1878.] Prof. Stokes. Ratio of Dispersions. 485 



Figure 8. (a.) Spores encapsulating and dividing. 

 (b.) A small group of capsules. 

 (c.) A large group of capsules. 



(d.) A group of capsules surrounded by a common envelope. 



(e.) Sporules escaping from their capsules. 



(/.) Large emptj capsules. 



(g.) Phases undergone by a single capsule. 

 Figure 9. (a.) Large finely granular brown sphere. 



(i.) Smaller coarsely granular spheres. 

 Figure 10. Patch of naked spores from surface of liquid. 

 Figure 11. Spores germinating into Spirilla, at first comma-shaped. 

 Figure 12. Spirilla resembling germinating spores. 



Figure 13. Successive drawings of a portion of same filament, showing extreme 



irregularity of division of spores. 

 Figure 14. Irregular division outside filament — (a) and (5), naked ; (c) within 



capsule. 



X. " On an Easy and at the same time Accurate Method of De- 

 termining the Ratio of the Dispersions of Glasses intended 

 for Objectives." By Professor G. G. Stokes, M.A., Sec. R.S. 

 Received June 18, 1878. 



In examining the dispersive powers of a great variety of glasses 

 prepared by the late Rev. W. Vernon Harconrt, I bad occasion to 

 examine several prisms which were too much striated to show clearly 

 even the boldest dark lines of the solar spectrum. I found that I was 

 able to get a fair measure of the dispersive powers even of these by a 

 method depending on the achromatizing of one prism by another. If 

 the method succeeded even with such prisms, it stands to reason that 

 it would be still more successful with prisms of good glass. 



For the construction of an objective we require but one datum as 

 regards the dispersions, namely, the ratio of the dispersions, or rather, 

 the ratio which on being treated as if it were the ratio of the disper- 

 sions gives the best results in practice. 



If it were not for irrationality, the matter would be comparatively 

 simple. The ratio of the dispersions would then be the same for 

 whatever interval of the spectrum it were taken ; and we should 

 merely have to take two well-defined lines, bright or dark, situated as 

 nearly as may be at the extremities of the spectrum, so that any errors 

 of observation should be divided by as large a quantity as practicable, 

 to measure the refractive indices of the two glasses for each of those 

 two lines, and to take the ratio of the increments in passing from one 

 line to the other. But in consequence of irrationality we get a 

 different ratio according to the particular interval we choose ; we are 

 obliged, unless we adopt some different method altogether, to observe 

 more than two lines in each glass ; and when we have got the results, 



