20 



REPORT — 1859. 



are slightly increased, and others slightly diminished in rapidity, beyond what they 

 would otherwise be. 



In conclusion, the attention of the British Association is invited to the unsatis- 

 factory state of a considerable number of the observations, and to the necessity of 

 having these repeated, and the whole series further extended, more especially the 

 observations on the same medium at different temperatures. 



List of Tables presented by the author in illustration of the paper. 



Tabli 



I. Elements of Calculation. 



II. Internal wave-lengths calculated from the observed Indices of Re- 

 fraction. 

 Internal wave-lengths freed from the Extrusions. 

 The Extrusions. 

 Logarithms of the wave-lengths of the fixed lines for each exponent 



from 1 to 3'5. 

 Indices of Refraction calculated from the Exponential Law. 

 Observed Indices of Refraction. 

 VIII. Differences between observed Indices and those calculated by the 

 Exponential Law. 

 IX. Differences between observed Indices and those calculated by the 

 law of M. Cauchy, with comparison of results. 



III. 



IV. 



V. 



VI. 



VII. 



On the Law of the Wave-lengths corresponding to certain points in the 

 Solar Spectrum. By Mungo Ponton, F.R.S.E. 



This paper commences by tracing, to their basis, the numbers given by Sir Isaac 

 Newton to express the wave-lengths corresponding to the borders of the coloured 

 spaces of the spectrum. There is first obtained, by geometrical construction, the 

 primary series 1-2857, 1*1428, 1-0714, 0-9643, 0*8571, 07714, 07232, 06429, the 

 length of the mean wave being = 1. Of these numbers the cube roots of the squares 

 are taken, giving the series 1-1824, 10931, 1-0470, 0-9761, 0-9023, 0*8411, 0-8057, 

 0-7449. The length of the mean wave being experimentally ascertained to be 

 0-00002247 decimal parts of an English inch, the Newtonian wave-lengths are 

 found by multiplying the second of the above series by this quantity. They stand 

 thus : 



0-00002657 \ 



Red 



Orange 



Yellow 



Green 



Blue 



Indigo 



Violet 



0-00002456 



0-00002353 



0-00002193 



0-00002028 



0*00001890 



0-00001812 



0-00001674 ) 



This is the estimate usually given of 

 these wave-lengths, in the English 

 works on Optics. 



The two series given by Fraunhofer to express the wave-length corresponding to 

 his seven principal fixed lines, are then stated in decimal parts of a French inch, as 

 under : — 



I. B 0-00002541, C 0000024-25, D 0-00002175, E 0'00001943, F 0-00001789, G 0-00001585, H 000001451 



II. 2141 2422 2175 1945 1794 15&7 1464 



+ 3 -2 -5 -2 —13 



It is mentioned that the only approach to a law regulating these numbers, hitherto 

 ascertained, is an approximation, in the second series, to the relation 



