TRACT 26. MEAN DENSITY OF THE EARTH.

43

i /,

■ V'

feet, and often within 5, which on an average might be aboutthe 100th part of the whole altitude ; and when we considerthat the number of such estimated altitudes is very great, andthat it is probable the small errors among them would nearlybalance one another, the defect of those that might be reckon-ed too little, being compensated by the excess in those whichmight be taken too great, we need not hesitate to pronounce,that the error arising from the estimation of the altitudes, isprobably still much less than that part.

It was necessary to determine these altitudes of the pillars,in order to compute the sines of the angles of elevation sub-tended by them, as the theorem requires the use of thesesines; and the very easy method used in deducing the latterfrom the former, is explained after registering the altitudesof all the pillars, as they were computed. This register con-sists of 16 tables, namely, 4 quadrants of spaces in the alti-tudes, and 4 in the depressions, for each observatory, asspecified in the titles of them. The numbers are feet, likeall the other dimensions. The numbers on the same horizon-tal line, from left to right, are such as are all in the samering ; and those in one and the same vertical column, are inthe same sector, or between the same two radii; the numberof the ring, counted from the common centre, is written inthe left-hand margin; and the number of the vertical column,or distance of the space, or sector, from the meridian, at thetop; also the radius of each ring, that is, the line from thecommon centre to the middle of the ring, is written on thesame line with it, in the right-hand margin. It may be fur-ther remarked, that in such little spaces as were cut throughby the boundary line, between elevations and depressions,thus making but a part of such spaces in each of those deno-minations, each space was accounted as a whole one; butthen the mean altitude or depression, in each part, was dimi-nished in the proportion of the whole space, to the part of itso included in the boundary. The altitudes and depressionsare set down first with respect to the Southern observatoryo; then for the Northern observatory p; and, in each, thealtitudes are placed first.

t :

■■ y