15t; DR. T. R. MERTON AND PROF. J. W. NICHOLSON ON 



general survey of the question, to discuss only typical lines, in view of the previous 

 tables. For example, in the Diffuse series of Helium, we found that the ratios of 

 intensity of the three members visible, XX587G, 4472, 4026, remained effectively 

 constant over the whole range of the photographs, so that their maxima must occur 

 at the same place, and the examination of X5876 is sufficient. The photographs all 

 had the same duration of exposure, and being on the same plate, those numbered 

 I.-V. are strictly comparable even as regards the intensities shown by an individual 

 line, except in so far as variations already seen in another connection to be very 

 small may occur owing to the difficulty of maintaining uniform conditions of 

 excitation throughout the exposures of the various photographs. We have, moreover, 

 in the preceding sections found no reason to believe that the other plate, on which 

 Vr.-VIII. were taken, is in any important respect different from the first. We shall 

 therefore assume, as a basis, that the sequence of eight photographs can be compared 

 as regards the intensity of an individual line. 



The sequence of intensities of X587G, which we may take as the first example, is 

 from Table I. 



14'8, 42'8, 49'3, 441), 24'1, 1.V5, 977, 2'67, 



and it is at once evident that the seat of maximum emission is at about 2 mm. from 

 the cathode. 



Attempts to fit these numbers to an interpolation formula of the type 



I = a + 1r,r + ex 2 + ... 



where I is the intensity and :r the cathode distance, are not successful. It is in fact 

 evident from the later members of the sequence that the law is partly exponential. 

 The sequence of logarithms of intensity is found to be, to base 10, 



1M7, 1'63, 1-69, r4, T38, 1'19, 0'99, 0'43, 



and these also, especially when the dark space is included, do not fit well into an 

 interpolation formula of the above type. It is probable that any law, in order to be 

 valid over this wide region, must be somewhat cumbrous. The dark space must, in 

 fact, be left out of consideration in obtaining such a formula, and an example of a 

 three-constant one is 



log, I = a + l).r + ex 2 , a = 1 '452, b = 0'235, c = OD575. 



which gives the second, third, fourth, and sixth numbers accurately and T47 for the 

 fifth, whose actual value was found to be T38. The formula is not very good, but 

 sufficient for our purpose, and the calculated maximum is at the point 



x = b/2c = 2 '05 mm. 



