270 
DR. T. R. MERTON AND PROF. J. W. NICHOLSON ON 
and calculating the constants k and hi from the first and last, the equation becomes 
0'5394.r 2 = 15*368 + O'l llx-y. 
When x = 2'65, 3'35, we find y = 11'9, 97, by calculation from this formula, against 
the observed values 11'9, 9'8. The agreement is almost exact, and the stronger com¬ 
ponent of H s follows the same law as that of H a . It is, moreover, evident that the 
error of measurement in x cannot exceed about one-tenth of a millimetre at any point, 
and we may credit, therefore, the final separation of the components on the plate with 
this rough degree of accuracy. The scale of the plate being, as stated above, 9'5 mm. 
for a separation e, equal to 0‘22, the error in the deduced separation could be as great 
as (07 x 0'22)/975 = 0'002 A.U., but this should be practically the limit of error in 
any individual determination. 
A simple inspection of the photographs indicates that there can be no second com¬ 
ponent of Ho with a separation comparable to that in H a . If the series H a , H^, ... is 
Diffuse or Sharp, the separation in should be O'07 A.U., and if it is Principal, 
0'03 A.U., according to a preceding calculation. The second component which can 
actually be seen on the photographs does not at first sight appear likely to lead to 
the former value, and accurate measurements show that the latter is the true value. 
A typical calculation is as follows :— 
At one definite height, the breadths of the pattern on the right and left of the 
centre were x x = 3'9, x 2 = 4'3, and at another height x\ — 4'4, x' 2 = 5'0, the points 
being selected away from the junction of the curves. The true breadths on the 
normal scale are, if ft = a/d 0 2 , 
£ = 3 9 (1 + 195/3), 4'3 (1-215 ft), 
£ 2 = 4*4(1+2-2/8), i' 2 = 5*0 (1 —2-5/3), 
and neglecting, as is legitimate, the effect of the correction for height, the separation 
a- is given by 
which becomes, to order ft 
a■ = (2-36 — 71/3)/(l 4 — 6*5 ft). 
But for this plate, ft = 0'5/(975) 2 = 0'0053, and finally <r - 1 *98/1 "37 = 1'44 mm. But 
on the plate, 975 mm. corresponds to SX = e = 0'23 A.U., and <r thus corresponds to 
SX = 0'033 A.U., which is the separation in H^. 
There is thus no doubt that the Balmer series is a Principal series. The limit of 
error to be expected in the results, as above, is roughly 0'002 A.U., and the true 
separation for a Principal series is 0'030 A.U., so that the result is within the limit of 
error. Not only, therefore, can the method be applied to the elucidation of the nature 
of this series, but it can separate lines whose interval is only 0‘010 A.U., or less with 
