On Immersion Objectives. 211 



air, water, or balsam, but also to affirm distinctly that it was not 

 possible to construct any objective whicli slionld transmit from 

 water or balsam through the front of the objective a pencil of 

 greater aperture than the maximum transmissible from air, which 

 is limited by the refraction from air to crown glass to about 82°.* 

 Notwithstanding the supposition of Mr, Brakey to the contrary,!. 

 I had not overlooked the ingenious experiments of Mr. Wenham, 

 referred to in his articles in the January and July numbers, and it 

 seemed strange to me that they did not suggest a broader view of 

 the possibilities of the case than he seems yet inclined to take. 



In the present paper I propose to show : first, that there is no 

 theoretical difficulty in the way of the transmission from balsam 

 through the front of an objective of a pencil of 100°; next, that it 

 is practically possible to correct the aberrations of the jDcncil trans- 

 mitted backward from a front of this aperture by two posterior 

 combinations only ; and, finally, I shall briefly reply to one or two 

 remarks in Mr. Wenham's July paper. 



I will begin by discussing the case of the front of an objective 

 made of crown glass of 1.'525 index, which shall have the same 

 dimensions as the immersion front for a T^th, figured by Mr. Wen- 

 ham in this Journal, January, 1871, p. 23, viz. radius -0315", 

 thickness, • 0340". I represent one-half the section of such a lens 

 in the figure (on next page) on the same scale as Mr. Wenham's 

 figure, viz. fifty times the dimensions above given. 



To simplify the discussion, I will suppose the medium in front 

 of the lens to be balsam, with its index reduced by some admixture 

 till (to make use of Mr. Wenham's favourite supposition) it shall 

 have the same refractive power as the crown-glass front. If, then, 

 a luminous pencil of 41° semi-aperture radiate from the point F 

 situated in the optical axis X Y at a distance of • 0264" from the 

 front surface of the lens, the extreme ray will pass from the balsam 

 into the glass in a straight line without any refraction, until it 

 reaches the posterior hemispherical surface of the lens at a point A, 

 78° from the central point Z, and will then emerge into the air 

 behind the front, suff'ering such refraction as to take the course A E, 

 which will form an angle of rather more than 11° (11*^ 24') with 

 the optical axis. For if the arc A Z be assumed to be equal to 78°, 

 and be the centre of curvature, we shall have in the triangle A C F 

 the angle C = 102° by construction, and the angle F = 41° by 

 hypothesis, whence the angle A = 37°. Also in the same triangle, 

 the side A C being the radius of curvature, is ' 0315" by hypothesis ; 

 so that we have one side and the angles of the triangle known, and 

 by trigonometry compute the side F = • 0289" (very nearly). 



* See his remarks on p. 118, vol. v., p. 30, vol. ix., and other places in this 

 Jonrnal. 



t August number, p. 98. 



