The President's Address. By E. M. Nelson. 
133 
There is another dispersion formula, by Watts ; it also is tedious to 
work out, and it is not more accurate than that of Cauchy ; space, 
however, does not permit me to enlarge further upon it. 
I have designed a new dispersion formula which, although not 
absolutely accurate, gives better results than either of the preceding ; 
it is only suitable for extrapolation, but it requires only two refractive 
indices to be known ; further, the work required is not a tithe of the 
former. 
In the ‘ Proceedings of the Eoyal Society ’ for June 1877, the late 
Dr. J. Hopkinson gives two tables of the refractive indices of seven 
of Messrs. Chance’s glasses, the v values of which vary from about 
60 to 30. The measurements of these glasses were made with a 
spectrometer constructed by Mr. Howard Grubb; the objectives of 
the collimator and telescope were of 2 in. aperture, and the arc 15 in. 
diameter, divided to 10', reading * by two verniers to 10". The first 
Table, which we will call “ Table A,” contains the “most probable 
value of ya,” according to Dr. Hopkinson’s views ; this may, however, 
be termed a hotch-potch, because the values are partly observed, partly 
calculated by Cauchy’s formula (lines B, F, and H being used), and 
partly graphically interpolated. The second “ Table B,” which to my 
mind is one of the most valuable tables published, contains the values 
of /x to 6 places of decimals, as observed by the spectrometer. The 
first five glasses had three angles measured, the sixth one, and the 
seventh two (the H line in the seventh glass not being given). 
Therefore, as regards the first five glasses in “ Table B,” we have pro- 
bably the most accurate list of refractive indices in existence, f 
Notwithstanding the great weight which must be attached to any 
opinion issuing from so eminent a physicist as Dr. Hopkinson, you 
will probably agree with me that the value of “ Table A” stands or falls 
with the accuracy of Cauchy’s formula. Now, since the publication of 
“ Table A,” Cauchy’s formula has been shown to be wholly unreliable ; 
this both Mr. Gifford, whose excellent spectroscopic work is well 
known, and I, have on more than one occasion verified ; consequently 
the importance of “ Table A ” is considerably diminished. 
Perhaps it ought to be explained that the raison d’etre for 
“ Table A ” is to round off the wobbles in the curves in “ Table B ” 
arising from instrumental and other errors. 
The problem I set myself was to construct a formula that, while 
not laborious to work out, would, when the refractive indices of C 
and D 2 were given, enable one to calculate those of B, E, F, G', and 
H x without an error appearing within 4 decimal places. 
With respect to “ Table A,” I have been completely successful, but, 
* It should be noted that an error of + 10'' in the measurement of a deviation of 
40°, when the angle of a 60° prism is accurately known, will occasion an error in the 
refractive index of + *000031; and an error of + 10" in the measurement of the 
above prism, when the deviation is coirectly known, will give an error in the refrac- 
tive index of — *000033. 
f This valuable “ Table B ” has somehow been overlooked by all writers, while 
“ Table A ” has been frequently quoted. 
