1880.] Strained Material, Ley den Jars, and Voltameters. 4,'2'd 



of the materials is indifferent, so that if there are several blocks of the 

 same substance, they may be subdivided, or united without altering the 

 phenomena. An investigation of the cases in which the materials are 

 arranged otherwise than in rectangular blocks of unit depth, would 

 lead to similar results, and if we may assume our hypothesis to be 

 true for other kinds of strain than shear, then the above equation may 

 be proved to be true for any strain of any heterogeneous body strained 

 in any way. 



The integration of the general differential equation (10), where v is 

 constant, is, putting ^ for u, 



w=A+Bt+ Ce-y* -f De-M + .... 

 where 7, B, &c, are roots of the equation 



C l C l °l 



and when v is maintained at zero during recovery after removal of 

 the load 



w=A 1 + C 1 e-^ + D 1 e- s '+ .... 



Of course if complete tables of the values of u and v, and their 

 differential coefficients, could be given, for all times during any experi- 

 ment, it would be best to use the general differential equation in de- 

 termining the constants. The method we have adopted is essentially 

 the same as that we have employed in the analogous cases for Leyden 

 jars, voltameters, &c. The wavy nature of some of the curves we have 

 experimentally obtained connecting strain and time in strained beams, 

 indicates that perhaps the equation given above may have imaginary 

 roots, and that possibly there may be terms in our solutions of the 

 shape 



C cos U 6- 0t . 



Much, however, of the waviness we have observed, we have traced to 

 variations of temperature, as it generally has a periodic time equal to 

 24 hours. 



Our theory for strained beams and twisted wires we have tested to 

 about the same extent as Professor Clerk Maxwell's theory for Leyden 



where v is the load on the beam or couple twisting the wire, and u is — if to is the 



dt 



deflection of the beam or twist of the wire. 

 If v is constant then the equation becomes 



(Pit) , dio n 

 dt 2 dt 



ffi and g 2 being certain functions of a, Jc, and r, and the solution of this is 



%o = A + 9 Jl t-Bt-^t. 



2 h 2 



