TRACT 26.

MEAN DENSITY OF THE EARTH.

23

and the angle g. For then it is, as sin. p : sin. g :: PG : vp,or log. p p = log. pg -f sin. g — sin./); so that the sum of thelogarithms of pg and sine of Z.G, is a constant number, fromwhich the numbers in the fifth column are to be subtracted,to find those in the sixth column. The rest of the work isthe same as in the first example.

As to the irregular sections, the computation of them dif-fers so little, in manner, from that of the usual vertical sec-tions, that an example of it is unnecessary: and as to the fewhorizontal sections, they need no computation, but only anallowance for the height of the theodolite.

In the following abstract, of the results of the computationof the sections, the first column contains the number of thepole, the second and third the vertical and horizontal angles,and the last the difference of altitude in feet, between thefoot of each pole, and the point from which the vertical an-gles were observed, after making the allowance for the heightof the theodolite above the ground. At the end of this ab-stract, is a plate, n°. 1, of the figures referring to the numberof the section, showing the direction in which it was carried,with the degrees and minutes in the angle formed by it andthe base line.