The Position of the Bands in Spectra. By II. C. Sorby. 271 
exactly the same as at first. Supposing then that when the circle 
is placed at zero an absorption hand seen in some spectrum were 
situated between the bands 3 and 4 of the scale, as shown by II of 
Fig. 2, by rotating the circle the baud 3 can he made to pass 
upwards until its centre exactly corresponds with that of the hand 
whose position is being measured, as shown by III, and if this 
occurs when the point used for reading off is at ’54 of the circle, 
we at once know that the true position is 3 '51. In a similar 
manner the situation of bands in any other part of the spectrum, 
can he referred to other bands of the scale. 
If it were necessary only to compare one spectrum with another, 
this alone would suffice ; bat, as I pointed out in a paper read before 
this Society last Aporil, it is very desirable to express everything in 
wave-lengths. In order to do this a table must he constructed, 
giving them in millionths of a millimeter for each tenth of a 
division between all the hands. For this purpose it is necessary to 
employ a diffraction spectroscope and strong illumination. I first 
made use of direct sunlight, hut the movement of the light was 
found to be very inconvenient, and to cause some uncertainty in 
the measurements. I therefore finally adopted the results obtained 
by using a limelight, since it could be fixed in a proper position 
and kept immovable during all the measurements. The angle of 
the inclination ( 0 ) of the telescope hearing the eye-piece with cross 
wires was read off to half-minutes of a degree in the case of all the 
bands. If two measurements differed by more than I-', other observa- 
tions were made, and the mean of all adopted. This was repeated for 
each Toth division of the ivory circle of the apparatus, since other- 
wise the irregular action of the quartz on light of different wave- 
lengths would have given rise to serious errors. All the calculations 
were based on the wave-length of the centre of the two principal 
sodium lines (D), which, according to both Angstrom, Huggins, 
Kirchhoff, and Thalen, is 589 • 2 millionths of a millimeter. The 
diffraction grating used was a photograph, for which I am indebted 
to the kindness of Lord Eayleigh, which by calculation must con- 
tain 6003 lines in a French inch, and the distance between each 
two lines must be ‘004509 millimeter. The wave-lengths were 
calculated by means of the following equation : 
X = '004509 sin. 0 , 
since I made use of the spectrum of the first order. On the whole, 
I think the results may he looked upon as true to a millionth of a 
millimeter. 
Of course it must be borne in mind that these measurements 
apply only to the quartz exactly H inch in thickness, cut and 
mounted exactly in the proper direction. 
u 2 
