and, on the 26th, all that could be done was to measure the twentysecond and twenty-first hypothenuses. On Friday the 27th, the work went on more expeditiously, having in the course of that day measured six hypothenuses, and placed the tripod at the fourteenth station. On Saturday the 28th, eight hypothenuses were measured, and the tripod was placed at the sixth station. In this day's operation, being arrived near the bridge laid over Wolsey River, double pickets were placed in the ground in the point answering to the extremity of the 1172d rod, reckoning from the north-west, or the 198th rod from the south-east end of the base, that we might recur to them in case of accident; and the eighteen rod lengths, between this point and the sixth station, were measured on the level, instead of the hypothenusal line, which required the alteration of the reduction, as distinguished by the asterisk in the general table. On Monday the goth of August, the measurement with the glass rods was completed; * when the extremity of the 1370th rod overshot the centre of the pipe terminating the base towards the south-east by 17.875 inches, or 1.49 foot. Hence, when the several equations for expansions are respectively taken into the account, we find, that the alteration of the deal rods from the humidity of the air, which, by comparison with the standard, was apparently most considerable in the first and second sections of the base, has now wholly vanished; that is to say, the total amount * The gentlemen who were present at, and assisting in, the last day's operation, were Captain Bisset, Mr. Greville, Sir William Hamilton, Mr. Lloyd, and Dr. Usher, Professor of Astronomy in the College of Dublin. This last gentleman was so obliging as to observe, with the most scrupulous attention, throughout the whole operation with the glass rods, that the coincidence of the second with the first remained undisturbed, while that of the third with the second was completing. of it has been over-rated by 20.964 inches; and this is the contradictory circumstance that has been formerly alluded to. I have already suggested what appear to me to have been the only three possible causes of this difference, found between the estimated and real expansion of the deal rods; and as we are to abandon that measurement entirely, it is of little or no importance now to endeavour to discover, were it possible, whence it may have arisen. If any error was actually committed, which is the least of all probable, it could only have happened at the place of the tripod, by bringing a wrong point of the stem over it when the operation was resumed. But it is well known, how much care and pains were taken to prevent any thing of that sort. Indeed the hypothenusal distances, as given by the chain, agreed so nearly among themselves, that even a foot or ten inches would have made so remarkable a difference in the situation of the next picket, as could not have passed unobserved. Besides, in returning with the glass rods, after passing the Staines Road, the measurement was gradually found (without any leap whatever) to overshoot the pickets, and at last over-reached the south-east pipe by 17.875 inches. I am therefore inclined to believe, that the difference arises partly from what may have been lost by constantly butting one rod against the other, whereby the end of the 1370th did not reach so near to the north-west pipe as it ought 1370 deal In. rods = +27.612 equation of the 1370 deal rods. +20.336 for 6° of the brass scale from 62° to 68°. 1.802 observed contraction of ditto from columns 11th and 12th. 17.875 space by which the 1370th rod overshot the pipe. + 6.648 equation of the 1370 glass rods. 20.964 over-rated in the total expansion of the deal rods. to, and would have done, if the rods had been applied to each other by coincident lines. It must, however, be confessed, that the near agreement between the glass and deal rods in the upper part of the Heath seems not perfectly reconcileable to this supposition. Nevertheless, the descent being quickest, and the irregularities of the surface much more considerable in the lower than the upper part, might produce some effect in one, which did not take place in the other. But the chief part of the difference I take to have proceeded from over-rated expansion; that is to say, the rods, when brought into use, contracted sooner than we imagined, and thereby gave a shorter measure than what was assignable to them from the mean of any two or more comparisons. The last day of August was employed in discharging the party, and removing the various parts of the apparatus to Spring Grove House. Description of the Microscopic Pyrometer, made use of for determining, by experiment, the Expansion of the Metals concerned in the Measurement of the Base. Pl. V. 15. Having, in the preceding part of this Account, given a very minute detail of the actual operations in the field, that the public, being thus informed of every circumstance, might be the better enabled to judge of the accuracy of the result, it remains yet to point out, in what manner the equations for the expansions of the standard scale, steel chain, and glass rods, applied to the apparent measurement of the base, in several of the preceding notes, have been obtained by means of experiments with the pyrometer. It is sufficiently well known, that many years ago, a very ingenious and valuable Member of the Royal Society did publish in the Philosophical Transactions (Vol. XLVIII. 1754, No. 79.) an account of experiments made with a pyrometer of his invention. No doubt was entertained of the accuracy of the experiments here alluded to; on the contrary, they will be confirmed by the account now to be given of these recently made, with which they very nearly agree. But as different pieces of metal of the same kind are certainly susceptible of different degrees of expansion, it was judged best, on the present occasion, to put rods to the test of those very metals that had been made use of in the actual measurement of the base. For, supposing both sets of experiments to have been made with instruments equally perfect, and to have been in other respects equally well conducted, this must always be considered as the most unexceptionable method. Besides, the expansion of rods of the length of five feet being ascertained, the unavoidable error of observations of this delicate nature, becomes lessened in proportion to the excess of their length above shorter rods. In these new experiments too, another sort of pyrometer, invented by Mr. Ramsden, has been applied, of such accurate construction, that it seems not easy to improve it. The microscopic pyrometer, so named, because by means of two microscopes attached to it, the expansion is measured, consists of a strong deal frame, five feet in length, nearly twenty-eight inches broad, and about forty-two inches in height. The elevation of the eye-piece side, or that which presents itself to the observer, and also of the micrometer end, or that which is towards his right-hand, as well as the general plan of the top, are represented by a scale of one inch to a foot, or one-twelfth part of the real dimensions, in Pl. V. where likewise may be seen the angular view of the fixed end, together with plans, sections, and elevations, of several of the principal parts, done to larger scales. From these, it is hoped, the construction of the machine will be easily understood, without entering into a minute description of the almost numberless smaller parts whereof it is composed. On the top of the frame, two deal troughs, upwards of five feet in length, are firmly screwed. That towards the observer overhangs the frame something more than an inch: that on the farther side is even with the back part. Each of these troughs, which are about three inches square in the inside, contains a cast iron standard prism, whose sides are 14 inch. The manner in which the prisms are fastened to the bottoms of their respective troughs, and the nature of the apparatuses they carry on their extremities, will be readily conceived, by referring to the particular plans and elevations of them, comprehended in the group of eight small figures towards the right hand of the general plan. Four of these appertain to the left-hand or fixed microscope; and the other four to the right-hand or micrometer microscope, so distinguished, because it has a micrometer attached to it. By means of the brass collars which embrace the prisms, their left-hand or fixed ends are screwed down extremely fast to the brass pieces whereon they rest, so as to be perfectly immoveable there with regard to their troughs; whereas their right-hand ends are kept easy, yet without shake, in their collars, that they may contract or lengthen freely as the temperature may require, without occasioning any strain upon the parts. The prism in the nearest trough may be called the eye-piece prism, because it carries the eye-pieces of the microscopes; and that in the farther trough, the mark prism, because it carries the marks or cross wires at which the microscopes respectively point. The troughs are covered with pitch in the inside, to make them hold water; and each has a cock in the left-hand end for discharging it. Between the two deal troughs, one of copper, as a boiler, is placed, somewhat shorter than the former, but still upwards of five feet in length. It is about 24 inches broad, and 31⁄2 in depth. The centre of the boiler, or rather the centre of the object lens which stands in it, as we shall have occasion soon to point out, is distant from the cross wires of the mark 5.81 inches; and |