138 On the Optical Advantages — [‘eurnsi, Sepu sto. 
deal of time to remember that when a ray passes from a rarer into 
a denser medium, it is bent ¢owards the perpendicular or normal 
at the point of emergence, and from it when the ray passes from a 
denser medium into a rarer. 
Thus, vision under water embraces nearly the whole horizon ; 
and the image within a hollow sphere, impacted in glass plate, em- 
braces nearly 180° of aperture, crowding the whole prospect into 
an exquisite miniature. No eye embraces so wide a prospect as that 
of a submerged animal. 
To find the deviation between plate glass (1 =1:500) and 
Canada balsam (u = 1°532). Suppose a ray passes from the latter 
into the former, then 
1-500 
1°532 
Sin. ¢’ = sin. @ = *9791 sin. ¢. 
If ¢ = 15°, o’ will be found = 14° 40’* and subtracting 9’ from 
it, deviation is only 20’. 
The deviation up to nearly 45° is just about 2 per cent. for 
mean rays. 
At 60° it becomes 2°; at 70° nearly 3°5 and at 80° nearly 4°; 
and at 85°, for the extreme aperture of the best objectives, 170°, 
¢ amounts to 
85 0 (incidence) 
77 40 (efraction) 
Deviation or difference = 7 20 
or the Canada balsam only causes as little deviation at 85° as 
water at 50° and air at 20° of incidence. 
In tracing the rays it will be easily remembered that whenever 
amongst several parallel plates the ray is examined, tts direction in 
two identically refractive media is always found to be the same 
after any number of intermediate refractions. 
The deviation between crown glass and flint glass is found in 
the same manner ; the index of refraction for the passage of a ray 
1:642 
between them being = 1-500 = 1:09466, as explained in Part I. 
Giving therefore a variety of angles to ¢ from 1° up to 90°, 
the following Tables have been calculated.| The method by which 
this is generally done is given in the Appendix. 
* See Appendix. 
+ The tables employed ranged to six places of decimals for the sines of ¢. If 
five plans only be used, rather different results will be obtained. 
