Or 
1888. ] Observations of Swpernumerary Rainbows. 28: 
. Number Deviation Number Deviation 
of Bar Calculated Observed of Bar Calculated Observed 
leit 40-8 ear IB Mose 6° 42"°7 
By «LAG 25 1 46:7 LAE Soe) TN pert 
oP 2 Zang A 8} 15 0 2 1 OAT 
Ay D5 Fb Oh Gis) off 1G Ae A403 7 Al ‘7 
By ae, 3 28 ey Yee) Sie Oli 
‘Sapesy, 1595) 3 58 Wey You Ils) 8 18 °7 
7 421 4 23°7 NEE Mae Ne 95) 8 36°7 
8 4 46°5 4 48 29 8 54°6 8 55 
OF cae bl, By er Zl Oe Oral, 
10 5 34 SEOORT, 22) a) 9 29 
i) We) Sao) 53 DOCh 23 9 48 9 47 
ia OVkSso G2 Oni 
The uncertainty in the value adopted by interpolation for the 
wave-length corresponding to the given index involves an error in 
the calculated deviations which, it has been found, cannot exceed 
1/400 of their values. 
An increase of ‘00012 in the index of refraction of the ight in 
the drop or cylinder, corresponding to a decrease of 1° C. in 
temperature, will so affect the value of X as to diminish the 
calculated deviations by 1/240 of themselves. An increase of 
‘0001 in this index will diminish the value of 6, by 07, and the 
radius of the geometrical bow by 1°9. 
But, what is more important to notice, an unobserved decrease 
of 1°C. in the value assumed for the temperature of the prism of 
water by which the index is determined will produce a decrease in 
the value of X estimated from the index, that will have the same 
effect on the calculated deviations as the corresponding increase 
of ‘00012 in the true index of refraction would have, viz. a diminu- 
tion of 1/240 of their amount. 
In Professor Miller’s observations the temperatures are not 
recorded. He remarks that all the observations were liable to be 
aftected by a sudden shifting of the bars, which was seen occasionally 
to take place through a small space to the right or left. It is 
possible that this may be explained as due to i guns varla- 
tions in the stream of water. 
The discrepancy between this value 264 here adopted for 
the displacement of the primary bow and the value 27°8 which is 
the result of the calculations corresponds to a difference of 12° C. 
of temperature. The observations would therefore agree exactly 
with theory if we supposed the hollow prism by which the 
index is determined to have been filled with water from a reservoir 
at 0°C. The sudden shiftings in the positions of the bars might 
then be explained (as above) as due to variations of temperature 
in the filament of water in which the bars are observed. 
From the table of deviations which has been calculated for 
VOM. VI. PL: Vv. 21 
