400 



In stating the results of his experience on this subject, the author 

 takes occasion to advert to some of the sources of fallacy by which 

 incautious observers with the microscope have so often been greatly 

 misled. When a pencil of rays proceeding from an indefinitely small 

 bright portion of an object is brought to a focus by the most per- 

 fect object-glass, the image thus formed is in reality not a point, but 

 a small circle, and will always appear as such if the eye-glass of the 

 microscope be sufficiently powerful. These circles have a consider- 

 able analogy to the spurious discs of stars viewed through telescopes. 

 Like the latter, they become much enlarged by diminishing the aper- 

 ture of the object-glass ; and they are also enlarged by increasing 

 the intensity of the illumination. The overlapping of contiguous 

 circles of diffusion has given rise to many fallacious appearances ; 

 such as the spottiness which some surfaces assume, and which has 

 been mistaken for globules. This optical illusion has been the basis 

 of some ingenious but visionary speculations on the intimate struc- 

 ture of organic matter. The appearance, in certain directions of the 

 light, of lines on the surface of an object, where they do not really 

 exist, may be traced to a similar cause. 



The author proceeds to describe the method he uses for measuring 

 the dimensions of the objects viewed, and notices different test ob- 

 jects with reference to their affording the means of judging of the 

 powers of the instrument. He next enters into a review of the com- 

 parative merits of various microscopes constructed by Cuthbert and 

 Dollond in this country, and by Chevalier, Selligue, Amici, Utz- 

 schneider, and Fraunhofer, on the continent. 



The concluding part of the paper is occupied by the developement 

 of a principle, from the application of which to the construction of 

 the microscope, the author expects that a still greater extension of 

 its powers will ere long be obtained. He remarks, that the circum- 

 stance which limits the magnitude of the pencil of light, admissible 

 with high powers by a single achromatic object-glass, is, that the 

 correction for spherical aberration by the concave lens is propor- 

 tionally greater for the rays that are remote from the centre, than 

 for the central rays. The degree of confusion in the image, thence 

 arising, is, in similar glasses, inversely as the square of their focal 

 lengths. It increases very rapidly with a small enlargement of the 

 aperture, but may be rendered much less considerable by distributing 

 the refractions equally among a greater number of lenses of smaller 

 curvature. Hence the advantage obtained by certain combinations. 

 The experiments made by the author have established the fact, that 

 in general an achromatic object-glass, of which the inner surfaces 

 are in contact, will have on one side of it two aplanatic foci in its 

 axis, for the rays proceeding from which it will be truly corrected 

 with a moderate aperture ; that for those proceeding from any part 

 of the interval between these two points, the spherical aberration will 

 be over-corrected ; and that for rays beyond these limits it will be 

 under-corrected. Methods are pointed out for ascertaining the situa- 

 tion of these aplanatic foci. The principle here explained furnishes 



