just made has been made on the supposition that the temperature of the escaping gas is 0° C. If the absolute temperature in Centigrade units of the gas be t, we must multiply the Now in no case has the rapidity above estimate by t 273 of tail-formation greatly exceeded one million miles in three days, except in the case of those comets which have approached very near to the sun, and where, consequently, the temperature at which the evaporation has taken place must have been very great. Donati's comet is one of the most striking examples of comets with large and rapidly formed tails which have not approached very near to the sun; and in Donati's comet the tail increased in length from 14 million miles on August 30 to 51 million miles on October 10, or at an average rate of somewhat less than a million miles in a day. Those comets which have formed large tails with exceptional rapidity have approached very near to the sun. Thus the comet of 1680, which formed a tail 60 million miles long in two days during its perihelion passage approached so near to the sun as to be exposed to a solar radiation 25,600 times more intense than that to which the earth is exposed. To use Sir John Herschel's words, "In such a heat there is no solid substance we know of which would not run like water, boil, and be converted into vapour or smoke." It seems probable that it is only the shortness of the time during which the comet is exposed to such a temperature which prevents its being altogether converted into vapour. The smaller fragments of the comet will, I conceive, be entirely evaporated; and the last portions of vapour from any fragment will, as I have shown, be carried backwards with immense velocity into the tail. After this vapour has arrived in colder regions, it seems probable that it will condense and become visible as a cloud of finely divided solid or liquid matter. In these cases then the visible tail will consist, not of matter which has resisted evaporation, but largely and perhaps almost entirely of matter which has evaporated and has recondensed. In conclusion, if this be the true explanation of the phenomenon of comets' tails, then every meteoric cloud of matter which approaches sufficiently near to the sun to undergo rapid evaporation must become tailed like a comet, as it passes through its perihelion passage. I would suggest that we may have here an explanation of the radiated structure of the sun's corona. As different masses of meteoric matter approach close to the sun, the smaller fragments will be almost or entirely evaporated, a large portion of the vapour from them being carried rapidly away from the sun, thus giving rise to a I coronal protuberance. Thus the radiated structure, and the irregular and variable form of the corona would be accounted for. Cheltenham College, October 21, 1878. LX. Notices respecting New Books. The Theory of Sound. LEIGH, M.A., F.R.S., bridge. Volume II. pp. 302. WE By JOHN WILLIAM STRUTT, BARON RAYformerly Fellow of Trinity College, CamLondon: MacMillan and Co. 1878. 8vo, E noticed the First volume of this work shortly after its publication (5th ser. vol. v. p. 66). The Second volume—which, we presume, completes the work -is now before us. We could not, perhaps, give it higher praise than to say that it is worthy of its predecessor. Not to speak of actual contributions to our knowledge of the Theory of Sound which have been made by the author, it is scarcely possible to overestimate the value to the student of a perfectly trustworthy work which brings together the substance of memoirs scattered through a variety of periodicals. Not fewer than about a hundred and twenty or thirty memoirs are referred to in the course of these volumes, most of which would be inaccesible to students living away from the chief centres of intellectual activity. These, however, are not the only students who are benefited by such a work as the present. Even those who are more favourably situated rarely look at the memoirs unless they are distinctly interested in their subjects at the time of publication; and this is particularly the case with memoirs on such a subject as the Theory of Sound, the mere reading of which may involve a considerable expenditure of time and labour. The subject of the present volume is Aerial Vibrations. In its general method it resembles its predecessor. Thus, in the former volume, the discussion of Vibrating Systems in general (chap. iv. and v.) is preceded by a very careful consideration of a particular case, viz. that of a system having one degree of freedom (chap. iii.); so, in the present volume, the discussion of the general problem of vibrations in three dimensions (chap. xiv. and xv.) is preceded by that of the cases of Vibration in tubes (chap. xii.), and of some other special problems, including the Reflection and Refraction of Plane Waves (chap. xiii.). These four chapters, together with an introductory chapter on "Aerial Vibrations" (chap. xi.), fill more than half the volume. The remainder is divided into chapters on the Theory of Resonators (chap. xvi.), on Applications of Laplace's Functions to Acoustical Problems (chaps. xvii. and xviii.), and on Fluid Friction (chap. xix.). * The Work, as it stands, might certainly be accepted as a complete treatise on what is generally understood by the Theory of Sound, viz. thể Kinetics of Acoustical Vibrations; and we should have supposed the work to be complete had not the publisher made himself responsible for an announcement of Vol. iii., and also for a notice as to volumes subsequent to the first. The seventeenth and eighteenth chapters are almost wholly occupied with contributions made by the author to the Theory of Sound. Thus the seventeenth chapter does, indeed, begin with a long extract from Professor Stokes's paper, "On the Communication of Vibrations from a Vibrating Body to a Surrounding Gas," in which he applies his determination of the complete value of (the symbol which represents a disturbance propagated wholly outwards) to the explanation of "a remarkable experiment by Leslie, according to which it appeared that the sound of a bell vibrating in a partially exhausted receiver is diminished by the introduction of hydrogen" (vol. ii. p. 207). The explanation of this seemingly paradoxical phenomenon, it may be remarked, had escaped the penetration of Sir J. Herschell, who "thought that the mixture of two gases tending to propagate a sonnd with different velocities might produce a confusion resulting in a rapid stifling of the sound" (p. 214, vol. ii.). So far the contents of the chapter are due to Professor Stokes; the remainder is taken from