28 Refracted and Diffracted Spectra. (January, 
At present, however, the observations are neither so 
numerous nor so correct as to admit of the determination 
of the law with perfect accuracy. It is nevertheless possible, 
by taking advantage of the observations as they exist, to 
determine the manner in which the exponent varies with 
such a degree of correctness as may be found available for 
practical purposes. 
The following investigation has been based on a care- 
ful comparison of Angstrém’s Atlas of the Diffracted 
Spectrum, and his Relative Tables of Wave-lengths, with 
the Maps and Indices of the Refracted Spectrum, by 
Kirchhoff, Hofmann, Angstrom, and Thalén. 
To find the value of the exponent « for any three lines, of 
which both the positions in the index of the spectroscope 
and the corresponding wave-lengths are approximately 
ascertained by observation, is a little troublesome; because 
it can be done only by the method of gradual approximation, 
or trial and error. It therefore becomes of importance to 
have the value of « determined and tabulated for every 
1o° of Kirchhoff’s scale; because the value of « being known, 
the calculation of the wave-length from the general formula 
becomes easy. Such a table must proceed on the assumption 
that the vate of variation of the value of e remains nearly 
uniform for 10° of Kirchhoff’s scale; and although this 
assumption cannot be said to be absolutely correct for every 
Io’, yet it is so nearly accurate as to be practically available. 
For the purpose of framing such a table, it is convenient 
to assume the extreme lines A, and the more refrangible H 
of the speétrum as constants; so that, in the formula, the 
quantities x, z, and y may be always the same. ‘Then if 0, 
the index position in the spectroscope of any line, be given, 
its corresponding wave-length y may be found by means of 
the tabular value of « in the region where 0 is situated. It 
is further convenient to assume the value of z to be 10, and 
to determine the wave-lengths, in the first place, in relation 
to this basis, converting them afterwards into the millimetric 
scale of Angstrém. By this method we have always 
e=log. x, which is a facility in calculation. 
The assumed position of Ain Kirchhoff’s scale is 404°5, 
and of the more refrangible H 3882'5, the difference being 
3478=r in the formula. Then the value of p is always 
= b—404'5, and that of g=3882°5—b. The log. of the wave- 
length x in relation to z is 1°2863197, and the log. of that 
log. is 0*1093490, which is one of the constants in the 
calculation. ‘The log. of y is 3°5413296, and is another 
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