G96 PROCEEDINGS OF THE AMEllICAN ACADEMY. 



intensity. But to draw conclusions as to the constancy of any or all of 

 the separate coefficients from the constancy of the ratio of transmission 

 is not in strictness possible. It might be that two or more of the coeffi- 

 cients changed together in such a way as to keep the ratio of transmission 

 constant. But the repetition of this coincidence in experiments with 

 different metals and with rays from tubes in very different conditions 

 is exceedingly unlikely, and the constancy of the ratio of transmission 

 with varying intensity is at least very good presumptive evidence 

 that the coefficients characteristic of the absorption of Ilontgen rays 

 in metallic sheets are all constant with varying intensity of the 

 rays. It may be of interest to examine the consequences of sup- 

 posing that the constancy of the ratio of transmission is not a result 

 of the constancy of each of the coefficients. To simplify the argument, 

 let us suppose that the metallic screen is very near the instrument. 

 Let .^1 and s^ represent respectively the fraction of a certain sort of 

 ray which the metallic screen transmits at the large intensity and 

 at the small intensity. Let jj be the fraction of the same sort of ray 

 which the platinum of the instrument transmits at all intensities. Let 

 /j and /o represent the two intensities of this sort of ray at the instru- 

 ment. Then the ratio of transmission for this ray alone at the large 

 intensity would be 



7i si (1 —p) 



or Si; and at the small intensity, 



I^s^ jl-p) 



or ^2. If the ratios of transmission for the whole beam are found to 

 be the same at the two intensities, the explanation must be either 

 that each .sj is e(iual to its corresponding ,%, or that some of the si's 

 are larger than their corresponding s^s while others are smaller. The 

 latter explanation is equivalent to saying that the absorption coefficients 

 for some sorts of rays are increasing functions of the intensity, while 

 others are decreasing functions ; and this seems highly improbable. 



The argument of this section may be summarized in another form, 

 as follows : 



The possible effects of transmission through a metallic screen upon 

 a beam of Rihitgen rays are three : 



(1) An eifect produced upon the beam by transmission across the 

 surfaces of the screen. 



(2) An effect of trdnsformatlon suffered by the several components 

 of the beam in passing through the substance of the screen. 



