168 Prof. S. P. Langleyorc 



>2 M i -v2> 



/l , ,n 2 , n 4 , 7 X 2 \ 



to the four points 



A(\=O-7601, 72=1-53670), 

 D 2 (X= 0^5889, n = P54418), 



^(X= 0^-5183, 7i = l-54975), 

 H 1 (X,= 0^-3968, 7i=l-56833); 



and the formula of Wullner, 



(rf-i--.p* + « s *A 



to the three points 



A(X=0"-7601, 71 = 1-53670), 



^(XzzzO^-5183, 7i = l-54975), 



H!(X= 0^-3968, n = 1-56833). 



All these are in the visible spectrum, and from them the 

 constants a, b, c, k, P, &c. are determined. With their aid 

 we next inquire by the formula what wave-lengths correspond 

 to certain given indices, and the resultant values in the infra- 

 red are then plotted from these computations. It is, however, 

 only just to observe that the wide departure from observation 

 here shown is by no means to be wholly attributed to error 

 in the formula ; for minute errors of measurement, such as are 

 always present even in the observations in the visible spec- 

 trum, are immensely exaggerated by extending the curve 

 through extrapolation. Wiillner's formula, for instance, 

 would give a line closely coincident with our curve in the 

 infra-red if we took all our points for computation from that 

 part of the spectrum. A similar remark may be made of 

 Briot's equations, whose actual tracing, however, with the 

 constants we obtain from the visible spectrum, shows that 

 beyond a certain point the curve, which is its geometrical 

 representation, from being concave to the axis of X, becomes 

 convex, so that the relation between n and X would, according 

 to it, be represented by a sinuous line ; and this is not so 

 within the limits of these observations. Its fair agreement 

 with observation, then, within the limits of the visible spectrum 

 and the upper part of the solar infra-red are all that can be 

 claimed for it. Our conclusion is that all theories of disper- 

 sion known to us prove inadequate to predict the relation 

 between wave-length and refraction. The actual relation 

 from direct investigation is here given for the first time from 

 the observations of the past year, which, it will be seen, thus 



