286 Mr J. Larmor, On Prof. Miller’s [Oct. 29, . 
this series of experiments, the values which apply for any other 
index and temperature may now be deduced by introducing cor- 
rections according to the data just given: while for different 
values of the radius of the cylinder the deviation is proportional 
to (radius) 8. 
In series (A) the index was 1°3318 and the radius of the 
cylinder of water 0:0103 inch. The light was not so homogeneous, 
and as a consequence the results are not so concordant. But treat- 
ing them as has been done for (C), they agree very well with 
theory so far as the first 10 dark bars, on the hypothesis that the 
displacement of the primary bow is 29’. 
The value of this displacement, deduced from that for (C) by 
applying the corrections given above for the change of index and 
of radius of the cylinder, is 294 for a temperature 0° C.: it would 
be 29’ if the temperature of the water cylinder were 3°'3 C. 
In series (E) the radius of the cylinder was 0:00675 inch. The 
index was somewhat doubtful; the value 1:33453 leads to 41° 52’ 
as the radius of the geometrical bow; the value 1:3348 leads to 
41°46'9. The second value of the index may be rejected at once, 
as not in agreement with the results. 
The theoretical value of the displacement of the bright primary 
bow deduced from that in (C) by the necessary corrections is 
36°5 for 0°C. This agrees with the mean value deduced from 
the observations of the first 8 bars, which is 36°3; but the 
succeeding bars deviate from the positions assigned by the theory. 
Consider now the circumstances of the secondary bow 
(n= 2). In the series (D) which corresponds to (C) for the primary 
bow, we find $6=71° 47°35, ¢’ = 45° 2275, radius of geometrical 
bow = 7 +26 — 6 = 51°18°2. 
An increase of ‘0001 in the index increases this radius by 
1°93. 
Thus for the index 1:33464, the radius is 51°19'1, which agrees 
with Miller’s result in series (D). 
The theoretical displacement of the bright secondary bow from 
the geometrical position is 4961 for a temperature 12°C. 
An increase of ‘0001 in the index leads to a decrease of 1/220 
of itself in the value of the displacement: so that for a temperature 
0°C. at the time of observation the displacement would be 47-4. The 
alteration is, as before, due to the different value of X which corre- 
sponds to the given index at the altered temperature. This value 
is in exact agreement with the result deduced from the devia- 
tions of the first and second dark bars, and agrees very well with 
the succeeding ones; though as usual (in accordance with Miller’s 
remark) the number given for the position of maximum bright- 
ness of the first band deviates considerably from it. It is to be 
noticed that the corresponding set of observations (C) of the 
primary bow required the same temperature correction. 
