GODSTONE BRIDGE.

The span is 30 feet, the weight of engine and tender 33 tons, and weight of half bridge 25 tons; the statical deflection was .19 inch. This was increased to .25 by a speed of 49 miles per hour.

The dynamical deflection

Statical deflection

showing an increase of nearly one-third.

=1.315,

A pair of steel bars, two feet three inches by two inches broad and one-fourth inch deep, gave the following results:

A bar of wrought iron nine feet long, one inch broad, and three inches deep, with a load of 1,778 pounds, gave the following results:

In the commissioners' report Mr. Hodgkinson has given the results of a variety of experiments on the transverse strength of cast, mixture of cast and wrought, and wrought iron. The experiments were made with great care, and every source of error that could be was eliminated, notwithstanding the trouble and expense which such a procedure necessitated. Still there was a great difficulty, which was always felt by Mr. Hodgkinson, and which occupied, at various times, much of his attention, viz., to connect the breaking-weight of the beam with its deflection in such a manner as to indicate true practical results. For this purpose he entered into a very general theoretical investigation on the transverse flexure of beams, which is given in the second volume of Tredgold "On the Strength of Cast Iron;" but, in order to make the results of this very general investigation practical, he is compelled to assume, first, that the forces of extension and compression are proportional to the extensions and compressions; second, that the force of extension is equal to the force of compression; third, the reaction at the points of support is always vertical. It is not surprising, then, that a formula, based upon so many assumptions, should fail to represent correctly the relation between the breaking-weight and the dimensions of the beam; this is exactly what has taken place.

The discordance here alluded to has arrested the attention of W. H. Barlow, esq., C. E., F. R. S,, and the results of his investigations are given in two very interesting memoirs, printed in the "Transactions of the Royal Society" for 1855-'57. It would be great presumption on my part to enter into any profound criticism on the mode of procedure and results of these memoirs, revised as they have been by Professor Barlow, who is justly distinguished by his genius, high attainments, and long life devoted to the interests of science; but still it may not be out of place here to make one or two observations which occurred to me while reading the memoirs. I quite agree with Mr. Barlow that there must be other forces in operation when a beam is broken transversely than those simply and usually designated tensile and compressive. If a beam is broken transversely, and the existence and position of the neutral surface are admitted, then it is not difficult to conceive the existence of a third force between two adjacent laminæ unequally extended or compressed.

This is really what happens, and the existence of which was well known to

Mr. Hodgkinson, who thought it to be so small in practical cases that its accumulated action would not produce much effect on the breaking strain of the beam. Be this, however, as it may, there is some little difficulty in subscribing to all that Mr. Barlow advances on this important and interesting subject. In the first place there might be an exception taken to Mr. Barlow's method of fixing the position of the neutral line. Does he not fix it by an appeal to his senses rather than by the result of the mathematical analysis of the data he has obtained from experiment? The position which he fixes upon, viz., the centre of the bean, necessarily involves the equality of tensile and compressive forces, a conclusion which is not justified by Mr. Hodgkinson's experience. In the second place Mr. Barlow makes it appear that the error in the breaking strain of a beam is nearly one-half by neglecting the force of adhesion between the adjacent laminæ. We hardly think this conclusion is based upon sound premises, although it necessarily follows from the results of a formula which has been obtained by considering only the two forces, viz., tensile and compressive. But it is hardly fair on the part of Mr. Barlow to institute a comparison between the resistance to flexure and the results of a formula (W=zadf÷1) in which that resistance to flexure is · neglected, without applying the well-known corrections to that formula. When a beam is strained to a considerable extent the deflection becomes sensible, and of course the reaction at the supports, being perpendicular to the surface of the beam, makes an angle with the vertical. This circumstance affects the above formula in two ways: first, it alters the amount of the moment about a line in the neutral surface; and, second, its tendency is to change the position of the neutral line. Therefore, unless these corrections are approximated to and applied to the formula, it is not safe to infer, as Mr. Barlow has done, that, by neglecting the resistance to flexure, the ordinary formula only gives nearly half the breaking weight.

Another source of error is in the law "ut tensio sic vis," as it is well known, from Mr. Hodgkinson's experiments, that the forces of extension and compression are neither equal nor vary with the extension and compression when the strains are large. I quite agree, as did Mr. Hodgkinson, with Mr. Barlow as to the existence of a resistance to flexure in the transverse strain of beams besides the ordinary forces of tension and compression; but the mode of estimating this resist ance to flexure in Mr. Barlow's second memoir amounts to the assumption that the force of extension varies by a law expressed by ax+b, where a and b are constants, and a the distance of the particle from the neutral axis. I may add, in conclusion, that Mr. Hodgkinson has computed the tensile and compressive forces, subject to a law much more general than the one here alluded to, with great clearness and adaptation to include practical cases.

Mr. Barlow's two memoirs, however, are the first on this subject to insist on the existence of a distinct force to resist flexure; and although I do not see the force of his comparison of the resistance to flexure with the results of the ordinary formula, or the theoretical method by which he estimates its amount, still I can with confidence recommend these memoirs to the engineering student as being worthy of his attentive perusal.

