2

CALCULATIONS TO ASCERTAIN THE TRACT 26 .

count of the measures of the lines and angles, and of thecalculations which I have raised from them, with all possiblecare and faithfulness, for the purpose of determining the mea-sure of the ratio of the mean density of the earth, to that ofwater, or any other known matter.

These calculations were naturally and unavoidably longand tedious; and the more so as the business was in a man-ner quite new, which laid me under the necessity of invent-ing and describing such modes of computation as should beproper to be applied, in so important and delicate a business.Having, at length, with close and unwearied application fora considerable time completed all the calculations, the follow-ing sheets contain an account of those operations, with theresults arising from them ; and are accompanied with suchdrawings as are necessary to illustrate the descriptions. Theyexhibit also a synopsis of the measures which were taken ofthe lines and angles; from which any person may at any timesatisfy himself of the truth of the computations that have beenmade, and are here described. These measures are here im-mediately subjoined, before proceeding to describe the com-putations made from them.

A synopsis' of the horizontal and vertical angles that were ob-served at the principal points in making the survey about

Shichallin.

In the first column are contained the names of the horizon-tal angles, the measure of which, in degrees and minutes, arein the second column ; and the vertical angles are in the thirdcolumn; in which it is to be observed, that the letter denot-ing the object is placed before the degrees and minutes, andE or d after them, to show that they are in elevation or de-pression respectively. The mark . , placed to the measureof any angle, denotes that it is the mean of the two observa-tions made with the instrument turned different ways; namely,after the first observation, reversing it to make the second.A1 so the mean height of the theodolite is set down to eachStation. In the vertical angles, the bottom of the object is