IV. An Inquiry into the Cause of the Interrupted Spectra of Gases. Part II. On the Absorption-spectrum of Chlorochromic Anhydride. By G. JOHNSTONE STONEY, M.A., F.R.S., Secretary to the Queen's University in Ireland, and J. EMERSON REYNOLDS, M.R.C.P.E., Keeper of the Mineral Department, and Analyst to the Royal Dublin Society*. Section I. Introductory. CONTENTS. Section II. On the periodic time of one of the motions in the molecules of Chlorochromic Anhydride. Section III. On the character of this molecular motion. 1. ONE of SECTION I. Introductory. NE of the authors of this communication endeavoured+ in 1867 to call attention to the circumstance that wherever the spectrum of a gas consists of lines of definite wavelengths there must be periodic motions in the gas, and that motions of this kind can exist only within the individual molecules of the gas; and more recently he has pointed out that from each periodic motion there will usually arise several lines, and that the lines which thus result from one motion will have periods that are harmonics of the periodic time of the parent motion. 2. In our endeavours to bring this theory and its various consequences to the test of observation, we commenced with absorp tion-spectra, for the examination of which the apparatus at our immediate command was best suited. The apparatus consisted mainly of the great Grubb spectroscope of the Royal Dublin Society, and of the appliances in the laboratory of the Society for keeping up an abundant supply of the oxhydrogen lime light. 3. The chief obstacles we anticipated were those that arise from the extreme closeness with which the lines are often found to be ruled, and those to be expected from the complexity of spectra; for usually lines belonging to several distinct systems are presented together to the eye within the same field of view, and this makes an apparently confused maze of lines, from which it is difficult to pick out those that are to be referred to any one motion in the gas. Accordingly, as a preliminary step, * Communicated by the Authors, having been read before the Royal Irish Academy, June 12, 1871. + Phil. Mag. vol. xxxvi. (1868) p. 132. Phil. Mag. vol. xli. (1871) p. 291, and Proceedings of the Royal Irish Academy of January 9, 1871. Report of the British Association for 1870, p. 41. we looked at several of the absorption-spectra of coloured vapours, to see whether amongst them we could find one in which there is a system of lines which we might hope to refer to a single motion in the molecules of the vapour, free from lines emanating from other motions in the molecules of the vapour, and sufficiently separated from one another to be easily measured. A few days after we commenced operations we were so fortunate as to meet with the object of our search. The brown vapours of chlorochromic anhydride (Cr O2 C12) when interposed between the lime-light and the spectroscope gave a spectrum of the requisite simplicity. 4. In order to test that part of the theory which indicates that the periodic times of the wave-vibrations of the several lines are harmonics of one periodic time, we find it convenient to refer the positions of all lines to a scale of reciprocals of the wavelengths. This scale of inverse wave-lengths has the great convenience for our present purpose, that a system of lines with periodic times that are harmonics of one periodic time will be equidistant upon it: it has also the minor convenience that it much more closely resembles the spectrum, as seen, than the scale of direct wave-lengths used by Angström in his classic map. Upon our scale the inverse wave-length 2000 corresponds to Angström's direct wave-length 5000. The numbers which Angström uses are tenth-metres, i. e. the lengths obtained by dividing the metre into 1010 parts; and from this it follows that each number upon our scale is the number of light-waves in a millimetre: thus 2000 upon our scale means that the corresponding wave-length is 2006 of a millimetre. Now, if k be the inverse wave-length, expressed upon our scale, of a fundamental motion in the æther, its direct wave-length will be th of a milli 1 1 1 2k' 3K &c. metre, and its harmonics will have the wave-lengths Accordingly the inverse wave-length of the nth harmonic will be Hence it is easy to see that a system of harmonics which are equally spaced along our scale at intervals of k divisions are harmonics of a fundamental motion whose inverse wave-length is k, 1 whose direct wave-length is th of a millimetre, and whose pe T k riodic time is where is the periodic time of an undulation in k' the æther consisting of waves one millimetre long. If we use Foucault's determination of the velocity of light, viz. 298,000,000 metres per second, the value of this constant is meaning by a twelfth-second a second of time divided by 1012, which in other words is the millionth part of the millionth of a second of time. SECTION II. On the periodic time of one of the motions in the molecules of Chlorochromic Anhydride. 