COKEESPONDENCE. 273 



condition under which the full aperture can be brought to bear on a 

 balsam-mounted object, viz. that of the tiny hemispheres. I am glad 

 of his announcement that he has succeeded in this, and should like to 

 see the same thing done in this country, j)articularly with large- 

 aperture glasses, say higher than ith. But to end the matter, I must 

 positively decline any further reply to Mr, Tolles on the question of 

 the passage of rays through refracting surfaces, as it is futile for him, 

 and a waste of time for others. I have merely to refer to his Fig. 2, 

 page 117 of the last Journal, as my apology for this. Starting fiora 

 the focal point, and accepting his position that the refractive power of 

 the covering glass, interposed medium (say balsam instead of water), 

 and front lens are nearly the same, the rays may be taken as straight 

 till they reach the outer convex siu-face : and here is a gross error 

 permanently recorded in black and white, for at the angle at which 

 they are made to reach that surface, instead of emerging in the direc- 

 tion he has shown, the refraction would be so small that they would 

 proceed more nearly in a straight line, so that no possible back 

 combination at jDrescnt known could take them in, or in due coiu'se 

 bring them to a focus behind.* The science of optics ranks amongst 

 the most exact of all, and no fanciful direction of rays is admissible. 

 In the object-glass question there have been imaginative diagrams 

 ad nauseam, when all deductions should have been taken from 

 drawings of the real thing. Mr. Tolles has made combinations that 

 have done well in practice, and if he will give us the correct radii, 

 diameters, distances, &c., of any one combination that has been 

 actually constructed, and transmitting a full aperture in balsam, and 

 show us the passage of the rays through to prove the result, then I 

 will strike my colours, or if he will furnish the drawing, the rays 

 shall be traced through for him. Nothing beyond what has been 

 known before, has yet been learned by the correspondence, unless the 

 fact that in America the single front, differing in thickness and slightly 

 in radius, is now employed both for the dry and wet lens in their best 

 object-glasses. I fairly claim to be the originator of this system. I 

 made but one object-glass with a triple front (in the year 1850). 

 I then found that the radii of the contact surfaces of this gave a large 

 excess of over-correction or negative aberration for parallel rays, and 

 under-correction or positive^ aberration with divergent ones. This 

 induced me to project the mean refractive rays through the entire 

 combination drawn as a large diagram, which analyzed the cause, 

 and led at once to the single front with a thickness proportioned to 

 correct the aberrations. Some particulars of this are given in my 

 paper " On the Construction of Object-glasses," commencing with this 

 Journal. I am happy to find that this formula has now become 

 almost universal, and that the triple front may be considered as 



* Fig. 1 is still more erroneous. In the dotted-line lens of Mr. Tolles, shown 

 within the copy of my front, it may be seen at a glance how his dotted ray will 

 emerge nearly as a radius. 



t These terms are so thoroughly known and descriptive of the conditions of 

 the marginal rays both in cliromatic and splievical corrections falling witliout or 

 within the central ones, that I am not disposed to reverse them on any theoretical 

 ground, or that they are " rule of thumb employed in the workshop." 



