41 o A. A. MICHELSON 



in which K< i. This would give P n instead of P, or, in better 

 agreement with experiment, 



F' = CPe hP . 



The elastico-viscous term is readily obtained by making the vis- 

 cosity coefficient a function of the time. 



Thus, if the restoring force be represented by aS, and the vis- 

 cous resistance by et m S* the integration gives 



c c / -~ V 

 o 2 = o l i — e r 



where a = ^ and r— — m+i. t 



To determine the effect of temperature, the behavior of zinc, 

 glass, ebonite, pitch, and wax was studied. The results, together 

 with the preceding, may be summarized in the following formulae: 



* The assumptions in both viscous and elastico-viscous hypotheses make the 



viscosity coefficient (that is, the coefficient of S) zero at the beginning of the motion 



and infinite at t = a, which is, of course, inadmissible. Instead of S n and t m we might 



B~\-S n r-\-t m B r 



substitute , , „ and — — , in which — and - are very small: but the resulting equa- 

 o+o" c+t m o c 



tions are far less simple and are not appreciably more accurate in expressing the results 



of experiment than those here given. 



f The usual assumption, m = o, gives r = i. 



{Instead of this series coupling, the following may be substituted: The unit 

 consists of four elements: (i), (2), and (3) are in viscous contact with (4); (1) and (2) 

 are in elastic coupling; and, finally, (3) of this unit is connected with (1) of the next 

 following unit by an elastic coupling. The resulting formulae, however, are not 

 essentially different from those here given. 



