FOURTH ORDINARY MEETING. ROYAL INSTITUTION, 30th November, 1857. THOMAS INMAN, Esq., M.D., PRESIDENT, in the Chair. The following were elected Ordinary Members : ROBERT HENRY Hall, Esq. WILLIAM HENRY GRIMMER, Esq. The Resignations of Messrs. George Holt, jun., H. V. Rudd, and the Rev. P. Haines, Hoylake, were accepted. Dr. RETSLAG took exception to the title of his paper as referred to in the last vol. of the Society's “Proceedings," taken from official documents; and to the brief report, which, he thought, did not correctly signify the nature of the communication.* Professor T. C. ARCHER exhibited one of Messrs. Wessel and Kukla's patent gas stoves, the construction of which is exceedingly simple, and its merits considerable.t * Dr. Retslag subsequently supplied the Secretary with a copy of his letter in the Liverpool Albion, dated May 6th, 1857, from which it appeared that the correct title of this paper was, “On the political philosophers of the 16th and 17th centuries ;” and not, as reported, “On the political philosophy of the philosophers of the 16th and 17th centuries.” The paper in question was a portion of“ an introduction to an essay" upon that subject, in which the author seeks “ to trace the gradual change in the public mind of Europe, and the effect of this change upon arts, sciences, and politics, particularly since the beginning of the 14th century, by preparation of the more materialistic views of modern times, in which nature and things material are no longer regarded as opposed and hostile to Spirit and God, but are his incarnation and one of his principal revelations." The Society is not responsible for, nor identified with, the individual sentiments of members which appear in print.–Editor. + The Secretary has tested one of these little stoves by using it exclusively since Christmas last in his study, a room 18 by 15 feet, and 12 feet high, containing 3240 cubic feet of air, and freely ventilated by chimney, window, and two doors, one opening into the hall, and the other into a large passage leading to the garder. The means have also been present, through a large aquarium, of keeping the apartment from becoming unduly dry. During these months he has found no inconvenience from the stove, and much to commend in it. The atmosphere has never been unpleasant, has been comfortably heated by an expenditure of gas equal to three jets He also exhibited a number of models of Tropical fruits, presented to the Museum of Applied Science by Mr. Dadabhoi Naoroji; and submitted two white Annelides (gen. Borlaria), found in one of the graving docks. Mr. ALFRED HIGGINSON exhibited a piece of charred wood taken from the interior of the cover of a house boiler. An interesting discussion arose out of this on the chemical changes effected in vegetable materials by long exposure to steam, and on spontaneous combustion. Dr. Innan opened a case of preserved milk, forwarded by J. B. Lloyd, Esq., in whose possession it had been for three years. The process of preservation was that after the Abbé Moigno's, but it had entirely failed, the contents being decomposed. The paper of the evening was then read. ON THE COMPOSITION OF ROTATORY MOTION. BY GEORGE HAMILTON, F.R.A.S., F.C.S., PROFESSOR OF CHEMISTRY, QUEEN'S COLLEGE. I. PRINCIPLE OF COMPOUND ROTATIONS. IF If a body situated at A (Fig 1) on a plain surface receives an impulse in the direction AB, sufficient to con(not burning always), and perfectly fit for respiration. In a single hour he has been able to raise the temperature in January to 56° F., and he has generally sustained it at that heat, though he has had it in that month as high as 67° in all parts of the room. One of its greatest advantages has been the entire absence of trouble attending its use, the power of regulating the temperature by turning off the gas at pleasure, and of lighting it during the night when the room might require to be heated. The facility with which this gas stove can be fitted up will render it a most important furnishing to the bath-room, as well as to small chambers where fires cannot be conveniently used : and it is not unworthy of remark, that by a simple contrivance it may be used for laboratory purposes, a flask of water being speedily boiled over it, and evaporation as steadily conducted as may be desired. The discussion which has taken place on the advantages and possible disadvantages of Wessel and Kukla's stove justify these remarks upon its merits.