5. We generally made use of the vapour of chlorochromic anhydride mixed with air, and at the temperature and pressure of the atmosphere. We tried the vapour freed from air, and also at somewhat higher temperatures; but in neither case did we observe any marked difference in the spectrum. An image of the lime-light was formed on the slit of the spectroscope by a condensing-lens of about 30 centims. focus, and of such a size that the whole of the collimating-lens was filled with light*. The column of chlorochromic vapour, if not too long†, was placed between the condensing-lens and the slit. The spectrum which then presents itself consists of a number of sensibly equidistant dark lines in the orange, yellow, and green. In the orange these lines fade away and leave part of the orange and the red unsubdued by lines. In the other direction the lines are gradually lost in an increasing obscuration of the spectrum, which entirely blots out the more refrangible colours. The lines are nowhere sharply defined or narrow, nor are the spaces between them devoid of duskiness; and the region of general absorption, which occupies the more refrangible part of the spec *This is a condition which is essential to making good measures. If only a vertical strip of the collimating-lens is supplied with light, the beam belonging to one line in the spectrum reaches the image in the observingtelescope as a thin wedge of light, upon which the eye does not readily focus itself. Under these circumstances the eye keeps continually altering its adjustment, feeling about for the right distance; and if the strip of light has not passed exactly centrally through the instrument, this causes the image of the line to appear to deviate in various degrees from its true position, accordingly as the adjustment of the eye fluctuates. + We used columns of various lengths, varying from 4 to 80 centims. From 15 to 20 centims. is a good average length. By increasing the length, the lines in the yellow and orange become more conspicuous; and by diminishing it the lines in the green are better seen. With the longest column we were obliged to place two condensing-lenses at the ends of the tube, one to send the light from the lime-light in a parallel beam along the tube, and the other to condense this parallel beam into an image upon the slit of the spectroscope. See further on, § 22. trum, seems to consist simply of lines of the same series so widened out that they are blended into one mass. 6. For the convenience of reference we have numbered the lines from a conspicuous one which happens to fall between the two D lines, nearer to the more refrangible one. There are 106 lines, counting from this line inclusive to a point somewhat beyond b; and we have measured the deviations of 31 of these in a spectroscope giving a dispersion from A to H of about 24°. We have from these measures deduced the inverse wave-lengths by a comparison with the deviations of forty lines of iron, copper, zinc, and sodium, extending over the same range of the spectrum, of which the wave-lengths in air are recorded by Angström and Thalen. The interpolation has been effected by a graphical method; and our measures in no case, when repeated, differed by one minute of arct. 7. The first column of the following Table gives the numbers of the several lines which we measured, reckoned from that line which lies between the two D lines. The second column gives the observed positions of the lines upon a scale of inverse wavelengths in air, viz. upon a scale of the reciprocals of Angström's wave-lengths, which are wave-lengths in air of standard pressure and 14° temperature. The third column contains the corresponding positions upon a scale of inverse wave-lengths in vacuo, obtained by applying to the numbers of column 2 the corrections for the dispersion of air at 760 millims. pressure and 14° temperature, deduced from Ketteler's values t. The fourth column gives the calculated positions, on the hypothesis that the lines of the spectrum are equally spaced upon this last scale, as they should be according to our theory. And the fifth column. gives the differences between columns 4 and 3, between the calculated and observed positions. *The zinc-line to which Thalen assigns the wave-length 5745, appears rather to have a wave-length of about 5739. †The measuring-apparatus of the spectroscope has only recently been completed. It is apparent to us that the instrument is capable of measuring deviations even far more accurately than we have yet attempted. This is due to the extraordinary precision with which Mr. Grubb's automatic arrangement returns over and over again to the same position. It has, indeed, almost made of the spectroscope a new physical instrument. See Phil. Mag. vol. xxxii. (1866) p. 336. in air. Differ. No. of positions sponding positions positions ences. line. TABLE I.-Positions of 31 lines of the absorption-spectrum of Chlorochromic Anhydride. Observed Corre- Calcu No. of positions sponding line. lated in vacuo. in vacuo. Differpositions positions ences. Observed Corre- Calcu- in air. in vacuo. in vacuo. The outstanding differences fall within the limits of the errors of observation and interpolation. Our theory is therefore verified in the case of chlorochromic anhydride. 8. The interval between two consecutive lines, which we used in calculating column 4, was 2.70 scaleins, or units of our scale. This value cannot be in error more than one five-hundredth part. Hence the periodic time of the parent motion in the molecules of chlorochromic anhydride, from which all these lines have proceeded, is within one five-hundredth part of T having the signification already assigned to it. T 2.7' 9. Having ascertained k, or the interval between two consecutive lines, we may by equation (1) determine n, or the number of the harmonic. Thus, if the inverse wave-length of our zeroline be 1697.3, and if k be nearly 27, n+1 must be an integer 1697.3 which is nearly = =628 6. The only possible values are 2.7 627, 628, 629, and 630, since any other integers would carry us beyond the errors of observation. And when the measures shall have been made with sufficient accuracy to decide which of these numbers is the true one, it will in turn be possible to fix the value of k with great precision. Thus, if, as is most probable, our zero-line is the 628th harmonic, and if its inverse wavelength in vacuo is 1697-3, then by equation (1) will |