284 Mr J. Larmor, On Prof. Miller's [Oct. 29, 
obtained to Miller’s series marked (C) we obtain the following 
results. 
The index from air to water is given as 1:3346; the radius of 
the cylinder of water is 0°01052 inch. There is considerable un- 
certainty as to the value of X which corresponds to this index, 
inasmuch as the temperature at the time of observation is not 
given. If we take it to be 12°C., it appears by interpolation from 
Landolt and Bérnstein’s Tables that the light corresponds to a 
place near the 6 lines in the spectrum, and that we may take its 
wave-length in air to be 5200 x 10™ metres. 
The value of m for the first bright band is 1:0845 (Airy), 
and the complete system of succeeding values for the other bands 
has been calculated by Prof. Stokes*. 
Calculating by ordinary logarithms, we obtain ¢ = 59° 19°03, 
f' = 40° 72, and for the radius of the geometrical bow 
Ad’ — 2h = 41° 50°7, 
which agrees sufficiently with Miller’s value 41° 50°4. 
The deviation of the first bright band (the primary bow) from 
its geometrical position comes out from these data to be 
y= — 278. 
This series (C) is the most consistent of those given. It con- 
sists of seven sets, of which the first two extend to 28 bars. But 
after the 23rd bar the law of succession breaks down completely, 
as is confirmed for instance by the fact that observations of the 
25th are entirely absent. .This is conceivably owing to mixture 
with another series of bands due to some other caustic, which 
there destroys the continuity of the system under consideration. 
If we exclude the bright primary bow, whose position of 
maximum was, it appears, difficult to fix upon, the series of 28 
dark bands agree very perfectly in the different sets, and correspond 
very closely throughout their whole range to the theoretical values 
assigned by Prof. Stokes’ table. 
The value for the deviation of the primary bow from its geo- 
metrical position which best suits the observations is, however, 
264, though this is 3 or 4 minutes greater than the observations 
of the primary alone would give. Calculating from this value, 
the following series of numbers shows how closely the observed 
deviations of the first 23 dark bars from the position of the 
geometrical bow agree with the theory. The observations are 
the mean of Miller’s first three series, and correspond very nearly 
to the second series. 
* Camb. Phil. Trans, Vol. 1x. part 1. Collected Papers, Vol. 11. p. 349, 
