Measurement of the Internal Resistance of Cells. 173 



Again, multiply (115) by x, (116) by y, (117) by z, and 

 add. Then integrating throughout the entire volume, we find 



— S$(*w +yy +S) dx d v dz + ^JXfaO* 8 +y*)dx fy = °> 



the surface-integrals vanishing as before. 

 But by the ordinary stress-strain relations, 



xx + yy + zz = 3k A, 

 where h is the bulk modulus, and thus we get 

 Sv = jjjAAa dy dz = g> 2 I/3&, 



where I has the same meaning as in (114). 

 Since 



v = 2Al, 

 we have 



8A/A==8t>/t>-B/Z, 



= (1~77>V7 E - 



Thus (111) and (114) are also proved to be absolutely true 

 in all right cylinders rotating about their axis of figure. 



The preceding formulae by which the solution has been 

 tested are particular cases of certain much more general 

 results*, to whose discovery the author was led by the 

 recognition of the coincidences pointed out in § 49. 



XVI II. Note on the Measurement of the Internal Resistance of 

 Cells. By E. Wythe Smith f. 



IN order to determine the actions which take place in an 

 accumulator during charge and discharge, it is necessary 

 to know the working electromotive force at the different 

 stages. This might be observed by breaking the circuit ; 

 but immediately on doing this the electromotive force varies 

 at a very rapid rate, so that if only four or five seconds be 

 occupied in taking the measurement an error of 25 per cent, 

 may be made in the difference between the electromotive 

 force and the terminal potential difference. If time-readings 

 be taken after breaking the circuit and a curve drawn con- 

 necting E.M.F. and time, this curve may be produced back 

 in the way described by Prof. Ayrton and others in a paper 



* Cambridge Philosophical Society's Transactions, vol. xv. part iii. 

 t Communicated by the Physical Society : read June 24th, 1892. 



