derstanding of the spirit in which it is to be pursued and the methods by which it is to be advanced.

Nor does there seem to be any reason to fear that the want of a locality for such assemblages will be found to place an impediment in their way. At the late meeting there were deputies present from five of the chief commercial towns in England to invite the Association and to offer suitable accommodation in their respective towns. Bristol stood first on the list of those from which invitations had been received on former occasions; and its situation being also far removed from the districts which the Association has hitherto traversed, it was determined to hold the ensuing meeting in that city in August next. The highly interesting and important country which forms the South-west of England will be conveniently embraced by this meeting, and the zeal which public bodies no less than individuals have shown to facilitate and encourage the arrangements for it, concurs with the high reputation of the men of science connected with Bristol, to hold out the confident expectation of a successful result.

NOTICES OF LECTURES DELIVERED AT THE EVENING MEETINGS OF THE ASSOCIATION.

PROFESSOR POWELL gave a lecture on the phænomena of prismatic dispersion, in relation to the undulatory theory of light.

After giving a general view of the phænomena, and a particular de-scription of the black lines in the spectrum whose position is taken as a measure of the refractive and dispersive powers of substances, Professor Powell proceeded to state the results of some recent labours undertaken by himself in order to ascertain whether the undulatory theory of light, which is admitted to explain almost every fact in optical science except dispersion, could be applied to explain that also. By reducing to calculation a formula suggested to the author by Professor Airy, as arising out of the researches of M. Cauchy, and expressing a relation between the refractive index of a ray and the length of the wave, a very close agreement was found between the numbers which result from the formula and those observed by Fraunhofer for ten different media, viz. four kinds of flint glass, three of crown glass, water, oil of turpentine, and solution of potash. Professor Powell is engaged in the arduous labour of testing the applicability of M. Cauchy's modification of the undulatory theory to the explanation of the phænomena of prismatic dispersion, by individual examples; and he states, that as far as the calculations have been executed, it appears that even the extreme case of that highly dispersive substance oil of cassia is comprehended with at least considerable accuracy by the theory. It appears, then, that

one of the greatest of the remaining objections to the reception of the undulatory theory is at least partially removed.

The Rev. W. WHEWELL stated the progress which had been made during the past year in Observations of the Tides, not only round the coasts of Great Britain and Ireland, but also under the direction of the Governments of Sweden, Denmark, Russia, Spain, France, Holland, and the United States. The dependence of the velocity of the tide wave on the depth of the ocean channels was pointed out as an instance of the collateral benefits arising from the advancement of any one branch of knowledge; for, in consequence of the perfection of this branch of hydraulical science, it might be possible for geologists to acquire some valuable information concerning parts of the ocean where no plummet ever sounded and no line was ever cast.

Mr. BABBAGE explained his views of a method of Natural Chronometry derivable from an examination of the annual layers of growth in wood. Considering these layers as liable to vary in thickness according to favourable or unfavourable seasons, and any series of them in one tree capable of being coordinated with a contemporaneous series in another, by means of these irregularities, it was shown to be possible to arrive at an accurate knowledge of the period of existence of trees in which life had become extinct, or which had been long enveloped in peat bogs, provided a sufficient number of trees of intermediate periods, which had been subject to the same irregularities of annual growth, could be examined. The bearing of the inquiry on historical records of seasons and on geological speculations was pointed out, and the process which it would be most convenient to pursue in the application of the method clearly indicated.

Professor SEDGWICK presented a general review of the labours of the Geological Section during the week, illustrated by a section of the Cumbrian and Silurian systems of rocks.

Dr. LARDNER delivered a lecture on Locomotive Engines, illustrated by drawings and working models.

Dr. BARRY gave an account of his ascent of Mont Blanc in 1834, illustrated by drawings.

Mr. BABBAGE described a remarkable Phænomenon in the Sea on the coast of Cephalonia (details of which had been communicated to him by Lord Nugent), which appeared to indicate the existence of a large cavity below the bed of the sea, and communicating therewith.

Professor WHEATSTONE exhibited his Speaking Machine, and explained the principles of its construction, and the progress which had been made in the mechanical imitation of the human voice.

NOTICES AND ABSTRACTS OF MISCELLANEOUS COMMUNICATIONS TO THE SECTIONS.

MATHEMATICS AND PHYSICS.

PROFESSOR HAMILTON gave a sketch of his new theory of logologues and other numbers of higher orders; (see Transactions of the Royal Irish Academy;) also a similar account of his new theory of varying orbits.

He likewise explained to the Section the method of investigation pursued by Mr. G. B. Jerrard, for accomplishing the solution of equations of the fifth or of higher degrees.

A short Account of some recent Investigations concerning the Laws of Reflexion and Refraction at the surface of Crystals. By Mr. M'CULLAGH.

