272 
DR. T. R. MERTON AND .PROF. J. W. NICHOLSON ON 
contours intersect in a definite kink on one side of the main contour, and sufficiently 
above this kink the contour entirely represents the stronger component only and its 
exact form can be found. There is no evidence of any third component. Measure¬ 
ments have shown that the parabolic form is very exact for this stronger component, 
and as an illustration of the degree of exactness obtained, we append one calculation 
made from a single plate—which was somewhat smaller than the majority. The 
contour could be measured with some certainty to W of a millimetre, by placing a 
scale along any required distance and observing through a magnifying lens. The 
true, or “normal ” breadth is, by the preceding section, the apparent breadth on the 
distorted curve, and is denoted by 2x. The height above a fixed base line is y. The 
following were the values of x and y for arbitrarily selected points :— 
mm. 
2.x = 0 ‘ 0 , y = 
2x = 2'8, y = 
2x = 3*4, y = 
mm. 
13-2, 
2x = 
U'8, 
2x - 
iro, 
2x = 
mm. 
mm. 
4b, 
y = 
10 - 0 , 
4-4, 
y = 
9-4, 
47, 
y = 
8 ’ 6 . 
The total change of height between two orders distant 88 '5 mm. was II'4 mm., 
giving a rate ll'4/88'5 per mm. The contour should, therefore, possess the equation, 
79 7 11 4x 
— K'X“ — 1] — h -? 
J 88*5 
and calculating from the second and fifth values of corresponding co-ordinates in the 
above list, we find, 
Jc = 0-847, h = 13*3 mm. 
The calculated height is therefore 13'3 against the measured value 13 ‘ 2 , so that the 
result is accurate to 1 part in 130 . With y — 8 ' 6 , we find by calculation, x = 2’38 
against the observed value 2 ' 35 . The other values are reproduced with similar 
accuracy, and we conclude that the undistorted curve is strictly parabolic, and that 
the probability distribution of intensity is correct for the case of the Hydrogen lines 
in the ordinary discharge. The intensity at a distance A—A 0 from the maximum at A 0 
is proportional to exp — J? (X — A 0 )~ where k 2 is some constant. The plate to which the 
above typical calculation relates is, in fact, much smaller than the others, so that the 
accuracy there obtained is a minimum. It is much greater in the calculations from the 
other plates, and we may, therefore, conclude that calculated distances are only 
subject to a possible error of about 1 part in 100 at most, and an error even less if 
the mean of several calculations is taken. The material is, therefore, at hand for 
a very accurate determination of the separation in H a and H^. 
The actual plates were taken slightly out of focus, in order to remove the trouble 
caused by the grain of the plate. The exactness of the parabolic forms which the 
