1179 
and HK respectively. The sum of the intensities of these emerging 
beams determines the intensity in the given direction. These two 
intensities may be replaced by those of the incident beams HA 
and AS. It is true that some light is lost by reflection, but no great 
error will be introduced by assuming that — on the inner side at 
any rate — all colours are weakened approximately in the same 
ratio by the reflections. The colour to be observed is not influenced 
by these losses: only the total intensity will be lessened. The 
intensities of the incident beams may be taken proportional to their 
widths and, as in the end we are only concerned with the ratios, 
the intensity may be put equal to the sum of the widths Ab + HK 
itself. 
Calling the width of the side of the prism a, the angles of 
incidence and refraction 2,,7, and 7,7, (see fig.), we find: 
cos 1, igs OE 
AB + HK= sinr, a 8: 
COS 7, ae - 
: CS rie COS 1, cos 2 
OK = EH cos 7, a OE ANR dS en 
COST, COST, ‚COST, 
Tae, COS 1, fe 
sin, a AB == AC t0st, = CH tg? cost, => sir} ved: ae 
Los Los, / 
For a ae value of « the intensity Z, leaving out a constant 
factor, may be put equal to: 
cos d COSÌ 
i= aie SEL BLU He pS Salo an re EA): 
COST,“ cos Pf, 
This function can be calculated for all values of 7 and 7. Computing 
the deviation YD corresponding to a given value of # the intensity 
for the direction determined by D is found by substituting in (1) 
that value of 7, and the corresponding values of 7,, 7, and 
The various refractive indices n of ice which are required were 
derived from measurements by PuLrricu’?) by graphical interpolation 
(with a small extrapolation, utilizing a remark of Purrricm’s, that 
the dispersion of ice is equal to that of water) taking for nm the 
mean of the values for the ordinary and extraordinary rays (for 
the whole spectrum the difference in the minimum deviation between 
the two amounts to only 6’). 
The values required for the purpose are as follows (/ refers to 
~ 
') For angles of incidence greater than that of the symmetrical case the indices 
1 and 2 interchange. 
2) C. Purrricu, Wied. Ann. 34, p. 336, 1888, 
