the rods. This will be explained by the following short description of the compensation bars and the method of using them. Two bars, one of iron and the other of brass, 10 feet long, placed parallel to each other, were riveted together at their centres, it having been previously ascertained, by numerous experiments, that they expanded and contracted in their transitions from cold to heat, and the reverse, in the proportion of three to five. The latter was coated with some non-conducting substance to equalise the susceptibility of the two metals to change of temperature; and across each extremity of these combined bars was fixed a tongue of iron, with a minute dot of platinum, almost invisible to the naked eye, and so situated on this tongue, that, under every degree of expansion or contraction of the rods, the dots at each end always remained at the constant distance of 10 feet. This will be better understood by reference to the sketch below. A is the iron bar (about five-eighths of an inch wide and one and a half deep), the expansion of which is represented by three; B the brass bar (of the same size), the expansion of which is five, the two being riveted together at the centre C; DE and de are the iron tongues pinned on to the bars, so as to admit of their expansion, with the platina dots at D and d. The tongues are by construction made perpendicular to the rods at a mean temperature of 60° Fahrenheit, and the expansion taking place from their common centre, when A expands any quantity which may be expressed by three, B expands at the same time a quantity equal to five, and the position of the tongues is changed to D F, df, the dots D and d remaining unalterably fixed at the exact distance of ten feet. It is evident from this construction, that the dots at the extremities of these bars could not, if desired, be brought either into actual contact or coincidence; but a more correct plan was adopted, which consisted in laying each rod so that the dot at its extremity should always be at a fixed distance from that at the end of the next rod. This was -effected by means of powerful microscopes, attached to the end of similar short compound bars *, 6 inches long, mounted on a stand, by which means they could be laid perfectly horizontal by a spirit level, the microscopes in these bars occupying the position of the dots on the longer rods. These dots, after the rods had all been carefully levelled, were brought exactly under the microscopes by means of three micrometer screws attached to the box in which each rod was laid, so that it could be moved to either side, backwards or forwards, elevated or depressed, as required, the rods being laid on supports equidistant from the centre of the box, that they might always have the same bearing. The point of starting was a stone pillar, with a platina dot let into its centre, with a transit instrument placed over it, by which the line was laid out with the greatest precision, with the assistance of sights at each end of the bars; an average of about 250 feet being completed in one day, and five boxes, giving a length of 52 feet, being levelled and laid together. About 400 feet of this measured base was across the river Roe, and clumps of pickets were driven at intervals of about 5 feet 3 inches apart from centre to centre, by a small pile engine, on the heads of which the boxes containing the compound rods rested. At the end of each day's work a triangular stone was sunk at the end of the last bar laid, with a cast-iron block fitting over it, having a brass plate with a silver disk let into the middle of the brass, which was adjustable by means of screws. This disk was brought exactly under the focus of the extreme microscope, and served as a starting point the following day, a sentinel being always left in charge of this stone, which was further secured by a wooden cover screwed over it. The total length of the measurement of this base amounted to about 8 miles; 2 miles were subsequently added by a method described in the next page, making the entire distance between the two extremities rather more than 10 miles. * This was the usual distance between the foci of the microscopes; but to meet cases where the uneven surface rendered it difficult to bring the short bars to a level at this distance, it was sometimes diminished to one half. Microscopes of different lengths were used where the inclination of the ground rendered it necessary to lay the boxes on different levels, so that the platina dots might be brought in the focus of each microscope. The old base of verification on Salisbury Plain has recently been remeasured with these compensation bars. Detailed descriptions of the various methods that have been at different times adopted to insure the correct measurement of base lines on the Continent, may be found in all standard works on geodesical operations*. A popular account of the mode of conducting these measurements, and of the nature of the rods, &c., used, is also given in Mr. Airy's " Figure of the Earth," in the "Encyclopædia Metropolitana," commencing at page 206. A base measured on any elevated plain is thus reduced to its proper measure at the level of the sea. Call A B the measured base at any elevation A a above the level of the sea a b its value at this level Cb the radius of the earth B b R h, And the altitude above the sea A a as ascertained by levelling, or by the barometer. R.B Then R+h: R:: B: b. &b=R+h And B-b the difference of the measured and re a A B b then, the log of the base, in feet, be added to the log of the altitude, and the log of the sum of the radius and altitude be subtracted therefrom, the remainder will be the log of a number to be * "Recueil des Observations Géodesiques, par Biot et Arago"-" Puissant, Traité de Géodesie "-" Base du Système Métrique decimal;" and the works of Cassini, Francœur, Colonel Lampton, &c. The bases of the original arc of Mechain and Delambre, described in the "Base du Système Métrique," were measured with rods of platinum two toises long; to each bar was attached at one end a rod of brass. The proportion of the expansion of brass and platinum being known, the expansion of the platinum rod was inferred from the observed difference of expansion of the two rods. The rods were laid in boxes, and placed on trestles; and their ends not brought into contact, but measured with a slider. The temperature was reduced to thirteen degrees of Reaumur. The length of the base of Perpignan was 6006.28 toises; and that of Melun 6075.9 toises. The calculation of the Perpignan base of verification from that of Melun differed only eleven inches from its actual measurement on the ground. These platinum bars are described in page 203, vol. i. Puissant's "Géodesie." Few bases have ever been measured solely for the determination of the value of an arc of the meridian, or of a parallel, but have formed at the same time the foundations of the survey of a country. deducted from the measured base, to reduce it to its value at the level of the sea. This correction, though generally trifling, is not to be neglected when the base is measured on ground of any considerable elevation. Mr. Airy, in page 198 of the "Figure of the Earth," in the "Encyclopædia Metropolitana," gives this formula :-" If r be the earth's radius, or the radius of the surface of the sea (which is known nearly enough), h the elevation, the measured lengths must be multiplied by the fraction,+h or they must be dimi or nished by the part of the whole. If the surface slopes uniformly, the mean height may be taken; if it is very irregular it may be divided into several parts." Beside the marks at the extremities of a base line-which, if it is to form the groundwork of a survey of considerable extent, should be constructed so as to be permanent, as well as minute— intermediate points should be carefully determined and marked during the progress of the measurement by driving strong pickets, or sinking stones into the ground, with dots upon a plate of metal, or some other indication of the exact termination of the chain, clearly defined upon them. These marks serve for testing the accuracy of the different portions, and reciprocally comparing them with each other. It has been already remarked, that the length of the base on the Ordnance Survey of Ireland was not obtained entirely by measurement, an addition of two miles having been made to its measured length by calculation. This calculation was also contrived to answer the purpose of verifying the measurement of intermediate portions of the base between marks left for the purpose, as alluded to in the last paragraph; and which will be explained by reference to the figure given below, in which AB represents the portion of the base actually measured, and BC, that to be added by calculation, for the purpose of extending the base to C, to obtain a more eligible termination. The points E and D have been marked during the measurement, and are thus made use of: The stations F and G are selected, so that the angles at E may be nearly right angles, and the points themselves nearly equidistant from the line, and about equal to AE. Similar conditions determine the positions of H, I, K, and L. At A the whole of the objects visible are most accurately observed with a large theodolite, which is then taken to the other points on the line, as well as |