110 
Proceedings of the Royal Irish Academy. 
glass be in tlie form of a prism the pendulous undulations correspond- 
ing to the successive terms of series (4), will emerge in different direc- 
tions, so that each will give rise to a separate line in the spectrum of 
the gas. 
We thus find that one periodic motion in the molecules of the 
incandescent gas may be the source of a whole series of lines in the 
spectrum of the gas. The n*^ of these lines is represented by the term 
Cn sin {n X a„), 
in which (7„ is the amplitude of the vibration, and, consequently, Cn 
represents the brightness of the line. If some of the coefficients of 
series (4) vanish, the corresponding lines are absent from the spec- 
trum. This is analogous to the familiar case of the suppression of 
some of the harmonics in music, and appears to be what usually occurs 
in those spectra which are called by Plticker, spectra of the Second 
Order. 
In spectra of this kind the lines which fall within the limits of the 
visible spectrum appear, at first sight, to be scattered at irregular in- 
tervals. This may arise, and probably does in most cases arise in 
part, from the circumstance that there may be several distinct motions 
in each molecule of the gas, each of which produces its own series of 
harmonics in the spectrum, which by their being presented together 
to the eye give the appearance of a confused maze of lines. But it 
appears also to arise in part from the absence of most of the harmonics, 
so that it is not easy to trace the relationship between the few that 
remain. To do so, without the assistance of spectra of the First Order, 
requires that we should have at our disposal determinations of the wave- 
lengths of the lines, made with extraordinary accuracy ; and perhaps, 
in a few cases, as, for example, in the case of Hydrogen, the marvellous 
o 
determinations which have been made by Angstrom, may have the re- 
quisite precision. 
The ordinary spectrum of Hydrogen consists of four lines corres- 
ponding to (7 in the solar spectrum, F, a line near G, and ^. To 
these it is possible that we ought to add a conspicuous line in the solar 
prominences, which lies near D, but which has not yet been found in 
the artificial spectrum of Hydrogen. Of these lines, three, viz. : C, 
F, and h, are to be referred to the same motion in the molecules of the 
gas. 
o 
In fact, the wave-lengths of these lines, as determined by Angs- 
trom,^' are — 
h =4101-2 tenth-metres. 
4860-74 „ 
a= 6562-10 
These are their wave-lengths in air of standard pressure, and 14* 
temperature, determined with extraordinary precision. We must cor- 
rect these for the dispersion of the air, so as to arrive at the wave- 
* Angstrom's " Recherches sur le Spectre Solaire," p, 31. A tenth-metre means 
a metre diyided by 10^<^ similarly a fourteenth-second is a second of time divided by 
101*. 
