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owing to what has been said above, I do not propose to inflict the 
formula or any particulars regarding it upon you. With regard to 
“Table B,” I have been partially successful, to the extent that out of 
the 34 lines calculated, only 4 contain an error in the fourth decimal 
place, while 27 have it in the fifth, and the remaining 3 in the sixth. 
Of the four which have an error in the fourth decimal place, it only 
amounts to a single unit in three of them. Now, considering the 
wobbles that are known to exist in these curves, the above results 
cannot he called altogether had. (See last Table.) 
To compare my formula with that of Cauchy, I worked out one 
line in one of the curves most free from wobbles, and the error came 
out in the third decimal place, and was 44 times greater than that 
given by my formula. 
Cauchy’s formula was used in the same way as mine, viz. for 
extrapolation, but four lines, B, C, D 2 , and E, were required to be 
known as against the C and D 2 in my formula. The time the sum 
took to work out was unfortunately not noted, but it took probably 
nearly as long to calculate the one line by Cauchy’s formula as it did 
the whole 34 by my formula. 
It may here be stated that my formula has been tried neither 
on fluid media nor on mineral substances, and it is quite impossible to 
foretell how it would work, as the curves of some fluids and minerals 
are of a very peculiar nature, and have little in common with those 
of glasses ; but I have confined my investigations solely to Dr. Hop- 
kinson’s two tables, which are distinguished in this paper by the letters 
A and B. 
The construction of a dispersion formula is a matter of extreme 
difficulty, and the examination, collation, and arrangement of a vast 
number of abscissas values of the curves, which take up a considerable 
amount of time, are merely preliminary stages of the business. 
It now only remains for me to give you the formula, by which the 
refractive indices of the lines B, E, F, G', and TC were calculated, 
when those of C and D 2 were given. The results of the work are 
tabulated, a list of the errors given in the last Table, and a copy of 
Dr. Hopkinson’s “ Table B ” is appended for reference. 
The subjoined fig. 26 exhibits the curve of the glass “Dense 
flint,” and shows the method of the calculation. The ordinates are 
the reciprocals of the wave-lengths (tenth-metres), multiplied by 1000 
for the purpose of eliminating the cyphers ; the abscissae are the re- 
fractive indices ; the straight oblique line is the C D 2 ratio, from which 
the curve departs as w r e proceed higher up the spectrum (towards the 
blue). Z is the distance between this oblique line and the D 2 line, 
which, of course, runs parallel to the ordinate; y ought to be the 
exact distance of the curve from this oblique line, and the tabulated 
error (last Table) shows the excess or default of this quantity. 
Fig. 26 is inserted merely to pictorially illustrate this subject. 
I may, however, state that graphic tracings of the curves were not 
employed in the construction of the formula ; for if they were of suf- 
