and quan- 

 tities of matter from one unit to another. 



The chief remaining difference between Mr. 

 Kent and myself is a verbal one: It seems to 

 me undesirable (because obstructive of clear 

 tliinking) to designate two distinct physical 

 quantities such as " quantity of matter " and 

 '' earth-pull " by the same name when there 

 is an easy way to avoid it; but I have no ex- 

 pectation of converting Mr. Kent to my opin- 

 ion on this point. 



The method advocated by Professor Hun- 

 tington can also without doubt be made effec- 

 tive if used with due persistence by an enthu- 

 siastic teacher like himself. The peculiar fea- 

 ture of this method is that it purports to be 

 independent of mass. The eleven propositions 

 which embody the latest presentation of the 

 method* are in fact free from any adequate 

 explanation of mass; but until the omission is 

 supplied the sufficiency of these propositions 

 can not be granted. The question of their 

 sufficiency may be put to a simple test: Do 

 they suffice for the solution of problems like 

 the following: 



A certain body has an acceleration of 10 ft./ 

 sec' when acted upon by a force F, and a second 

 body has an acceleration of 15 ft./sec' when acted 

 upon by an equal force F; if the two are combined 

 into a single body, what acceleration will this body 

 have if acted upon by a force F^ ^ 



« Science, March 3, 1916. 



'The problem might be generalized as follows: 

 A certain body has the acceleration a' when acted 



