56 Transactions of the Royal Microscopical Society. 
beautiful, explanations of the great resolving power of immersion 
lenses. The diffraction spectra arising from the structural peculi- 
arities of the object, on the exact superposition of which the resolving 
power exclusively depends,* are by the retardation brought nearer 
to the illuminating pencil; the invisible portion of the spectrum 
becomes luminous, and the blue and violet assume the colours of 
the less refractive or light-giving rays, and thus the surrounding 
spectral images, being thus drawn together, or, if I may use the 
expression, are so shrunk in, as to be admitted into the apparently 
reduced aperture of the objective. 
Thus the angle of the oil immersion lens which I have endea- 
voured to describe, being 113^, gives a semi-angular aperture of 
56J°, of which the sine is 0*839, which, multiplied by 1*50, the 
refractive index of the oil, gives a “ numerical aperture ” of 1 * 25 ; 
hence we see that we have in it a resolving power exceeding the 
possible limit of a dry lens (sin. 90 = 1) by no less than 25 per 
cent. 
This numerical aperture of 1*25 is, however, as I have said 
before, effective to the full extent only, on condition that the 
refractive index of the medium in which the object is mounted is 
not less than 1*25; but if a dry object adhere to, and is in 
physical contact with, the thin glass, the resolving power will be a 
mean between 1 and 1*25 = 1*125, i. e. a mean between the 
maximum resolving powers in air and in balsam. 
Hence it will be seen that the resolving power of an immersion 
objective is greater on an object in balsam than in air, if its “ nume- 
rical aperture” be > 1 ; provided always that the difference in the 
refractive indices of the object observed and the medium in which it 
is mounted is sufficiently great to render the diffraction images 
bright enough for observation. 
In conclusion, I beg to tender my warmest thanks to Dr. Abbe 
for the prompt, efficient, and extremely kind manner in which 
he responded to my appeal, as by his ability alone my idea has 
been carried into effect, and the use of high powers rendered 
more facile and therefore, as I hope, more popular. 
* Dr. Abbe’s article in Schultze’s ‘ Arcliiv Mikroscopische Anatomie,’ vol. ix. 
