10 C. Barns — Change of Heat Conductivity on 



the upper plate (and it is here that the thermo-electric measure- 

 ment is made) is after a short time (60 s ), 



u = Z7sin qAe~ liTt/p \ .... (6) 



"where q is the smallest root of the transcendental referred to. 



10. Continuation. — Now the change to be made in these 

 deductions in my own case, where the environment may have 

 any temperature excess r, given by replacing the condition (3) 

 by the equation — 



- FJ >^)r hF ^)* +KF ' ( ">- T) ■ ■ ■ ■ {z ' ] 



where /?, and p are respectively the densities of the copperplate 

 and the charge. Imposing this condition on (6) I obtain 



A x p Y c~- sin qA = kq cos qA + h--^ sin qA—h^ = e 



or after further reduction 



Ape 1 



qA tan qA = 



A x p x c x k F Aq- \ u} ' ' ' K } 



Hence the value of q in (6) is to be the smallest root of (7). 



If therefore consecutive temperatures, u, u', .... are 

 measured at consecutive times t, t\ . . . . equation (6) may be 

 solved with reference to k as follows : 



7 pc 1 u' pc tflogw . . 



k= — ■. In — = H- 2-303 == — .... (8) 



q* t—t u q> St v ' 



Equations (T) and (8) show that the arithmetical results can 

 only be obtained by successive approximation. Disregarding 

 the corrective factor in (7) approximate values of k and q are 

 first found. These are then put in (7) and (8) and closer values 

 of k and q computed. I often repeated this operation again, 

 taking full cognizance of the change of q with the mean tem- 

 perature of the charge. 



11. Special cases. — (1) If in (7) the temperature excess of 

 the environment, r = 0, the conditions revert to those of Weber. 



(2). If as in my case, the initial temperature be the same for 

 the plates and the environment, or if initially r = u, the correc- 

 tion vanishes at the beginning of the work but increases in the 

 lapse of time. 



If u = r, throughout, the radiation correction would alwaj'S 

 vanish. Now it struck me that it might be very well worth 



