142 On the Optical Advantages  [Mvivnca, Sept, 4810. 
ordinary “collar” or objective adjustment thoroughly 
compensates, when the objective has been nicely balanced 
to perform its best for one kind and thickness of covering 
. glass. 
(3.) The aperture of the nascent pencil actually transmitted. 
(4.) The depth at which the observed particle is immersed in 
the balsam. 
(5.) The change in the interval separating the objective lenses. 
Such is the subtlety of adjustment required for the successful 
definition of very difficult objects. 
APPENDIX. 
No. 1.—A ray of light having passed out of plate glass («= 1°500) 
into air, is striking the plane front of the objective lens at its extreme 
angle of semi-aperture 85°. What deviation has it suffered in its 
passage ? As the ray is passing from a denser into a rarer medium, 
1 
Sin. ¢’ = — . sin. ¢, 
in. " sin. > 
or log, sin. ¢’ = log. sin. @ — log. uw 
0 
log. sin. 85° . = 9°998344 
— log. uw (log. 17500) = — 0°176091 
or log. sin. ¢’ .. .. =  9°822253 
But log. sine 41° 36’ .. = 9°822120 
Difference .. .. = 133 
Difference for 60” = 142 
Hence 142 : 133 3: 60” : 56”. 
Tho value of ¢' is therefore 41° 36’ 56”, and as ¢ = 85°, the deviation 
required = 43° 23' 4”, or 
48° 23’ 
nearly, as given in Table I., and 
41° 37’ 
the angle of refraction, as shown in the first and second columns 
opposite 85, Table I. 
No. 2.—For index of refraction between plate glass (u = 1:500) 
and water (4 = 1°336) for mean rays: 
1 1°336 
W.G 
‘Gap is 
sin, = — Sil. 9d. 
? 7 p 
Hence log. sin. $’ = log. sin. ¢ + log. - - 
Suppose it be required to find deviation of a ray entering water 
from plate glass at an angle of incidence 50°. 
