fixed from a mean of at least six independent determinations. with the accuracy stated above.

The reader will perhaps gather a clearer idea of this action if he imagines the map before him hung up at right angles to its actual position, so that a rise in the energy-curve given would be seen to correspond to a deflexion to the right, and a fall, to one to the left; for in this way the deflexions were written down on the moving photographic plate from which this print has been made. The writer was now speaking of the refinements of the most recent practice; but there was something in this retrospect of the instrument's early use which brought up a personal reminiscence which he asked the Academy to indulge him in alluding to.

This was that of one day in 1881, nearly twenty years ago, when being near the summit of Mount Whitney, in the Sierra Nevadas, at an altitude of 12,000 feet, he there, with this newly invented instrument, was working in this invisible spectrum. His previous experience had been that of most. scientific men-that very few discoveries come with a surprise, and that they are usually the summation of the patient work of years.

In this case, almost the only one in his experience, he had the sensations of one who makes a discovery. He went down the spectrum, noting the evidence of invisible heat die out on the scale of the instrument until he came to the apparent end even of the invisible, beyond which the most prolonged researches of investigators up to that time had shown nothing. There he watched the indications grow fainter and fainter until they too ceased at the point where the French investigators believed they had found the very end of the end. By some happy thought he pushed the indications of this delicate instrument into the region still beyond. In the still air of this lofty region the sunbeams passed unimpeded by the mists of the lower earth, and the curve of heat, which had fallen to nothing, began to rise again. There was something there. For he found, suddenly and unexpectedly, a new spectrum of great extent, wholly unknown to science and whose presence was revealed by the new instrument, the bolometer.

This new spectrum is given on the map, where it will be observed that, while the work of the photograph (much more detailed than that of the bolometer, where it can be used at all) has been stated to extend, as far as regular mapping is concerned, to about 1.1", everything beyond this is due to the bolometer, except that early French investigators had found evidence of heat extending to 18". Still beyond that

Ultima Thule, this region, which he has ventured to call the "New Spectrum," extends. It will be found between wavelengths 18" and 5.3" on the map.

The speaker had been much indebted to others for the perfection to which the apparatus, and especially the galvanometer, had been brought. He was under obligations particularly to Mr. Abbot, for assistance in many ways, which he had tried to acknowledge in the volume; but before closing this most inadequate account of it, he would like to draw attention to one feature which was not represented in the spectrum map before them, although it would be found in the book.

During early years the impression had been made upon him that there were changes in the spectrum at different periods of the year. Some of these changes might be in the sun itself. The major portion of those he was immediately speaking of, he believed, were rather referable to absorptions in the earth's atmosphere.

Now these early impressions had been confirmed by the work of the Observatory in recent years, and charts given in the volume would show that (the sun being always supposed to be at about the same altitude, and its rays to traverse about the same absorbing quantity of the earth's atmosphere) the energy spectrum was distinctly different in spring, in summer, in autumn, and in winter. The lateness of the hour prevented him from enlarging on this latter profoundly interesting subject. He would only briefly point out the direction of these changes, which were not perhaps to be called conspicuous, but which seemed to be very clearly brought out as certainly existing. With regard to them he would only observe, what all would probably agree to, that while it has long been known that all life upon the earth, without exception, is maintained by the sun, it is only recently that we seem to be coming by various paths, and among them by steps such as these, to look forward to the possibility of a knowledge which has yet been hidden to us of the way in which the sun maintains it. We were hardly beginning to see yet how this could be done, but we were beginning to see that it might later be known, and to see that the seasons, which wrote their coming upon the records of the spectrum, might in the future have their effects upon the crops prevised by means somewhat similar to those previsions made day by day by the Weather Bureau, but in ways infinitely more far-reaching, and that these might be made from the direct study of the sun.

Phil. Mag. S. 6. Vol. 2. No. 7. July 1901.

K

We are yet, it is true, far from able to prophesy as to coming years of plenty and of famine, but it is hardly too much to say that recent studies of others as well as of the writer strongly point in the direction of some such future power of prediction.

