Mr. T. Grubb on the Improvement of the Spectroscope. 533 



be rendered perfectly straight simply by returning them (after 

 their first passage through a series of prisms arranged for mini- 

 mum deviation) by a direct reflection from a plane mirror ; and, 

 further, that this has been accomplished in a spectroscope in con- 

 struction for the Royal Observatory. 



Such a statement has, as might be expected, produced several 

 inquiries ; in one case the querist is much interested, viz. by having 

 a very large spectroscope in hand which, from its construction, 

 involves the question of straight or curved lines resulting. It 

 therefore seems desirable to remove any illusion which may be 

 entertained, by a short consideration of the economy of the spec- 

 troscope, so far as the question of curvature is concerned. 



The curvature of the spectral lines may be considered a function 

 of the dispersion of a prism ; it (the curvature) not only always 

 accompanies the dispersion, but, further, its character is always 

 the same with respect to the dispersion — that is to say, the centre 

 of curvature will be found invariably to lie in the same direction 

 with respect to the direction of the dispersion, the lines being 

 invariably concave towards that end of the spectrum having the 

 more refrangible rays*. This (which admits of the clearest proof) 

 is adequate to show the impossibility that, by any kind of inver- 

 sion, whether by reflections or otherwise, we can neutralize the 

 curvature while doubling the dispersion. 



If we examine the spectrum, as produced by a series of prisms 

 placed in the position of minimum deviation, we necessarily find 

 that the lines of higher refrangibility, also their centres of cur- 

 vature, lie towards the centre of the polygon which the prisms 

 themselves affect ; and if we arrest the rays at any part of the 

 circuit, and reflect them directly back by a plane mirror, this 

 reflection reverses (right for left) not only the direction of the 

 centre of curvature of the lines, but also the direction of the spec- 

 trum itself, both which are consequently doubled in amount after 

 the rays have performed the second, or return, passage through 

 the prisms ; or (conversely) if, after the first passage through the 

 prisms, we reflect the rays so as to pass through a similar set in 

 such manner as to neutralize the curvature of the first set, we 

 shall find the resulting dispersion reduced to zero. 



The writer of the article having alluded to a difference between 

 the reflection as given by a plane mirror and a prism of (double) 

 total reflection, it may be observed that, so far as the dispersion 

 and curvature are concerned, the cases are practically identical, 



* Professor Stokes has indeed investigated a form of compound prism in 

 which the resulting lines are straight, and on the same principle we may com- 

 bine prisms (using of course media of different optical powers) in which, with 

 a balance of dispersion remaining, the curvature might be found reversed ; but 

 this does not affect the general law. The curvature in that compound prism 

 (which was the result of various trials, and first used in the spectroscope of the 

 Great Melbourne Telescope, and now, I apprehend, in pretty general estimation 

 and use) probably has a less proportional curvature of the lines than the simple 

 prism. 



