PAPERS READ. ON THE DIFFUSION OF HEAT IN HOMOGENEOUS RECTANGULAR MASSES, WITH SPECIAL REFERENCE TO BARS USED AS STANDARDS OF LENGTH. By R. S. WOODWARD, U. S. Geological Survey, Washington, D. C. [ABSTRACT.1] THIS paper discusses the laws of diffusion of heat in rectangular masses of any dimensions, and aims to give to the various problems that arise, solutions which may be readily used in computing numerical results. The assumptions on which the work is based are the following: (1) that the mass has initially a uniform temperature; (2) that it cools or heats in a medium of sensibly constant temperature; (3) that the exterior and interior conductivity and thermal capacity of the mass remain constant. Starting from Fourier's solution of the general problem defined above, the obstacles met in applying that solution are pointed out. Fourier's method requires a certain number of the roots of the three transcendental equations which express the boundary conditions of the mass. The new solution either avoids the difficulty of determining those roots altogether, or makes use of the first root only of each equation. Incidentally, however, methods of computing the roots are given. The pervading idea of the investigation is this, viz.: to separate the terms independent of from those dependent on the exterior conductivity, or emissivity. In accordance with this idea, the problem divides itself into two cases, in the first of which the ratio formed by the product of the emissivity and a linear dimension of the mass is less than unity, and in the second of which that ratio is greater than unity. Formulas for certain average temperatures of special interest relative to standards of length are given, viz. : the average temperature of the whole mass, of any face and of the axis of a bar. Special attention is given to the needs of the computer in the derivation and arrangement of formulas, and the application of nearly every formula is illustrated by a numerical example. 1 The paper will be published in full in Annals of Mathematics, Vol. 4, No. 4. A NOTE UPON RETINAL PHOTOGRAPHY. 1507 Locust St., Philadelphia, Pa. By CHARLES A. OLIVER, M.D., [ABSTRACT.] IN a desire to place upon record the author's progress in this direction, he would state that at the present writing (July, 1888) he, in conjunction with Dr. Wharton Sinkler, has obtained a fixed and easily adjusted apparatus consisting of an ophthalmoscopic attachment to a small field camera that can be adjusted to any position, a boxed oil light so arranged that the emergent rays pass through a two inch focus biconvex lens before becoming impinged upon the ophthalmoscopic mirror, a small fixed headrest for the subject, and a spectacle frame lens attachment to be placed before the subject's eye. The experiments, which were at first conducted with the artificial eye of Perrin and which resulted in negatives with clearly cut discs of about twenty-five millimetres in their long diameter, surrounded by an area of one hundred millimetres upon which the retinal vessels and gross changes in the retina and choroid could be plainly seen for nearly seventy-five millimetres area around the disc, the whole being entirely devoid of any disturbing light reflexes (these were untouched and unremagnified), have now been transferred to studies with the living human eye. Here the only difficulties have been the interfering corneal reflex and the heat experienced. The latter has been successfully combatted by resource to Dr. Howe's alum bath, while the former is the part of the subject now under experiment. The entire method with a full description of the completed apparatus will be published as soon as obtained. THE QUALITY OF MUSICAL SOUNDS. By W. LECONTE STEVENS, Brooklyn, N. Y. [ABSTRACT.] In this paper a brief sketch is given of the method adopted by Helmholtz in his investigation on musical quality, which resulted in the conclusion that "differences in musical quality of tone depend solely on the presence and strength of partial tones, and in no respect on the differences of phase under which these partial tones enter into composition." A résumé is given of a paper on the "Beats of Imperfect Harmonies," read by Sir William Thomson in 1878 before the Royal Society of Edinburgh, in which he expresses conclusions inconsistent with those previously reached by Helmholtz. A description is then given of the wave siren invented by Rudolph Koenig of Paris, for the purpose of testing the effect of change of phase on quality of tone. This instrument was brought to America a few years ago, but was injured in transit so that it could not be operated. It has since been further improved. The writer has had an opportunity to test its action in company with M. Koenig, and believes that through this instrument the truth has been established, that variation in phase among the components of a compound sound is a distinct element in determining musical quality. Helmholtz's view is that generally found in text-books. ON DYNAMICAL UNITS. By Prof. T. C. MENDENHALL, President of Rose Polytechnic Institute, Terre Haute, Ind. [ABSTRACT.] CONFUSION exists in the use of the terms weight and mass, much of which arises out of the use of the word pound in two senses. It is generally and properly used both as a unit of mass and as a unit of force. This fact should be clearly recognized in text-books of engineering and it is desirable that the pound as a unit of force should be accurately defined. The definition suggested is that it is the force of attraction between the unit of mass called a pound and the earth. Dynamical equations should be freed from "g" (gravity), the units being poundals, if force, or foot-poundals if work. These can afterward be units reduced to the more common gravitation units if desired. PROTECTION OF WATCHES AGAINST MAGNETISM. By C. J. H. WOODBURY, Boston, Mass. [ABSTRACT.] THE growing and even general use of electricity for illumination and for the transmission of power has added much to the knowledge of electrical phenomena, and also called the general attention of the public to matters long known to those familiar with physical science. Public attention was first called to the influence of magnetism on watches at the Paris Electrical Exposition, where visitors could leave their watches near the entrance. My first experience with the effects of electricity on a watch were decidedly unpleasant; for I was