In concluding this memoir of one of the most distinguished members of the society, I cannot help feeling that the description herein given of his character and labors falls short of the real position which they occupy in the public mind; and although I have had much pleasure in reading and collating the discoveries of Mr. Hodgkinson, I regret that the preparation of this memoir has not been placed in abler hands. One thing, however, consoles me, and supplies me with an ample reward, which no criticisms on my effort can possibly cancel, and that is, I have been engaged, to the best of my ability, in the endeavor to perpetuate the memory of a great and good man, whose singular praise it is to have spent his life and his great powers for the good of mankind, with a single aim to truth and science, without desiring or gaining pecuniary reward.

RECENT PROGRESS IN RELATION TO THE THEORY OF HEAT.

BY A. CAZIN.

Translated for the Smithsonian Institution.*

The study of heat presents a remarkable example of the connection which exists between the physical properties of matter. Restricted as the limits of this discourse must necessarily be, I propose on the present occasion to consider heat under two points of view only, first in its relations to light, and next in its relations to movement. It may thus be practicable to furnish a rapid sketch of the actual state of this part of physics.

The fact that the same laws are applicable to the propagation of heat and to that of light, is one which science leaves no longer in doubt. To every experiment in optics there corresponds a similar experiment in thermotics. The methods of observation are to-day carried to such perfection that M. Desains has been able quite recently to reproduce with heat the remarkable phenomenon of the luminous interference from striated surfaces.

A pencil of horizontal luminous rays traverses a plate of glass on which are traced parallel lines extremely close to one another, (6,000 lines in an extent of one inch.) This pencil is divided by the plate into many distinct pencils, which spread themselves in fan-shape in a horizontal plane, and we see, on the screen upon which these pencils are made to fall alternate intervals of light and obscurity. With the violet light the dark intervals are not so large as with the red. This is the phenomenon of diffraction discovered by Frauenhofer. By applying a thermo-electric battery, the most delicate of thermometers, at different places in the plane where the pencils transmitted by the luminous rays are distributed, M. Desains has verified the existence of pencils of heat distributed likę those of light. Moreover, by causing obscure heat, proceeding from a solar pencil which has passed through M. Tyndall's solution of iodine in bisulphide of carbon, to fall on the rays, M. Desains has observed that the intervals without heat are greater than the obscure intervals given by the red light. Remark now the gradation: the violet is more refrangible than the red, the red more refrangible than the obscure heat, consequently the magnitude of the intervals destitute of rays varies in inverse proportion to the refrangibility.

Several other experiments in optics have been transferred by M. Desains to the domain of radiant heat. I will cite one of those relating to the polarization of obscure heat. The rays of heat employed issue from a common oil lamp; a lens of glass collects them and causes them to converge on a prism of Iceland spar achromatized. Two pencils issue from this spar: that which is called the ordinary pencil encounters a second prism of spar like the first; it is bifurcated in its turn. Of the two pencils thus obtained, that which is called ordinary-ordinary falls on a lens and converges towards the thermo-electric battery. When the principal sections of the two spars are perpendicular, neither light nor heat arrive at the battery; the ordinary-ordinary pencil is said to be extinguished. If one of the spars be now made to turn upon itself, light and heat immediately appear in this pencil. Let us now place between the two spars a trough, containing Tyndall's solution; the luminous rays are arrested, and beyond the trough there remains only the obscure heat. The destruction of this heat is complete when

*From the Revue des cours scientifiques de la France et de l'étranger, "Association Scientifique de France, (conférences de la Sorbonne,”) 1867.

the principal sections of the two spars are perpendicular. Here, then, we have the experimental demonstration of the polarization of obscure heat.

Let us next place between the trough and the second spar a lamina of quartz, the thermo-electrie battery manifests heat anew, just as if, without interposing the quartz, we had caused the first spar to turn by a certain angle. It is usual to say that the ordinary pencil which issues from the spar is polarized in the principal section, and that the transmission of this pencil through the quartz causes the plane of polarization to revolve. To conclude the experiment, we cause the first spar to turn until the ordinary-ordinary pencil which encounters the battery is extinguished anew, and the angle of this rotation measures the rotation of the plane of polarization.

The perfect resemblance of a luminous and a calorific ray has led to the inference that the forces which are at play in the two radiations place matter in a similar state of movement. Would we figure to ourselves a state of movement capable of producing all the phenomena of light, we have but to imagine an infinitude of particles situated upon the ray and oscillating from one side to the other of an intermediate position, like the particles of a chord which yields a sound; two consecutive particles act one on the other in such a way that every modification of movement in the one induces a determinate modification in the other. While a particle executes a complete oscillation the movement is transmitted to a certain distance which is called length of wave. Here we have the point of departure of the theory of undulations; the same hypothesis is applicable to heat.

