1877.] 



Magnifying-power of the Half-prism. 



25 



In considering the most advantageous combination of prisms in a spec- 

 troscope, it will be necessary to bear in mind the different purposes for 

 which the instrument is used. The requirements in a spectroscope may 

 thus be divided into the following heads :-— 



(1) Wide separation of the lines, with little loss of light and moderate 

 purity in the spectrum. 



(2) Great purity in the spectrum. 



(3) Wide separation of the lines accompanied by considerable purity. 

 In (2) and (3) loss of light is of secondary importance. Tor measuring 



the displacement of lines in the spectra of stars and work of a similar 

 character (1) must be specially considered ; and here the width of the slit 

 is determined by the size of the star's image rather than by the angle 

 subtended at the object-glass of the collimator. With prisms of fair size 

 sufficient purity will usually be obtained for measurement of the strong 

 lines without limiting the slit further ; the most important point is large 

 aperture in the equatoreal, as the amount of light collected varies with 

 the aperture. This will readily be seen by considering that the angle 

 subtended by the diffraction image of a star at the optical centre of the 

 object-glass (or mirror) varies inversely as the aperture ; hence for prisms 

 of a given size the purity of the spectrum will be the same for all aper- 

 tures, if the focal length of the collimator correspond. 



For a bright-line spectrum, such as that of the solar prominences, which 

 is seen projected on the continuous spectrum of the sky and of which the 

 visibility depends on the contrast with the background and not on the 

 absolute brightness, (2) is of the greatest importance; whilst special 

 attention must be paid to (3) in the case of the sun. 



We may compare three arrangements of prisms : — (1) Half-prisms mag- 

 nifying ; (2) Half-prisms diminishing ; (3) Whole prisms ; but in doing 

 this we must take account of the width of the slit and the breadth of the 

 pencil as determining the purity of the spectrum and its brightness. At the 

 same time, as the size of the prisms practically fixes the limit to the power 

 of the spectroscope, the quantity of glass used in the different cases should 

 also be borne in mind. This latter consideration is important, because in 

 a train of half -prisms magnifying the breadth of the pencil is diminished 

 in the ratio 1 : m with each half-prism (the height remaining unaltered), 

 and the reverse takes place with a train of half -prisms diminishing. Thus 

 in both cases the half-prisms may be made narrower and narrower in 

 geometrical progression, starting with that end which begins with a per- 

 pendicular face. The difference between the two cases is, that in the first 

 case the train (counting from the slit) begins with the broadest prism, and in 

 the second case with the narrowest, so that with the latter arrangement 

 we have a narrower pencil and consequently less light. In the case of a 

 train of whole prisms the pencil is narrower than for the half-prisms 

 magnifying, in the ratio of 1 : m. The thickness of the glass through 

 which the rays pass is another important consideration ; and from this 

 point of view the half-prism train has a great advantage. The breadth 



