274 
DR. T. R. MERTON AND PROF. J. W. NICHOLSON ON 
and for two other abscissae £ 2 , £' 2 , measured on the normal scale, 
and, by subtraction, h±—h 2 is eliminated. Investigation shows at once, as in the 
following numerical examples, that the term in /3 in the result of this subtraction 
cannot affect even the third decimal place in the calculated separation and we may, 
therefore, omit it at once. 
Thus finally, 
= (£YWi 2 -£V+& 2 )/2(£W' 2 ). 
These magnitudes £ are true normal breadths, deduced from the observed values by 
correction for dispersion. 
(XVII.) Separation of the Components of H a . 
In a series of fringes for H a , the intervals between one fringe and its neighbours on 
either side were 14'0, 15‘3 mm., and the next interval in the direction in which they 
decrease was 127. The law of maxima stated already is fulfilled, for these numbers 
are in arithmetical progression. The appropriate normal separation for the fringe 
in question, now the subject of examination, is the mean of 14'0 and 15'3, or 14‘66. 
In other words, a separation 14'66 mm. corresponds to the interval S\ — e = 0'4301 
A.U. for H„. Moreover, a = 1*3, d 0 = 2(14'0) —15‘3 = 127. 
A real normal breadth £ on the right of the axis of the main component indicates, 
therefore, an apparent breadth x, where 
x = £- ^ = f-0'0048^ 2 , £ = .t + 0'0048V, 
and the same breadth £ on on the left, an apparent breadth x' where 
V = f+0’0048^, £ = V + 01)048V 2 . 
We can also calculate the real breadths on the right from the equation to the 
parabola for the main component. Actual measurements of the total breadths at 
the points y = 19‘4 cm., y = 16"5 cm. give 2£ — 4'3, 2£ — G'4 respectively. These are 
points which depend only on the main component. The corresponding equation of the 
main parabola becomes 
f= l-969(22'0 + 0'l (-y), 
when the coefficient O'l is calculated. It agrees completely with the value derived 
by comparison with neighbouring fringes, which is 0T05, and the whole interpretation 
of the curves is justified. At the heights y — 12'8 cm.,?/ = 11 ’0cm., we thus find 
directly from the equation, 
£i = 4‘355 mm., 
£ 2 — 4753 mm., 