To understand the nature of the general problem which a complete theory of double refraction requires to be solved, let it be supposed that a ray of light is reflected and refracted at the separating surface of an ordinary medium and a doubly refracting crystal, the light passing out of the former medium into the latter. This limited view of the subject is taken merely for the sake of clearness of conception; since we might suppose that both media are crystallized, without increasing the difficulty of the problem. The question, it is obvious, naturally divides itself into two distinct heads. The first relates to the laws of the propagation of light in the interior of either of the two media, before or after it has passed their separating surface; and this part of the subject has been fully treated, according to their different methods, by MM. Fresnel and Cauchy. The second division of the subject had been left completely untouched. It relates to the more complex consideration of what takes place at the separating surface of the media, the laws according to which the light is there divided between the reflected and refracted rays, including a determination of the attendant circumstances indicated by the wave theory, with regard to the vibrations in the reflected and refracted rays. In the case above mentioned, when the incident light is polarized, there are four things to be determined, namely, the magnitude and direction of the reflected vibration, with the magnitudes of the two refracted vibrations. The four conditions necessary for this determination are furnished by two new laws, which could not be easily stated without entering too much into detail. The results, applied to determine the polarizing angle of a crystal in different azimuths of the plane of reflection, agree very closely with the admirable experiments of Sir David Brewster on Iceland spar. In the course of these experiments it was observed that the polarizing angle remained the same when the crystal was turned half

round (through an angle of 180°), although the inclination of the refracted rays to the axis of the crystal was thereby greatly changed. This remarkable fact is a consequence of the theory. After some

complicated substitutions in the primary equations, the value of the polarizing angle is found to contain only even powers of the sine or cosine of the azimuth of the plane of reflection, and therefore a change of 180° in the azimuth produces no change in the polarizing angle.

The two new laws above mentioned, on which the theory depends, occurred to the author in the beginning of last December; but, owing to an oversight in forming one of the equations, they were not fully verified until the beginning of June.

In this theory it is supposed that the vibrations of polarized light. are parallel to the plane of polarization, according to the opinion of M. Cauchy. This is contrary to the views of Fresnel, whose theory of double refraction obliged him to adopt the hypothesis that the vibrations are perpendicular to the plane of polarization. It is further supposed, that the density of the vibrating æther is the same in both media; and this hypothesis of a constant density in different media, which was found necessary for the theory, seems to accord, better than the supposition of a varying density, with the phænomena of astronomical aberration.

This

If we conceive the three principal indices of refraction for the crystal to become equal, we shall obtain the solution of a very simple case of the general problem with which we have been occupied, the case of an ordinary refracting medium, such as glass. simple case, it is well known, was solved by Fresnel. The foregoing theory leads to a simple law, expressing all the particulars of the case, but differing with regard to the magnitude of the refracted vibration, from the formulæ of Fresnel. The law may be stated, by saying that the refracted vibration is the resultant of the incident and reflected vibrations; the first vibration being the diagonal of a parallelogram of which the other two vibrations are the sides, just as in the composition of forces. The plane of this parallelogram is the plane of polarization of the refracted ray. It is to be remembered, that the vibrations in each ray are perpendicular to the ray itself, and parallel to its plane of polarization.

This simple case has also been considered by M. Cauchy, in a short paper inserted in the Bulletin Universel, tom. xiv. ; but it does not seem to have been observed by any one that his solution is erroneous. His formula for light polarized parallel to the plane of reflexion, is that which belongs to light polarized perpendicular to the plane of reflexion and vice versa.

Mr. Whewell read his report on the Mathematical Theories of Electricity, Magnetism, and Heat.

[This report will be printed in the next volume of the Transac tions of the Association.]

On certain points connected with the recent Discoveries relative to Radiant Heat. By Professor POWELL.

In this communication the author expressed his particular satisfaction in finding that M. Melloni (in his second memoir) describes a repetition of the experiment originally made by him, and recorded in the Philosophical Transactions, 1825, with perfect success, by means of his extremely delicate apparatus. The confirmation is the more complete, as the experiment was made by M. Melloni with a different view.

It is thus now established beyond question, that luminous hot bodies are sending out two distinct sorts of heat, or two distinct heating agents, at the same time, differing in their properties and mode of operation.

Hence the whole series of results of M. Melloni must be interpreted with reference to this distinction, and possibly the consideration of it may remove some of the apparent anomalies.

Another question of importance which has occurred to the author is this, Whether, in the polarization apparatus, supposing one glass or pile of mica heated, it will radiate the same quantity of heat to the other in the two rectangular positions. The question is purely a mathematical one, and has been in some degree considered, at the author's suggestion, by Mr. Murphy, of Cambridge. The integration has not been completed, but Mr. Murphy thinks it clear that there will be a difference.

On the Phænomena usually referred to the Radiation of Heat. By HENRY HUDSON, M.D., M.R.I.A., Dublin.

For the purpose of repeating Leslie's experiments with variations of the temperatures of the surface of the mirror and of the thermometer, the author procured a parabolic zinc mirror with a hollow back, so that its surface could be heated or cooled by filling it with hot or cold liquids.

The following are the results obtained: 1st, Whatever be the temperature of the room, if the mirror and canister be at the same temperature also, there is no effect produced by either the metallic or the varnished side of the canister. 2nd, If the canister (alone) be above the temperature of the air, the varnished side produces a greater heating effect than the metallic side, in the proportion of about 12: 1. 3rd, If the canister (alone) be below the temperature of the room, the varnished side produces a greater cooling effect than the metallic in the same proportion of about 12: 1. 4th, If the mirror be heated considerably (say to 200° Fahr.), and the thermometer so arranged that both balls are equally warmed by the mirror (one of them being in the focus), a canister (at the same temperature as the room) produces a cooling effect on the focal ball, and the varnished side displays its superior efficiency. 5th, The mirror and thermometer being as in the last experiment, the canis