struck by lightning in July, 1881, at a time when I was thoroughly drenched with water. The only permanent damage was received by my watch, which was marked on the back of the case with two straight black stripes, each about half an inch in width, extending across the back and joined together at one end like a letter V. Three of the arbors in the movement were broken, but there was no discoloration except on the outside. Another watch, which possessed a remarkably uniform rate and was highly valued for its accuracy, yielded to the temptation offered by the magnetic fields around dynamos and became very uncertain, losing time at irregular intervals and at varying rates. The usual methods of demagnetization were all tried with the result of lessening the evil, but not removing it, as it seemed to be impossible to bring back the movement to the old rate. It is surprising how weak a magnetic field will stop a watch, a small magnet being sufficient for the purpose; and far weaker magnetic fields will interfere with the rate of a watch to an extent which will injure its value as a timepiece. There are two types of attachments designed to protect watches against magnetism; one being a small disc of iron taking the place of the inner cover of a watch case; and the other a box or case surrounding the watch case, like the outer case of a bull's eye watch. Without endorsing any of the extreme statements declared to be fundamental principles of magnetism by those engaged in the sale of either of these devices, it is evident that any magnetic body will distort lines of force in a magnetic field; and it was considered worth while first to submit the metal case to direct experiment. The magnet used was a small dynamo containing cast iron to the weight of about four hundred and fifty pounds. The armature was disconnected from the apparatus and the field coils connected to an electric circuit, in order that the watches should not be subjected to jar from a revolving armature. A circular piece of cardboard was placed in the case and dusted over with iron filings which had not been magnetized, and the box was closed and placed on a block of wood a foot from one of the poles of the magnet. An electric current sufficient to saturate the magnet passed through the field coils for a few moments, and the circuit was broken before the case was opened in order that the contents should not be directly exposed to any attraction except what was transmitted through the iron forming the case. On opening the case it was seen that the iron filings had been drawn towards one side of the card and arranged in striæ in the ordinary manner whenever they are exposed to a magnetic field. A watch which had been set to exact time with one in an extreme part of the room was placed in the case, and in a like manner exposed to the magnetic field for five minutes. When the case was opened it was found that the watch had stopped at the instant that the magnet was charged; and the movement has been magnetized to an extent which has robbed it of any present value as an accurate timepiece. As it was evident that the case did not adequately protect the watch, experiments were not made with the shield referred to, which contained a small fraction, perhaps one-tenth, as much metal as the case. These watches were not exposed to any more severe tests of magnetism than would be liable to be offered to a watch worn on the person of one around a dynamo or motor, except that a passenger in a motor car would naturally be in a sitting position and the watch would be exposed for a longer time to any lines of force than would be the case around a dynamo, where the person would not probably remain in a stationary position so long a time. Some time ago I examined a watch containing the inventions of C. A. Paillard, of Geneva, in which the hair spring and balance were made of alloys of palladium, the escapement being made of steel, and found that although a weak magnetic field did not produce any apparent effect upon the movement, yet it was stopped by exposure to a very strong attraction. This difficulty would be intermittent in its nature even under the extreme conditions of magnetic force which stopped the watch, because the balance and hair spring were composed of non-magnetic alloys. Subsequently, when the same make of watches were produced containing the whole escapement as well as balance and hair spring composed of alloys of palladium, I exposed one to the tests mentioned above without stopping it or interfering with its rate. It is probable that long continued exposure to an intense magnetic field would tend to accelerate the rate of such a watch, because the resistance to cutting the lines of force would slightly reduce the length of the arc of vibration and therefore increase the number of beats during a given time; but I have not had time to learn by experiment whether these conditions of continuous exposure to an intense magnetic field could under any cir cumstances affect the rate of such a watch. It is evident, however, that a watch worn on the person would not be exposed for a sufficient length of time to receive any modification of rate. In any event, such influence upon rate would not be permanent, but would continue only while the rapidly moving parts were cutting lines of force in a magnetic field. The alloys of palladium referred to possess an elasticity comparable to steel, as is shown by their practical operations in watches and chronometers. It is undoubtedly not oxidizable in moist air; and the alloys, being composed of both paramagnetic and diamagnetic metals, must approximate more or less closely to a neutral substance. Several of the types of watches made in this country and in Europe have contained non-magnetic movements, using alloys of other metals than palladium. The present extensive use of dynamos, and the prospective general introduction of motors, especially upon street railways, will render watches which are unaffected by magnetism a general necessity to all desiring accuracy in their watches. SOME PHOTOGRAPHIC EXPERIMENTS ON THE COLOR OF THE SKY. By LORD RAYLEIGH, in discussion of Tyndall's theory of the color of the sky, showed that the scattering of light from small particles is sufficient to explain most of the phenomena connected with skylight, especially its color and polarization. His experiments on the subject seemed to substantiate the theory. |