396 VISION THROUGH SMALL APERTPURES IN WALLS. 
If the mirror is shorter, the reflections cease sooner, and assuming 
the mirror to be equal in length to r=4 R, the limit would be reached 
for a=90°, e=45°. The mirrors will here be parallel to the line I P, 
when the point of reflection reaches their outer edges. 
If n ig greater than 2, the maximum deviation will be less; and if 1 
is less than 2 the maximum deviation will be greater, to a certain limit 
of the value of n, dependent on the length of mirror that can be used. 
For the measuring instrument, the value of n=2 need alone be con 
sidered. 
For use in a turret for obtaining a wide angle of vision, the extent 
would be limited by the cavity that could be allowed for the apparatus 
leaving strength enough to the wall. (See figure 4). Fifteen to 
twenty degrees might probably be obtained. 
end. Trisection of an angle with the instrument. 
PC m=a+d C m=a+ (a—a) =2 a—«@ 
When n=2, 2=1 a=d C m, 
Therefore, P C m=3 2=3 x (d Cm). 
Hence, if an observer at C lays off any angle P C K, and turns the 
mirrors until he sees the reflection of J from the direction of K, the 
angle « will be one third the angle P C K, and this can be laid off 
from the direction C K by sighting from C along the line C d perpen- 
dicular to the mirror. Tor this process, but one mirror is needed. 
With two mirrors this angle can be laid off from the direction I P, 
by sighting from J along the line J m, when the change of position 
from C to J will not be appreciable in comparison with the distance of 
objects sighted on. 
, Seconp Form. 
Two plane mirrors Mf and M' (figure 7) are made to revolve about 
Fie. 7. 
\p 
separate centres, C and C’, but keep always parallel. If P and Lare at 
equal distances from C, midway between the centres of revolution, the 
rays from P reflected to [ will cross at C. 
This arrangement would answer, like the first method, either for 
obtaining a continuous image, or for measurement, but the exact values 
of the deviation for different inclinations of the mirrors to the line J P 
have not been worked out. a3 
