DR. T. R. MERTDN AND PP.OF. J. W. NICHOLSON ON 
1 5() 
o-eiieral survey of the questiou, to discuss only typical lines, in view of the previous 
tables. For example, in the Diffuse series of tielium, we found that the ratios of 
intensity of the three members visible, AA587(), 4472, 4026, remained effectively 
constant over the wliole range of the photographs, so tliat their maxima must occur 
at the same place, and the examination of A5876 is sufficient. The photographs all 
had the same duration of exposure, and being on the same plate, those numbered 
I.-Y. are strictly comparable even as regards the intensities shown l)y 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 
Vf.-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 A587G, which we may take as the first example, is 
from Table I. 
14-8, 42-8, 49-3, 44-0, 24T, ’IS'S, 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 = ffl + hx -I- cx^ + ... 
where I is the intensity and x 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, 
ri7, 1-63, 1-69, 1-64, r38, 1T9, 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 cund^rous. 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 + h.r -\- rx^, a = 1‘4.52, h — 0'235, c — 0'0575. 
which gives the second, third, fourth, and sixth numbers accurately and 1'47 for the 
fifth, whose actual value was found to be 1‘38. The formula is not very good, but 
sufficient for our purpose, and the calculated maximum is at the point 
X — hl'2c = 2"05 mm. 