VII. On the Practical Attainment of the Thermodynamic Scale of Temperature. By J. ROSE-INNES, M.A., B.Sc.* N this paper I hope to develop the theory of the gas

readings

that instrument readily reducible to the thermodynamic scale. As I have already written two papers on this subject, it might be as well to indicate briefly wherein this paper differs from my earlier ones.

The subject of gas-thermometry has been often investigated, but the first theoretical treatment which need be seriously considered is that given by Joule and Kelvin in 1862 (see Kelvin's Reprinted Papers, vol. i. pp. 429-431). They assumed that the Joule-Thomson effect for air varied as the inverse square of the temperature at all temperatures, and from this assumption obtained the characteristic equation of the gas (loc. cit.). The correction for the constant-volume air-thermometer obtained from this equation was first given by Rowland (Amer. Acad. Arts & Sciences, xv.).

In my first paper on this subject (Phil. Mag. xlv. pp. 227234), I suggested the use of a different empirical formula for the Joule-Thomson effect; this formula suited the experimental results rather better than Lord Kelvin's; and it led to the conclusion that there is no thermodynamic correction for the constant-volume air-thermometer of the kind calculated by Rowland. Both Rowland's result and my own suffered from a defect, inasmuch as they assumed that an empirical formula which had been found to hold over a limited range of temperature necessarily held at any temperature however high. But the mere fact that two contradictory results could be reached from the same data seemed to show that the Joule-Thomson results by themselves were not capable of leading to the proper correction for the constant-volume thermometer.

In order to avoid the difficulties occasioned by the extrapolation to infinity, I proposed in my second paper (Phil. Mag. 1. pp. 251-260) to change the independent variable. The end aimed at was attained, as the resulting formulæ did

* Communicated by the Author.

not involve an extrapolation to infinity; but they laboured under the disadvantage of requiring us to know the isothermal compressibility for the same range of temperature as that for which the Joule-Thomson effect is known. Such knowledge is not at present in our possession, and we are not likely to obtain it for some time, as experiments on compressibility are exceedingly difficult to carry out at temperatures even moderately high.

I have accordingly devised a method of treating the differential equations which necessitates our knowledge of the Joule-Thomson effect as before, and of the isothermal compressibility at one temperature only. For this method of treating the equations the experimental data at present available are sufficient, and yet the extrapolation to infinity is avoided.

Integration of the Fundamental Differential Equation.

It was first shown by Lord Kelvin that for a gas streaming through a porous plug we must have the equation

(Reprinted Papers,' vol. i. p. 428; see also Reprinted Papers,' vol. iii. p. 179). The right-hand side of this equation was found by experiment to be very small for such gases as hydrogen, oxygen, nitrogen, air, and carbonic acid. It was also found that the difference of temperature was proportional to the fall of pressure to a considerable degree of accuracy; and we may therefore treat JK as a function of the temperature only if we are neglecting squares of small quantities.

at

др

at Assume that for our present purpose JK may be suffiдр. ciently well represented by an ascending series of powers

1

of; thus

t

where n may be zero or positive, but not negative.

Integrate with respect to t along an isopiestic, and we

where P is a function of p only. Multiply by pt, and we have

Denote pr by the single symbol and differentiate with regard to p, keeping t constant,

P+ rdp = The quantity (d),

dP

P + P dp S

is found by experiment to be a function of t only to the degree of accuracy to which we are at present working. Hence the right-hand side of the last equation is a function of t only; while we readily see that the left-hand side of the equation is a function of p only. We infer that both sides must be equal to a constant quantity, say e; thus

where R is an arbitrary constant introduced by the integration, Employing this value of P, we obtain

If v is kept constant while p and t are both made to increase together, the term ept will ultimately become more important than Rt. As it seems improbable that this can represent the true state of things at high temperatures, we ought to try to make e vanish. We e can secure this result if for a single isothermal we can put