290 THE ROYAL SOCIETY OF CANADA 



point may also be found by interpolation with precision using the 

 standard method of finding the abscissa corresponding to a maximum 

 ordinate. 



The curves of Fig. 3 show these maximum positions. It will be 

 seen that as D increases the maximum point moves downward toward 

 the spectral region of shorter wave-length and there are very great 

 changes in the value of n^ax- In fact, on Fig. 3 the maximum points 

 actually plot out a curve showing the relation between the dispersive 

 power and the wave-length since the ordinates of these points are 

 proportional to the powers. In Table 1 are shown the values or 

 the maximum orders corresponding to the various plates, together 

 with the corresponding wave-lengths and dispersive powers, and 

 the relation between the last two are illustrated by Fig. 4. 



6. The values of the dispersive powers permit a test of the ap- 

 plicability of the various dispersion formulae. Assuming that the 

 principal absorption line of the glass is in the extreme ultra-violet the 

 Lorentz-Lorenz dispersion formula may be written 



^2- 1 ^ V X2 / 



Differentiating in order to introduce the dispersive power in which 

 this paper is particularly interested, 



d\ SA 



Hence one may test out the formula in terms of the numerical values 

 shown by plotting 



-M ^ /(/^'-l)' against 1/X^ 



with the expectation of obtaining a straight line. This curve is 

 plotted in Fig. 5 and shows a slight but definite deviation from the 

 rectilinear. 



7. Consider rays traversing the interference system parallel to 

 the vertical plane but making a small angle a v/ith the mirror normals. 

 From Fig. 2 it may be seen that such rays are focussed at a point on 

 the spectrum distant aff'/f from the central element so that this is 

 the y co-ordinate of such point referred to the central element as axis. 

 X is a function of the x co-ordinate which may conveniently be written 

 X. Let us examine the distribution of the interference fringes in the 

 plane of the spectrogram. 



For the rays above specified the difference of path introduced on 

 account of the distance D/2 is D cos a/X wave-lengths and on account 

 of the insertion of the glass plate T sin {a — b)/X sin b. 



