bearings taken from them to the same object; for, if the relative situations of such stations are not correctly determined, these bearings will not all intersect in the same point on the plan. The last operation at each station is to measure the forward angle. In this manner proceed to the stations d, e, f, g, &c., and having arrived at g, measure the angle to the pole A, as to a forward station, and, placing the theodolite upon that spot, direct the telescope to g, as a back station, in the usual way; this done, release the upper plate, and direct the telescope to the first station, a, from which A had been observed, and if all the intervening angles have been correctly taken, the reading of the two verniers will be precisely the same as when directed to A from the station, a; this is called closing the work, and is a test of its accuracy, so far as the angles are concerned, independent of the compass needle. If the relative situation of the conspicuous points, A, B, &c., were previously fixed, there would be no necessity to have recourse to the magnetic meridian at all, as a line connecting the starting point, a, with any visible fixed object, may be assumed as a working meridian; and, if it be thought necessary, the reading of the compass needle may be noted at a, when such fixed object is bisected; and upon the theodolite being set to the reading of this assumed meridian, at any subsequent station, the compass needle will also point to the same reading as it did at first, if the work is all correct, and no local attraction influences the compass.

While the instrument is at A, take angles to all the conspicuous objects, particularly to such as you may hereafter be able to close upon, which will (as in the above instance) verify the accuracy of the intervening observations; having done this, return to g and ƒ, &c., and proceed with the survey in the same manner as before, setting the instrument up at each bend in the road, and taking off-sets to the right

and left of the station lines; arriving at i, survey up to, and close upon, B; then return to i, and proceed from station to station till you arrive at m, where, if the whole work is accurate, the forward angle taken to b will be the same as was formerly taken from b to m, which will finish the operation.

SECTION VIII.

GENERAL OBSERVATIONS ON SURVEYING.

SURVEYING may be defined, the art of representing a country, or any portion of the earth's surface, upon paper, in such a manner that we may be able, by means of a scale, to measure the horizontal dimensions of its features; as territorial boundaries, lakes, rivers, forests, roads, &c.

"Accurate surveys of a country are universally admitted to be works of great public utility, as affording the surest foundation for almost every kind of internal improvement in time of peace, and the best means of forming judicious plans of defence against the invasions of an enemy in time of war; in which last circumstance, their importance usually becomes the most apparent. Hence, it happens, that if a country has not actually been surveyed, or is but little known, a state of warfare generally produces the first improvements in its geography: for in the various movements of armies in the field, especially if the theatre of war be extensive, each individual officer has repeated opportunities of contributing, according to his situation, more or less towards its perfection; and these observations being ultimately collected, a map is sent forth into the world, considerably improved indeed; but which, being still defective, points out the necessity of something more accurate being undertaken, when times and circumstances may favour the design."-Introduction to an Account of the Trigonometrical Survey of England.

The foundation of every survey is a base line; and upon the accuracy with which the length of the base is obtained, the correctness of the entire survey must depend.* The measurement of a base, then, is not only the primary, but also the most important work to be performed. Various methods have been pursued to effect this object.

Previous to the measurement of the Hounslow base, deal rods were considered very good for the purpose, and had been extensively used on the Continent; but experiments made on that occasion proved their unfitness, owing to the uncertainty of their expansion; perhaps, however, our more humid climate may have produced a greater effect upon them, than the comparatively dry atmosphere of situations where they had before been tried; and it appears, from the account of the operations on Hounslow Heath, in 1784, that the season was a very wet one. On the whole, if I may presume to offer an opinion in the matter after their condemnation by men of so much science, I should still advise the use of deal rods under other circumstances, and where glass tubes and steel chains, such as were used on the occasion above mentioned, with all the vast preparation made for their application to the object in the most perfect man

* The length of the base measured on Hounslow Heath, for the grand Trigonometrical Survey of England, in 1784, was, when reduced to the level of the sea, 27404-1037 feet. Three modes of measuring were tried, viz., with deal rods, with a steel chain of peculiar construction, and by means of glass tubes. The uncertain expansion and contraction of the deal rods, was found to produce a very fallacious result. The steel chain does not appear to have had a fair trial upon this occasion. The method proposed with glass tubes obtained the preference. Accordingly, the measurement took place with these, and was conducted in a scientific manner, with all the care due to so important an operation. In 1791, a careful measurement of the same base was made with the improved steel chain, which only differed from the original one performed with glass tubes, by about 2 inches. Subsequently, in 1794, a base of verification was measured on Salisbury Plain, which varied only about 3 inches from its computed length.

ner, cannot be had; and, more than all, when the contemplated survey is not of the most important character.

Indeed, Mr. Dalby, the associate of General Mudge in the grand survey, recommends the use of such rods on ordinary occasions; and, as I look upon that gentleman's opinion with respect, I shall quote from his work on Mathematics what he says on the subject; concurring, as I do, with his views, and not being aware of any better plan to substitute for the one he proposes.

"But the most difficult and tedious operation connected with a survey, is that of measuring a base line accurately. We shall, therefore, recommend a perusal of the account of the Trigonometrical Survey, to those who may engage in an undertaking of this kind, when great exactness is required. A base for common surveys may be measured with a 20-feet deal rod: for this purpose, a rope, not less than 100 yards, should be stretched very tight along the ground; the rod must then be applied to the rope, and its extremity may be marked with a small pin stuck in the rope, to preserve the distance while the rod is removed. When the measurement is carried on to the extent of the rope, a peg should be driven in the ground, and a notch cut on its top, exactly under the end of the last rod. The rope must then be taken up, and stretched again in the direction of the base, and the measurement continued as before.

"When the measurement is carried over hollows or ditches, it may be necessary to support the rod in the middle: it should not, however, be made very slender.

"If rising grounds intervene, the slant distances must be measured as hypothenuses, and afterwards reduced to the corresponding horizontal lines: the elevations and depressions may be taken with a theodolite which has a vertical arc.