the case may be) was unity at a certain standard temperature, as for instance at the temperature of melting ice. Thus if the length of a brass bar be unity at 32° Fahr., at 33° it will be 1.00001: hence .00001 is the linear coefficient of expansion of brass for 1° Fahr. 34. Linear dilatation. Lavoisier's method. Several methods of finding the linear dilatation of solids have been proposed. In one of these, namely that adopted by Lavoisier and Laplace, a telescope is placed upon a horizontal axis between two pillars, as in Fig. 8. This axis carries a the cross piece in the direction denoted by the arrow-head. This pressure will move the cross piece and turn round the axis of the telescope to which the cross piece is rigidly attached, so that the telescope will now point to a different object. Suppose that the object to which it is pointing is a vertical scale of inches at a considerable distance. If a horizontal wire be placed in the telescope so as to appear in the centre of its field of view, this will seem to have travelled over a considerable distance on the vertical scale for a very small expansion of the bar. It will be seen that this apparatus is similar to that of Fig. 7, the telescope and vertical scale of inches performing the part of the pointer and graduated quadrant. 35. Ramsden's method. In Roy and Ramsden's appa ratus there are three troughs, the first and the last containing iron bars, while the middle one contains the bar of which the dilatation is to be measured. To the two extremities of the iron bar contained in the first trough there are fixed the eye-pieces of two microscopes, the object-glasses of which are fixed to the corresponding extremities of the bar in the middle trough. These microscopes are directed towards two marks attached to the extremities of the iron bar in the farther trough. The first and third troughs are kept filled with melting ice, so that the iron bars in these are always of the same temperature. (These bars are permanently fixed at one end and moveable through a collar at the other.) Hence the points of attachment of the eyepieces of the two microscopes to the first bar may be regarded as rigidly fixed, as well as the points of attachment of the two marks, which are fastened to the extremities of the iron bar in the third trough, inasmuch as there is no expansion or contraction of these two bars through change of temperature. On the other hand, the bar in the middle trough is first of all placed in ice, and afterwards in water, of which the temperature is varied by means of lamps, in order that the dilatation of this bar may be measured. This middle trough rests upon rollers, and by means of a screw attached to the table (not shewn in the figure) the left-hand end of the bar is always kept in the same position, so that the object-glass of the left-hand microscope which is attached to the middle bar may be regarded as fixed. But the righthand extremity of the middle bar, and consequently the object-glass attached to it, is moveable, and will move towards the right when an expansion takes place. At the left side therefore the eye-piece, object-glass, and mark are fixed, while at the right side the eye-piece and mark are fixed but the object-glass is moveable. Now the right-hand eye-piece has in its field of view a vertical thread, which at the beginning of the experiment, when all the three troughs are filled with melting ice, may be supposed to coincide precisely in position with the right-hand mark. But when the object-glass of this microscope has been moved owing to the expansion of the middle bar, this thread will no longer coincide with the mark: nevertheless it may be made to do so by means of a screw attached to the eye-piece and which moves the thread. It is thus apparent that the number of turns and fractional parts of a turn of this screw necessary to bring back the thread to coincidence with the mark affords the means of calculating the expansion of the middle bar, which may thus be determined with very great precision. 36. Pouillet and Daniell's methods. In the last method, as well as in that previously described, the bar of which the dilatation is to be measured is immersed in a liquid, and therefore cannot be heated to a very great extent. If we wish to measure the dilatation of a substance at a high temperature we must use some other method. Pouillet has devised an instrument by which the amount of dilatation may be measured at a distance, while Daniell has effected the same object in the following manner. The bar of which the expansion is to be measured is inserted into A, a black-lead tube, B and pushed to the bottom; above it is c placed an index B, which is pushed down into contact with the bar, and which is kept somewhat tight by means of a collar CD. When the bar expands through heat this index is pushed up, but is left in its place when the same bar again contracts. Thus by an arrangement similar to that of the maximum thermometer the expansion of the bar may be determined. It may be easily shewn that in this apparatus the index B (neglecting its contraction since it is small) will remain pushed out by a quantity which represents the difference. between the expansion of the bar and of the tube containing it. For suppose that at the highest temperature reached the bar and the index B are in contact together. temperature falls the bar will contract, leaving a vacant space between the bar and the index; but, on the other hand, the whole tube as it contracts will tend to diminish this vacant space, and to push the bar and the index nearer together. The vacant space will thus be the difference between the expansion of the tube and that of the bar, and indeed it is evident that if the bar be composed of the same material as the tube there will be no vacant space. In using Daniell's instrument it is therefore necessary to obtain independently the expansion of the tube. Fig. 10. As the 37. The following table will exhibit the results obtained by these various instruments, and it is instructive to notice |