Thus far the computations have been made from the base on Hounslow Heath (27404.2 feet). We shall now proceed to the base of verification on Romney Marsh, by the fewest triangles which present themselves; but it may be necessary to premise what follows respecting the data.

As that part of the earth's surface to which the operation is confined, has been considered as a plane, it is evident that the mode of correcting the angles for computation must, in some degree, have been arbitrary; and therefore it follows, that in reducing the observed angles to those of plane triangles, each angle may be varied to certain limits; and consequently the opposite sides may be varied to certain limits also; but it is evident, that the means of the extreme results, obtained in this manner, must be very near

the truth, and perhaps will be considered more accurate than the distances deduced from a single correction of the same angles. Accordingly, if we vary the angles (in reducing them to 180°), from Hounslow Heath, to the XIII. triangle, so as to produce the greatest and least lengths of the opposite sides, we shall have 141746 feet, nearly, for the mean distance of Hollingborn Hill from Fairlight Down; which, however, is only about 11⁄2 feet more than the distance in the xIII. triangle.

The computation may be carried on to the base of verification by means of the three following triangles; and the xxIII. and

Those triangles, with 141746 feet (Hollingborn from Fairlight), give 41534.4, for the distance of Lydd from Ruckinge; hence, from the xx. triangle, the base of verification is found to be 28533.3 feet: which is about 28 inches short of the mea

surement.

For the distance of Hollingborn Hill from Fairlight Down, deduced from the measured base on Romney Marsh.—As 28533.3 : 28535.66 (the measured base): : 141746: 141758 feet, the distance required: the mean of this, and 141746 is 141752 feet.

From this mean distance, all the sides of the remaining triangles in the principal series are derived. And it has not been thought necessary to alter any of the angles, as originally corrected for computation, because of the trifling variations which would consequently arise in the distances on that account.

We should have computed the distances in the vicinity, and to the eastward of Romney Marsh, from the base of verification only, but there are reasons to suppose that it was not measured so accurately as the other on Hounslow Heath.