—Editor. vey it to B in a certain unit of time, the body will move over the line AB with a uniform velocity, and arrive at B at the end of the given time. If it receives an impulse in the direction of AC, of such an intensity as would convey it to C in the same unit of time, at the end of the time the body will be at C, having moved uniformly over the line AC. If both forces, at the same instant, act on . the body at A, it will move uniformly over the line AD, the diagonal of the parallelogram of which AB, AC, are adjacent sides, and arrive at the point D at the end of the given time. Instead of considering A as a moveable body on a plane, let it be a fixed point on the surface of a sphere, the sphere being free to turn in any direction whatever. The force applied at A (Fig. 2) in the direction of a tangent to the arc AC, will cause the point A to move uniformly through the arc AC. The force applied at A, A in the direction of a tangent to AB, will cause the point A to move uniformly through the arc AB. If both forces be applied at the same instant, the point A will move neither over AC nor AB, but over arc AD intermediate between the two; and if the time be indefinitely small, the arc AD will be the diagonal of an indefinitely small parallelogram constructed on the same principle as that which applies to compound rectilinear motions. In order to pass from the consideration of the motions of a point on the surface of a sphere, to the consideration of the axes on which the sphere would turn in obedience to the impressed forces, let AB (Fig. 3) be the axis on which a sphere revolves with a velocity represented by the magnitude of the line AB, and let a force be applied to turn the sphere about the axis AC with a velocity represented by the magnitude of AC; then it may be demonstrated that the sphere will revolve about the axis AD, some which lies in the plane BAC, with a velocity represented by the magnitude of AD, AD being the diagonal of the parallelogram ABDC, of which AB and AC are adjacent sides. For this purpose assume any point on the surface of the sphere, let the projection of this point on the plane BAC be a, situated between AB and AC; then ab, perpendicular to AB, is the projection of the arc described by the assumed point, in a given time, about the axis AB; and similarly ac is the projection of the arc described by the same point, in the same time, about the axis AC, and if the time be indefinitely small, the diagonal ad of the parallelograin abdc will represent the direction and magpitude of the resulting motion, when both the component forces are impressed at the same instant of time. But since ab is perpendicular to AB, and ac to AC, the angle bac is equal to BAC, and the sides about these equal angles are proportional, for they are proportional to the velocities, therefore the parallelogram ABDC is similar to the parallelogram abdc. It may be shewn that ad is perpendicular to AD, therfore AD is the new axis. Instead, therefore, of taking the parallelogram abdc, which refers to the motion of a point on the surface of a sphere, we may take the parallelogram ABDC, which refers to the axes on which the sphere turns. Thus it appears that if the adjacent sides of a parallelogram represent respectively the axes on which a sphere turns in obedience to two given forces, and also represent the velocities which the forces impart, the diagonal represents the direction of the resultant axis, and its magnitude represents the resultant velocity. From the trigonometrical relations of the sides and angles of the figure, it is easy to deduce the most important propositions of the doctrine of compound rotatory motion. Thus : a or or : or v" = AC : CD = sin ADC : sin DAC = sin BAD : sin DAC because AB and AC represent the velocities v and v'. Thus the component velocities are to each other reciprocally as the parts into which the whole angle, between the component axes, is divided by the new axis of rotation. Again AC : AD = sin ADC : sin ACD = sin BAD : sin ABD sin BAD : sin BAC. Let ALBK (Figs. 4 and 5) be a sphere rotating about the axis KL, in the direction HAFB, and let an impulse be applied at A, in the direction AR, tending to make the sphere rotate about the axis HF. If the point at A, at the instant of impact, could be carried to B in a time infinitely short, the impulse at A would then be equivalent to two equal forces acting on the lever AB at equal distances from the fulcrum C, and in directions AR, BR", parallel to each other, the line AB therefore would remain at rest. But since the sphere cannot rotate with a velocity in finitely great, AB (Fig. 4) tends to assume the position ab immediately after impact, and the point A begins to move in the diagonal of an indefinitely small parallelogram (Fig. 5), in which Ad : Aa = velocity about KL : velocity about HF. The axis AB, therefore (Fig. 4), has not remained at rest, but has moved through an indefinitely small angle, ACa. The maximum effect of disturbance on the line AB is produced when the particle struck is at A, acting in the direction AR. When the particle which receives the impulse at A arrives at F by the rotation of the sphere, it tends to move in the direction FR' parallel to AR; here it has no effect on the position of the axis AB, but it tends to turn the whole sphere about that axis in |