From the fact that the propagation of heat and light takes place as well in a vacuum as through ponderable bodies, the above hypothesis must be thought incomplete unless it be supposed in addition that the matter which transmits the undulations is different from ponderable matter; to the former, therefore, has been given the name of ether. Were this vibrating matter even of the same nature with the matter of ponderable bodies, it would still be useful to employ a special word to indicate that it is in a particular state, capable of propagating light; as the purpose in using it is to represent to ourselves the possible mechanism of the phenomena, we should, above all, seek simplicity of language, and the use of the phrase luminous ether satisfies this condition.

It may naturally be asked whether there is a calorific ether distinct from the luminous ether, or whether one sole ether is sufficient for the mechanical representation of the radiation of light and of that of heat. Only one, it is evident, should be admitted, if that suffices for the explanation of all the known facts, and the question here relates to facts which take place in the material world, outside of ourselves and independently of our sensations. To the well-known researches of MM. Jamin, Masson, and Delaprovostaye, which corroborate the hypothesis of a single ether, we should now add the late investigations of M. Desains on the rotation of the plane of polarization of the rays of obscure heat in passing through quartz.

When the question relates to luminous rays we know that the rotations of the plane of polarization are inversely proportional to the squares of the lengths of wave. If there be luminous rays having a length of wave four times greater than that of the violet rays, their rotation, according to this law, would be 16 times smaller than the rotation of these last. Now, MM. Delaprovostaye and Desains had heretofore established that calorific rays and luminous rays of the same length have the same rotation. And now M. Desains shows us that the rays of obscure heat satisfy the law as enunciated, and among these rays there are such as have, in fact, a rotation 16 times less than that of the violet, and a length of wave four times greater.

Instead of assuming that two like systems of waves propagate, the one heat, the other light, while they undergo the same modifications by reflection and refraction, is it not more simple to admit but a single system, the longest waves producing the effects of heat, and the shortest those of light? Such is the import

of the principle of the identity of heat and light; it explains all observed peculiarities of radiation, whether chemical, calorific, or luminous.

If we would comprehend, for example, how a solution of sulphate of quinine is luminous in a dark chamber, when it is placed in the ultra-violet region of the solar spectrum? Imagine a series of tuning forks of different magnitudes assembled together in the same place, and a sound produced at a distance. Several of the forks will be thrown into vibration, namely, those which are capable of rendering the harmonic sounds of the exciting sound. Sonorous waves, longer than the incident wave, will proceed from the forks which render grave harmonic sounds: the exciting sound will have generated graver sounds. Such is the analogy of fluorescence. The radiations incident to waves too short to excite the retina generate in the sulphate of quinine longer waves, which are capable of producing the sensation of light. Inversely an obscure radiation of a wave too long to be luminous may, by encountering certain bodies, occasion therein more rapid ethereal vibrations, and generate shorter waves, which shall be luminous. These vibrations are analogous to those which correspond to the sharp harmonics in the acoustical experiment which I have adopted for exemplification. Here we have the image of that kind of calorific and luminous phenomenon which M. Tyndall has termed calorescence.

The ray of heat which penetrates into a body is absorbed therein either in whole or in part. So long as the question concerns a solid or liquid body we feel no doubt as to the exactness of this proposition; it is the simplest expression of observed facts. But when it relates to a gas or to vapor the absorption is much more difficult to demonstrate. We owe to M. Tyndall, in England, and to M. Magnus, in Germany, the experimental proof of the absorption of heat by gases and the measure of that absorption.

The experiments of M. Pouillet on the solar heat long since taught us that the atmosphere retained a considerable portion of the rays emanating from the sun; but which of the gaseous elements of the air exerts the greatest absorption? At present some approximation has been made to the solution of this important question, and I shall attempt to show at what point it has arrived.

To ascertain the absorption of heat by a gas, we will take, like M. Tyndall, a tube of plate-tin of the length of two metres, which bears a tubulure in the middle and a tubulure towards each end. A pencil of obscure heat traverses this tube, and encounters the thermo-electric battery. The calorific effect indicated by the galvanometer is due, in part, to the rays which pass into the tube parallel to its axis, in part to those which have undergone sundry reflections on the walls of the tube; the tube contains at this time only common air, naturally humid. We exhaust this air by the tubulure of the middle, by means of a pneumatic machine; as the tube is open at both ends the atmospheric air enters freely, and notwithstanding the removal of the strata of air, the needle of the galvanometer remains at rest. If coal gas be now introduced through the terminal tubulures the deviation of the needle diminishes, which shows that heat no longer traverses the tube as freely as before. Arrest the introduction of the gas by continuing the action of the pistons of the pneumatic machine, air replaces the gas, and the needle returns to its former deviation. From this experiment it is inferred that coal-gas has an absorbing power superior to that of atmospheric air.

M. Tyndall varied this experiment by causing dry air to pass into the tube, and observed an augmentation in the deviation of the needle of the galvanometer. From this he concludes that the absorbing power of humid air is greater than that of dry air, and that aqueous vapor exerts on heat a considerable degree of absorption. A great number of experiments made by other methods has led him. to the same conclusion. On the other hand M. Magnus, in operating after M. Tyndall's or by other methods, found that humid air acted very nearly as dry air, and that any great difference was only manifested when water exists in the air in a vesicular state, similar to the water of clouds.