170 Prof. S. P. Langley on 



curve is approaching a straight line is that, unless there is 

 some immediate change in its character, such as we have no 

 right to expect, extrapolation considerably beyond the point 

 to which we have measured will be comparatively easy and 

 safe. I am aware of the danger attending all extrapolation, 

 but I must insist upon the fact that the old ones, which we 

 have seen falsified by experiment, rested on an extremely 

 limited region of the curve, that namely for the visible region 

 of the spectrum, in which the relation between n and \ is also 

 wholly different ; while those on which we now briefly enter 

 depend upon far greater material for induction (about eight 

 times that included in the visible spectrum), which we can 

 also use under much more favourable conditions. 



Since the curve still presents a slight convexity to the axis 

 of abscissae, unless its character changes in a way which we 

 have no ground to expect, a tangent at any point will meet 

 that axis sooner than the curve itself will. Accordingly, if 

 we now ask what wave-length corresponds to any point in the 

 hitherto unexplored region, for instance the maximum in the 

 spectrum of boiling water, whose index * for the 60° rock-salt 

 prism is 1*5145, or that of melting ice, whose index is 1*5048, 

 we can answer as follows : first, this unknown wave-length 

 is at any rate greater than 5""3, since to this point we have 

 investigated by direct measurement; second, since the tangent 

 to our curve, even at the point 5^ meets the line correspond- 

 ing to the index of the maximum heat in boiling water at 

 over 7^, and a line corresponding to the maximum ordinate 

 in the spectrum of melting ice at over 10 , and since the 

 curve without some change in its essential character cannot 

 meet these lines, save at still greater wave-lengths, it follows 

 that the wave-length of the maximum of the spectrum from 

 boiling water is probably at least *0075 millim., and that of 

 the maximum in the spectrum from melting ice is over O'Ol 

 millim. In an article in the Comptes Rcndus of the In- 

 stitute of France, Jan. 18, 1886, and in preliminary memoirs, 

 we deferred giving the actual values, but gave (explicitly as 

 minimum values which we believed much within the truth) 

 5^ to 6*\ That our caution led us to understate ihe, even 

 then, most probable value, may be seen from the statements 

 just made, which are founded on still later observations. 



As we proceed further out, extrapolation becomes, of 

 course, more untrustworthy. We can only say that if the 

 curve maintains its present inclination to the axis of X, the 

 wave-lengths of the extreme radiations recognized in the 

 rock-salt prism must indefinitely exceed 0'03 millim. 



* See this Journal for May 1880, plate iv. fig. 3. 



