1877.] 



Magnifying -poiver of the Half-prism. 



31 



train in the same ratio as the dispersions ; and if there is no tendency to 

 a repetition of similar errors throughout the train, these must be com- 

 bined according to the ordinary law of errors of observation, and thus we 



/ m 2 ' 1 — 1 



should get probable error from whole train = a / — — — x probable 



error from one half -prism. 



The train of " half -prisms diminishing" would give the same result, 

 since a magnifying-power of m n must be used to give the same separa- 

 tion. In the case of the whole prisms, a magnifying-power of — — I . — 



is required, and therefore probable error from whole train = 



-1 2Vp 



X probable error from a whole prism. Thus, considering that a higher 

 magnifying-power must be applied where few prisms are used, the case 

 of a long train of prisms would be equivalent to the arithmetical mean of 

 a large number of fallible surfaces ; but, independently of the fact that 

 after a very moderate number the gain in accuracy of definition is very 

 slight, practical experience seems to show that, owing probably to syste- 

 matic errors in the surfaces or the glass, an increase in the number of 

 prisms is accompanied by a corresponding loss of definition, and that con- 

 sequently the law of errors does not apply. Hitherto a long train of 

 prisms has been considered necessary, partly because it has been the only 

 means of obtaining purity, i. e. dispersion as distinct from mere separation, 

 and partly because the use of high magnifying-powers involved the 

 weakening of the light by increase in the apparent breadth of the spec- 

 trum. As regards the effect of air-bubbles and other defects in the glass 

 in stopping out light, it falls under the head of absorption, and consti- 

 tutes a very serious objection to the long train of prisms. 



Probably, from want of proper data, the effect of absorption in spectro- 

 scopes would appear to have been generally overlooked ; and in many cases 

 where compound prisms are employed the brightness of the spectrum is 

 far inferior to what would have been obtained with much smaller prisms. 

 Even with a train of simple prisms the loss by absorption is very great, 

 and to this is superadded the loss by reflexion at the numerous surfaces, 

 so that the disadvantages of a long train are sufficiently obvious. To 

 obtain some information on this point, I have made several series of mea- 

 sures of the brightness of the light transmitted through various thick- 

 nesses of different kinds of glass, using a polarizing photometer and a 

 chromatometer (on the principle of Prof. Clerk-Maxwell's colour-box) ; 

 and though the observations I have made are not so extensive as I could 

 wish for the elucidation of this interesting physical question, they are 

 amply sufficient for the immediate object in view, showing conclusively 

 the wasteful loss of light in the ordinary construction of the spectroscope. 

 There would seem to be great differences in the absorptive power of 

 different specimens of glass, depending on the manufacture rather than 

 on the density, though all the specimens of very dense flint which I have 



