908 PEOPESSOE BimSEN AWD DE. H. E. EOSCOE’S PHOTO-CHEMICAL EESEAECHES. 
When thenp=j9i, and s=Sy 
When e— ia? then^=|? 2 ? s=S 2 - 
Suppose that a ray of light be reflected from both the mirrors 1 and 2 (fig. 14. 
Plate XLIII.), of which the first is of speculum metal and the second of steel, with the 
angles of reflexion and and suppose that the angle which the two planes of 
reflexion make with each other be The incident ray has the intensity 1, and consists 
of white light ; the intensity of the twice reflected ray is then 
cos® ^+§2 sin® sin® cos® (B). 
The observed chemical action, therefore, divided by S, gives the action which would 
have been observed if the sunlight had fallen directly without pre\ious reflexion on the 
insolation- vessel. In order to calculate S, the values of ^l, ^ 2 , and /3 must be deteimined 
for each observation. The second angle of incidence (4) was measured once for all. 
In order to calculate the angle of incidence (^I) varying with the position of the sun, 
we conceive the point of reflexion of the ray on the mirror of the heliostat to be the 
centre of a sphere, from which centre lines are drawn to the sun, to the earth’s pole, to 
the south point of the horizon, and in the direction of the reflected ray. Let the four 
points produced by these lines cutting the sphere be represented by SPMKi, fig. 15, 
Plate XLIII. The angle SEj is twice the angle of incidence of the ray ; it is found 
from the spherical triangle PSKi. In this triangle we know the side PS— 90— S, when 
h is the sun’s decimation. The sides EjP and the angle EiPS are thus found. In the 
spherical triangle PMEj the side MEj, the azimuth of the opening in the shutter, 
directly measured, is known; the angle PMEj is a right angle, and MP=180--^ when 
y) is the latitude of the place. 
Hence 
cos PEj— cos MEj cosj? 
and 
sin MPEj 
sin MRj 
“ sin PRj 
The angle SPEj is, however, =MPE,-|-#, when t signifies the hom-angle of the sun, 
positive before noon. Hence we have for EjS, or for the angle 2?’i which the incident 
rays make with the ray reflected from the heliostat mirror, 
cos EjS — cos 2^J= cos PEj cos (90— §)+ sin PEj sin (90—^) cos (EiPM-j-'^). 
The angle (3 is thus obtained : SR,, fig. 15, is the first plane of reflexion, EjEj is the 
second plane of reflexion ; hence 
|3=PE,M™PE,S, 
and 
sin PE,S= 
sin PS sin SPR, 
sin SRj 
When there is only one reflexion, we have for the value of S simply 
s=i(p;+s!}. 
If we consider all these corrections together, we find that the action (Wo) expressed in 
