112 
Proceedings of the Royal Irish Academy. 
in this spectrum of Hydrogen. But two other spectra of Hydrogen 
are known to exist, in which there are a great number of lines ; and 
possibly the missing harmonics will be found amongst them when 
their positions shall have been sufficiently accurately mapped down, 
A far more moderate degree of accuracy will suffice in this case than 
was required by the foregoing investigation. 
But it is from the examination of spectra of the First Order that 
the most copious results may be expected. These spectra consist of 
lines ruled close to one another, and presenting in the aggregate the 
appearance of patterns which often resemble the flutings on a pillar. 
When these spectra are more carefully examined it is probable that 
the whole series of lines, occasioning one of the fluted patterns, will 
be found to be the successive harmonics of a single motion in the mole- 
cules of the gas. It may readily be shown that such patterns as are 
met with in nature may in this way arise. Por this purpose it is only 
necessary to make some suitable hypothesis as to the original undula- 
tion impressed by the gas upon the aether. Thus, if the law of 
this undulation were the same as that of the motion of a point near the 
end of a violin string, and of a periodic time sufficiently long, as for 
example, two million-millionths of a second, this undulation, when 
analysed by the prism, would give a spectrum covered with lines, ruled 
at intervals about the same as that between the two D lines, and of 
intensities varying so as to become gradually brighter and then gradu- 
ally fainter several times in succession in passing from line to line 
along the spectrum. These alternations would give a fluted appear- 
ance to the spectrum ; and from appropriate hypotheses as to the original 
vibration all the patterns met with in nature would result. Possibly, 
it may prove to be practicable to trace back from the appearances pre- 
sented within the limits of the visible spectrum to the character of the 
original motion, to which they are all to be referred. But, however 
this may be, it will be easy in a spectrum of this kind, in which we 
have a long series of consecutive harmonics, to determine, at least, the 
period of this motion — and it is in the examination of these spectra 
that the most easily-obtained results maybe expected. But the neces- 
sary observations are, at present, almost altogether wanting. The only 
case in which the author had been able to arrive at any result has been 
in the case of the Mtrogen spectrum of the First Order, observed by 
Pliicker. It would appear from his observations'^' that the more refran- 
gible of the two fluted patterns observed by him is due to a motion in 
the gas having a wave-length of about 0-89376 of a millimetre, which 
corresponds to a periodic time of 3 Xllth-seconds : one of the flutings 
consisting of the thirty-five harmonics from about the 1960th to 
the 1995th. 
This result, however, does not command the confidence which the 
preceding determination of one of the periodic times, in Hydrogen does ; 
but it will suffice to show the character of the much easier investiga- 
tion which has to be made in the case of gases which produce spectra 
of the First Order. 
"Philosophical Transactions" for 1865, p. 7, s. 16. 
