Bemarks on the Aperture of Object-glasses. 273 



I am in hopes that the foregoing brief explanation will be suffi- 

 ciently explicit, and that Mr. Wenham himself will frankly admit 

 that he has overlooked the possible case of an objective made to 

 perform only in water or balsam, without reference to its perform- 

 ance in air. Whether the increased angle which theory demonstrates 

 can be gained at this price, will have any practical value, or be any 

 addition to our optical resources, is another question altogether, and 

 one into which I do not propose to enter at the present time. 



Memorandum on the foregoing. By Professor Simon Newcomb, 

 U.S. Navy, Foreign Associate of the Eoyal Astronomical Society. 



I assisted in the measures above described by Dr. Woodward. 

 The angle in balsam, when the lenses were fully closed, measured 

 more than 100°. 



The reason why the angle exceeded the limit laid down by Mr. 

 Wenham was quite obvious to me during the experiments. Whether 

 the objective was open or closed, the light was dispersed in air at all 

 angles up to 180°, showing that the light which struck near the 

 circumference of the anterior surface of the objective must have 

 suffered total reflexion, and so made an angle with the normal to 

 the surface exceeding the hmit assumed by Mr. Wenham. 



Simon Newcomb. 



Memorandum. By Mr. Benel Keith, of Georgetown. 



I witnessed the measurement, by Dr. Woodward, of the balsam 

 angle of the ith of Mr. Tolles, the method used being that described 

 in the foregoing communication. The angle was over 90° when 

 the lenses were fully open, over 100° when they were fully closed. 

 This result does not seem to me inconsistent with theory. Mr. 

 Wenham's experiments, alluded to in his article in the 'Monthly' for 

 January, indicate an explanation, and it seems singular that they 

 did not suggest to him long ago a method of obtaining what 

 Mr. Tolles has obtained — an objective with large angle for objects 

 covered in balsam. Let O, Plate XIX., lower portion, Fig. 3, 

 be the lenses of an ordinary objective in adjustment for an 

 object uncovered. Let B be the radiant at such a distance 

 that a cone of large angle is brought to a focus at the eye- 

 piece. In order that this state of things shall not be disturbed, 

 when the object at B is covered in balsam, mount in front of O the 

 lens B, so that when in water-contact with the cover it shall be part 

 of a sphere with its centre at B. It will exactly neutralize the 

 negative surface of the cover, and the light will radiate from B 

 without refraction until it meets the objective at O. 



