TRACT 26.

MEAN DENSITY OP THE EARTH.

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to be drawn from thence made with ns, and these are placedin the third column. And since, in every triangle rs p, theangle s is constant, and the sum of R and p is equal to theconstant quantity 75° ; therefore each of the angles r, or thenumbers in the third column, being subtracted from 75°, thereremains the corresponding angle p ; and these remainders areplaced in the fourth column. Then, since the method of so-lution is this, as sin. p : sin. r :: rs : Sp — * RS 5 anc ^

again, as radius 1 : tang. elev. : : s p : alt. of p above s, whichwill he = sp x tang. elev. = x rs x tang. elev. Orin logarithms sin. r — sin. p + rs + tang. elev. = log. ofthe altitude of the point. Therefore, having taken, from atable, the sines of r and p, and placed them in the fifth andsixth columns, subtract the latter from the former, and writethe remainders in the next or seventh column ; to these addthe constant logarithm of rs, and write the sums in the eighthcolumn ; take out then the tangents of the angles in the se-cond column, and having placed them in the ninth column,add together the adjacent numbers of the eighth and ninthcolumns, placing the sums in the tenth column, which beingthe logarithms of the altitudes or depressions of the points p,take the corresponding numbers from a table of logarithms,and set them in the eleventh or last column, for those alti-tudes or depressions with respect to the point s, with theheight of the theodolite included, and which is afterwardsallowed for, its height being generally about 44 or 4-f. feet.In the second column, d denotes depression, and e elevation;in the last column, d denotes depression and A altitude.