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take, had the care of the trigonometrical survey committed to them, and received their instructions from the Master-General of the Ordnance. They began by the remeasurement of the base on Hounslow-heath with the new steel chain, (of the same nature with the former, but somewhat improved,) and found its length, as before stated, two inches and three quarters greater than when measured with the glass rods. The chain was here reduced, as it had been before, to the temperature of 62°, Captain Mudge having previously ascertained, by a series of experiments made with the chain extended at its full length, and stretched with a considerable weight, that it lengthened 0.0075 of an inch for one degree of heat, on Fahrenheit's thermometer; which agrees well with General Roy's determination of the same by means of the pyrometer.

As a series of triangles was now to be carried from Hounslow-heath to the coast of Kent and Sussex, and from thence westward to the Land'sEnd, it was thought right to measure another base of verification on Salisbury-Plain. This was done with all the precautions used in the former measurements; the length of the line was found to be 36574.4 feet; and when this was connected by a series of triangles with the base on Hounslowheath, and its length deduced from this last by trigonometrical calculation, it did not differ by more than an inch from the actual measurement as here

set down.

This singular coincidence was a sufficient proof of the accuracy with which the two bases and the angles of the connecting triangles had been measured.

One of the principal objects now in view was of importance, both in general geography, and in the topography of England. This was the measurement of a degree of a circle perpendicular to the meridian, for which two stations on the coast of the Channel, Beachy-Head in Sussex, and Dunnose in the Isle of Wight, afforded a good opportunity, being visible from one another in fine weather, though more than sixty-four miles distant, and the line between them being not far from the direction of east and west. The distance between the two stations just mentioned, as deduced from a mean of four different series of triangles, is 339397 feet, =64.28 miles ;) and it is remarkable, that the extremes of these four determinations do not, even in so long a line, differ more than seven feet from one another. But coincidences of this sort are frequent in the trigonometrical survey, and prove how much more good instruments, used by skilful and attentive observers, are capable of performing, than the most sanguine theorist could have ever ventured to foretell. In two distances that were deduced from sets of triangles, the one measured by General Roy in 1787, the other by Major Mudge in 1794, one of 24.133 miles, and the other 38.688, the two

measures agree within a foot as to the first distance, and sixteen inches as to the second. Such an agreement, where the observers and the instruments were both different, where the lines measured were of such extent, and deduced from such a variety of data, is probably without any other example. We believe it is quite unnecessary to add, that these deductions are all made in the fairest and most unexceptionable manner, without any means being taken, purposely to bring about a coincidence that would not have otherwise taken place.

Besides the determination of the distance from Dunnose to Beachy-Head, the azimuth or bearing of the line between them, with respect to the meridian, was carefully observed, by means of the pole-star, after the manner practised by General Roy. From these observations Major Mudge has drawn the following conclusions. At Beachy

Head, in latitude 50° 44' 24", the degree of longitude, measured on the above parallel, is 38718 fathoms; the degree of a circle perpendicular to the meridian 611832; the degree of the meridian itself in that latitude being taken at 60851 fathoms, as deduced from General Roy's measurement. From the lengths of these degrees of the meridian, and of the circle perpendicular to it, it follows, that if the earth be an ellipsoid, the diameter of the equator is to the polar axis as 149 to 148, which makes the inequality between these two lines more

than twice as great as it appears to be by taking the most probable average, deduced from all the observations that have been made in different latitudes. What reason can be assigned for this peculiarity in the physical constitution of our island, seems impossible at present to explain, though the continution of the Trigonometrical Survey may be expected to throw some light on it. Local causes may perhaps affect the direction of gravity in the south of England, and may make that country appear to be a portion of a smaller and more oblate spheroid, than agrees with the general configuration of the earth's surface. Or perhaps, too, as many have imagined, and as Major Mudge seems disposed to think, the figure of the earth is not a solid formed by the revolution of an ellipsis on its axis; and the agreement or disagreement of the measures of degrees with one another, is not to be judged of by their agreement or disagreement with this hypothesis. To attempt to judge of them in that manner, may be offering violence to nature, and may be only trying to reconcile her phenomena with our conjectural or arbitrary theories.

From the prosecution of the Trigonometrical Survey we may expect a solution of these questions: the unexpectedness of the results makes the work more valuable to science; and as we are sure that the observations are accurate, the less they agree with our preconceived opinions, the more interest

ing do they become, and the more likely are they to furnish important information.

It has already been observed, that Major Mudge deduced the results of his observations on a principle more accurate than General Roy, by reducing every angle measured with the theodolite to a plane passing through the three angular points of the triangle, and thus computing the chords instead of the arches themselves.

"As the lengths," says he, "of small arcs and their chords are nearly the same, it is evident that the calculations might be performed sufficiently near the truth in any extent of a series of triangles, by plane trigonometry, if the angles formed by the chords could be determined pretty exact. We have endeavoured to adopt this method in computing the sides of the principal triangles, in order to avoid an arbitrary correction of the observed angles, as well as that of reducing the whole extent of the triangles to a flat, which evidently would introduce erroneous results, and these in proportion as the series of triangles extended." Vol. I. p. 271.

Now, concerning the method of calculation here referred to, we must observe, that though it is certainly much preferable to that which supposes the triangles to be all spread out over one flat surface, and is not liable to any considerable inaccuracy, yet is it much more complex and operose than one which we have already pointed out as being de

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