two papers by the author published in the Proceedings of the Mathematical Society '—" On the Vibrations of a Gas contained within a Rigid Spherical Envelope," and an "Investigation of the Disturbance produced by a Spherical obstacle on the Waves of Sound." The eighteenth chapter contains a discussion of considerable interest from a mathematician's point of view, viz. “ a Proof of Laplace's Expansion for a Function which is Arbitrary at every point of a Spherical Surface." But to put this in a proper light we must look back to vol. i., where a proof is given of Fourier's Series. The method adopted may be indicated as follows:-The author first considers the motion of a vibrating string when the ends are not absolutely fixed-a state of things which he represents by supposing a mass (M), treated as unextended in space, attached to each end and acted on by a spring (u) towards the position of equilibrium, and then particularizes his solution in two ways, first, by supposing M=0 and μ=∞, so that the ends of the string are fast; secondly, by supposing that both μ and M are zero, a case which might be represented by supposing the ends of the string capable of sliding on two smooth rails perpendicular to its length. From the results thus obtained Fourier's Theorem is shown to follow. In connexion with this proof, the author remarks :-" So much stress is often laid on special proofs of Fourier's and Laplace's Series, that the student is apt to acquire too contracted a view of the nature of those important results of analysis" (p. 159, vol. i.); and he adds, in a note, that "the best system for proving Fourier's Theorem from Dynamical considerations is an endless chain stretched round a smooth cylinder, or a thin re-entrant column of air inclosed in a ring-shaped tube" (p. 160, vol. i.). It will be observed that the remark above quoted implies a promise of a similar discussion of Laplace's Series; and this is fulfilled in chap. xviii. The "system "adopted is that of a thin spherical sheet of air. In chap. xvii., as we have seen, there is a discussion of the vibrations of a gas contained within a rigid sphe rical envelope; and it is observed (p. 238) that a similar treatment will apply to the vibrations of air between two concentric spherical envelopes; but when the difference between the radii is very small in comparison with either, the problem reduces itself to that of a spherical sheet of air. The case in which the velocity-potential is symmetrical with reference to the poles, is treated first; and it is shown that it can be represented by a series whose general term is Pr(u) An cos at√n(n+1)+B2 sin at √n(n+1) P2(μ) { с с where n is an integer even or odd, and P(u) Legendre's function. If now t=0, is an arbitrary function of the latitude, and we see that ↓=A ̧+A ̧P1(μ)+. . .+AnPn(μ)+... This is, of course, only a particular case of Laplace's Series. But by similar reasoning on the general value of Laplace's Series is established. At each step of the process the case is considered in which the radius of the sphere becomes infinite, and we pass physically to the case of a plane layer and analytically from Laplace's to Bessel's functions. The vibrations of a plane layer of gas are of course more easily dealt with than those of a layer of finite curvature; but I have preferred to exhibit the indirect as well as the direct method of investigation, both for the sake of the spherical problem itself with the corresponding Laplace's expansion, and because the connexion between Bessel's and Laplace's functions appears not to be generally understood" (p. 265, vol. ii.). This discussion is, as we have already remarked, of purely mathematical interest; and, indeed, from the nature of the case, by far the largest part of the work is addressed to mathematicians. Here and there, however, are discussions of which the interest is purely physical, such as, in the present volume, that on Whispering Galleries (p. 115), that on the Refraction of Sound by Wind (p. 123), and others. But our limits will not allow us to do more than mention their existence. LXI. Intelligence and Miscellaneous Articles. A FEW MAGNETIC ELEMENTS FOR NORTHERN INDIA. HAVING recently had occasion to measure the dip of the needle and the strength of the horizontal component of the earth's magnetic force at Calcutta, Jubbulpore and Allahabad, with a view to ascertaining to what extent the indications of an arbitrarily calibrated galvanoscope uncorrected for the local value of the earth's magnetism, would be trustworthy, I think it desirable to put the results on record. The horizontal intensity was measured with a Kew-pattern portable unifilar magnetometer; and the observations have been corrected for temperature, torsion and scale error. Dividing the horizontal component by the cosine of the dip, we obtain the total force thus :: There are on record several observations of the dip in Calcutta, which it will be interesting to bring together here. The dip appears to have been measured for the first time when the French corvette La Chevrette' visited these waters in 1827, by M. de Blosseville, who found it then to be* 26° 32′ 38′′. Ten years later, in 1837, on the occasion of the visit of another French corvette, La Bonite,' to the Hugli river, the dip was measured at Kalagachia (Diamond Harbour) by the chief Hydrographer, who found it to bet 26° 39' 04", exhibiting a change of only 0° 06′ 26′′ from the result of the earlier measurement. The next and most recent measurement was made by the brothers Schlagintweit in March 1856 and in April 1857, in which years it was found to be respectively ‡ 28° 06′ 43′′ and 28° 22′ 56′′. The same observers found the dip at Jabalpur in December 1855 to be § 28° 31' 08" Their measurements of the horizontal force gave : 0-37386 dyne at Calcutta in March 1856, in April 1857, 0.39959 at Jabalpur in December 1855. A very valuable series of observations was made in 1867-68 by the late Captain Basevi, R.E., under the orders of Colonel J. T. Walker, C.B., R.E., Superintendent of the G. T. Survey (now Surveyor-General of India), at 14 stations, extending from 15° 6' to 30° 20' north latitude; but none of them are coincident with the three stations under consideration. The values of the dip and horizontal intensity at the limiting stations of the series were as follows:: Asiatic Researches, vol. xviii. part i. p. 4. + Proceedings, Asiatic Society of Bengal, Wednesday, 3rd May, 1837. 'Observations in India and High Asia,' vol. i. $ Loc. cit. General Report of the Operations of the Great Trigonometrical Survey of India during 1867-68. Phil. Mag. S. 5. Vol. 6. No. 39. Dec. 1878. 2 H |