98 



Trans. Acad. Sci. of St. Louis. 



by simplifying and putting tan <p = f. This formula gives 

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

 6 being 0^ 



1 — — -)/= h in the above. Integrating as indicated 

 — log e (sin d l —h cos X ) — h (-^- —OA 



1 +Jc 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 action 

 of each driving tooth be constant. 



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

 and (3) becomes 



Substituting the value of l' v simplifying and integrating from 



rrr 



- to d 2 we get 



4r 2 /l 1\ 



V (j — 2 ) —log. (sin 2 + A;' cos 6 2 ) 



X 



1 + k' 2 



(6). 



in which &' = (l+-^)/. 



This formula gives the energy lost during the recess. 



