1893.J On the Failure of a Law in Photography. 143 



Cylindrical Elastic m Wave compared with corresponding Diffusive Wave 

 through the Operators. 



76. The formula? [e] and [E] are of a somewhat different kind, 

 since the operand is the reciprocal of the independent variable. 

 They are proved at once by carrying out the differentiations. Thus, 



for [E], 



2 2 ' 2 2 4" ' /lit 



by (178) 



So, by [C] and [B] we have 



'1 = 7^-^- (179) 



There is an interesting analogue to this transformation from K to 

 I occurring in the theory of pure diffusion. Change the meaning 

 of q from dfd(vt) to {d/d (*)}*> tliat is > to its S( P are root - Tnen we 

 shall have 



1 eT 2 /** 



?K o(r)2 = I ( 5 ,)^ = -^ r - (180) 



The quantity v is no longer a velocity, however. In the theory of 

 heat diffusion it is the ratio of the conductivity to the capacity. 

 This example belongs to cylindrical diffusion, and is only put here to 

 compare with the preceding example, which belongs to the corre- 

 sponding problem with elastic waves without local dissipation. 



IX. " On a Failure of the Law in Photography that when the 

 Products of the Intensity of the Light acting and of the 

 Time of Exposure are Equal, Equal Amounts of Chemical 

 Action will be produced." By Captain W. DE W. ABNEY, 

 C.B., F.R.S. Received June 13, 1893. 



It has been generally assumed that when the products of the intensity 

 of light acting on a sensitive surface and the time of exposure are 

 equal similar amounts of chemical action are produced, and with the 

 ordinary exposures and intensities of light employed such, no doubt, 

 is practically the case, and any methods of measurement hitherto 

 practicable have been insufficiently delicate to discover any departure 

 from this law, if such departure existed. In some recent experiments 



