632 
WELDON EANGE ETNDER. 
a horizontal section of the prism. The light from the object at a 
enters at the surface A B; is then refracted more nearly normal to this 
surface; is then reflected internally from the silvered surface B C, and 
again internally from the unsilvered surface A B; passing out through 
the surface A C, where it is again refracted, but away from the normal; 
and reaching the eye of the observer at f. The angle f a! b , between 
f e prolonged and a b , is the deviation of the light, or the angle 
reflected by the prism. 
It is evident that the deviation would be the same if the observer 
and the object changed places, the course of the ray passing from f to a 
along the broken line a b c d ef instead of from a to f. 
The reason for making the angle B one-half the angle A appears 
from the following discussion :— 
After the light enters the prism the two surfaces A B and B C act 
as mirrors, and, from the well-known principle that light reflected twice 
from a combination of two plane mirrors undergoes a deviation equal' 
to twice the angle of the mirrors, the angle made by d e with c b is 
twice the angle B. In order now that this deviation shall not be 
changed by refraction in passing, through the surfaces A B and A C, 
the rays b c and d e should make equal angles with the latter surfaces— 
that is, B b c should be equal to A e d. The refraction will then be the 
same at both surfaces. 
The following relations subsist among the angles in Fig. 7 :—- 
B c$=180°^B-B bc=C cd, 
B dc— C cd— B = 180°-~2 B—B 6c=kde, 
A=180°—A ed—K d e=180°—A e d — (180°—2 B-~B be). 
Now, since A. ed must be equal to B b c, A must be made equal to 
2 B in order to obtain an invariable deviation equal to A. 
To give a deviation of 90°, A should be 90°; B and C each 45°. In 
this form it can be used as a earnera-lucida. 
For a deviation of 88° 34' 3", A should be 88° 34' 3", and B 
44° 17' 1"’5. In this case C, not being equal to B, the angle B should 
alone be used for determining the deviation. 
In prism No. 1, A is less than 90°, and B, which is equal to C, is 
greater than 45°. The deviation will therefore be variable and greater 
than 90°. 
These results are confirmed by observation. 
It is evident that the deviation given by the prism is chiefly dependent 
upon the angle B, because a slight error in B produces twice that 
change in the deviation ; a slight error in A affects the deviation only 
by a slight difference in refraction at the two surfaces, and though the 
deviation will not be invariable it will change but slightly. This is 
illustrated with prism No. 2, in which B is not exactly one-lialf A. It 
requires, also, the multiplier 18*3 instead of 20. The table appended 
shows, however, that very good results can be obtained with it as it is, 
and doubtless less variation would occur in the measurements were the 
prism accurately ground. Accurate grinding was found to be difficult 
with the instruments at command, but the defect can be readily 
supplied if more prisms are required. 
The cost of prism No. 2 was $12, but Mr. Alvan Clark, who made 
