98 



Trans. Acad. Sci. of St. Louis. 



by simplifying and putting tan^=/. This formula gives 

 the energy lost during the "approach," the initial value of 



being 0^ 



= k in the above. Integrating as indicated 



Let (l — ^\f=k'm 

 r 2 / 1 1 \ 



— log e (sin L — h cos 6 X ) — k (~ — 0,\ 



X 



1 +ft 2 



(5). 



4. The above assumes that but a single pair of teeth are in 

 action. It does not appear that the introduction of more 

 pairs would affect the ratio I am aiming to get provided the 

 pairs are in all respects alike, and the moment of the actiou 

 of each driving tooth be constant. 



5. During the " recess " dq is positive and we have 

 and (3) becomes 



«,,-*,« f (l + i)(_-^) 



Substituting the value ot l' v simplifying and integrating from 

 | to 2 we get 



4?- 2 /I 1 \ 



* = -*-{;+})»/ 



k' (j — a ) -log e (sin 0, + # cos 2 ) 



X 



1 + k' 2 



(6). 



in which &' = (l +^)/« 



This formula gives the energy lost during the recess. 



