ascii art of Immersion Lenses. 25 
In the first table comparative deviations and refractions, and the 
angles of total internal reflexion beyond which obliquity no ray 
can pass, corresponding to given angles of obliquity of a ray just 
about to enter the front lens of the objective, have been carefully 
calculated and verified. 
The semi-aperture of an objective being given, the middle column 
representing that aperture at once gives on inspection, in the left 
and right columns, the deviations which the ray had suffered in 
entering air or water, and the diverging of the pencil radiating 
within the slide (mounted with Canada balsam) from the observed 
microscopical particle supposed to be brilliant with illumination. 
If the action of the Canada balsam be required in addition, which 
is neglected in this table, the deviation will require a minus cor- 
rection exactly given in Table III., which is one minute for each 
degree of incidence or obliquity up to 10° nearly, and so on. 
The table requires but little explanation. It will be at once 
seen on inspection that a ray of light up to 50° obliquity in water, 
just entering the objective, suffers only one-third the deviation that 
a ray of the same obliquity would have undergone through air. 
Again, a pencil of 35° 16’ emanating or diverging from an ob- 
served particle in Canada balsam will enter the objective through a 
film of air at an obliquity of 60°, and therefore cannot be trans- 
mitted, unless the objective possess an aperture of 2 x 60°, or 
128°; whilst the same aperture of objective will, with the optical 
advantage of water immersion, transmit an oblique pencil radiating 
from the brilliant particle of 50° 29’ instead of 35° 16’ as with the 
dry lens. 
This example at once demonstrates that the addition of a water 
film is equivalert to largely increasing the aperture. So that wid 
water a given objective will admit with a small aperture as large a 
radiant pencil diverging from the observed particle asa much greater 
aperture-objective will admit with the dry lens. 
In other words, when we use an immersion system we can im- 
mediately reduce the aperture, 2. e. reduce eccentrical aberration, and 
secure less deviation (one-third nearly), and the mystery of the 
superiority of the water lens is at once laid bare by a study of this 
table. The relative semi-apertures of dry and immersion objectives 
to admit identical divergent pencils from this particle are therefore 
found in the extreme left and right hand columns marked ¢’ in each 
case; > being the angle of incidence on the objective. So that in 
each case 
Sin.¢=yzsin. ¢’. (4, ¢ and ¢’, being general.) 
Thus by the table the apertures of dry and immersion lenses 
transmitting the same pencil from the object mounted in balsam are, 
doubling the semi-apertures (for water films), 
