43 ■ REPORTy-1870. 



periodic time of the original disturbance, and the rest having periodic times which 

 are submultiples of this. Thus, if T be the periodic time of the origuial motion 

 in the gas, we are at liberty to regard the undulation, whilst traversing the open 

 ffither, as consisting of a multitude of coexisting pendulous undulations with pe- 

 riods T, JT, gT, &c. So long as the motion is propagated through undispersing 

 aether, the waves of all lengths travel at the same speed. The component imdula- 

 tions therefore strictly accompany one another; and accordingly the resultant 

 general undulation maintains whatever complicated form it may have had at first. 



But if the light enter a dispersing medium, such as glass, an entirely new 

 state of things arises. In glass, waves of different lengths travel at unequal velo- 

 cities. Each pendulous undulation will accordingly proceed across the glass at 

 a rate determined by its own special periodic time. In this way the component 

 undulations part company, and if the glass be in the shape of a prism they will 

 emerge in different directions ; each giving rise to a distinct line in the spectrum 

 of the gas. It thus appears that one of the periodic motions in the molecules of a 

 gas will iu general be the source of several lines in its spectrum, and that all the 

 lines thus arising from one original motion will have periodic times which are 

 terms of the harmonic series T, 5T, jT, &c. ; T being the periodic time of that mo- 

 tion in the gas to which they are all due. 



Moreover it farther appears from the structure of Fourier's theorem, that the 

 form of the original disturbance will determine whether all the harmonics exist, or 

 only some of them. Where only some at irregular intervals exist, we have lines of 

 a spectrum of the Second Order ; where all or a long series of consecutive harmonics 

 exist, we have the beautiful spectacle of one of the fluted series in specti-a of the 

 First Order. The fluted appearance is due to the varying brightness of the suc- 

 cessive lines, or, in other words, to the values of the coefficients of the successive 

 terms of Fourier's series, which again depend on the character of the original dis- 

 turbance. Drawings were exhibited of the patterns of the flutings which would 

 result from various simple hypotheses as to the original disturbance ; and some of 

 these drawings bore a striking general resemblance to patterns which occm* in 

 nature. 



Sufficiently detailed observations on spectra of the First Order have not yet been 

 made fully to test this theory or afford materials for its application to the various 

 inquiries of interest which it suggests ; and Mr. Stoney was engaged in endeavouring 

 to supply this want. Meanwhile it may be observed in general that the closeness 

 of the ruling in spectra of the First Order indicates that the lines are very high 

 harmonics of relatively slow original vibrations — vibrations which in many in- 

 stances correspond to wave-lengths of more than a milUmetre in length, and conse- 

 quently have a periodic time of several twelfth-seconds (the Xllth-second meaning 



—— of a second of time). 



In the case of nitrogen, two systems of lines giving fluted columns have been 

 observed — one at the red end of the spectrum, formed oy lines very closely packed 

 together, the other at the blue end of the spectrum, consisting of lines more widely 

 spaced. Pliicker coimted 34 dark lines (i. e. 35 bright hues) in one of the blue 

 flutings, viz. that one which lies to the left of the letter C in his diagram (Phil. 

 Trans, for 1865, plate 1). Judging from the diagram, this fluting would seem to 

 extend about from wave-length 44'8 to 4o'6 eighth-metres. If so, we may con- 

 clude that the 35 bright lines of graduated intensity of which it consists are from 

 about the 1960th tip to the 1995th harmonics of a wave-length of about 0-89376 of 

 a millimetre. This wave-length corresponds to about 3 Xllth-seconds of time, 

 which may accordingly be regarded as a rough approximation to the periodic time 

 of the motion iu the molecules of nitrogen by which the blue flutings are occa- 

 sioned. 



When lines of spectra of the Second Order are the result of motions iu a gas so 

 slow as this, it would not be practicable to determine the periodic times of the ori- 

 ginal motions from observations upon spectra of this kind ; for in this case the 

 harmonics, if the positions of all of them were laid down on a map of the spectrum, 

 would be so crowded together that it would be difficult to determine with certainty 

 to which of them a line of a spectrum of the Second Order should be referred. Per- 



