408 PHILOSOPHICAL TRANSACTIONS. - [aNNO 1778. 



the two barometers in lOths of an inch; (3 the number taken out of the adjoined 

 table; j^ the height in feet: we have then the following expression, — — = x, 

 the height required. 



XXXI II. An Account of the Calculations wade from the Survey and Measures 

 tahen at Schihallien, in order to ascertain the Mean Density of the Earth. By 

 Charles Button, Esq., F. R. S. p. OSQ. 



The survey from which these calculations have been made, was taken at and 

 about the hill Schihallien in Perthshire, in the years 1774, 1775, and 1776, by 

 tlie direction, and partly under the inspection, of the Rev. Nevil Maskelyne, 

 D. D., F.R. s , and astronomer royal, by whom the manner of making the survey 

 has already been fully explained in the Philos. Trans, for 1775. I have therefore 

 only to give an account of the measures of the lines and angles, and of the cal- 

 culations which I have raised from them with all possible care and faithfulness, 

 for the purpose of determining the measure of the ratio of the mean density of 

 the earth to that of water or any other known matter. These calculations were 

 naturally and unavoidably long and tedious; and the more so as the business was 

 in a manner quite new, which laid me under the necessity of inventing and de- 

 scribing such modes of computation as should be proper to be applied in so im- 

 portant and delicate a business. Having, at length, with close and unwearied 

 application for a considerable time, completed all the calculations; I have, in the 

 following sheets, drawn up an account of those operations, with the results 

 arising from them; and have accompanied them with such drawings as are neces- 

 sary to illustrate the descriptions. I have also inserted a synopsis of the measures 

 which were taken of the lines and angles; from which any person may at any 

 time satisfy himself of the truth of the computations that have been made, and 

 are here described. These measvires I have here immediately subjoined, before 

 proceeding to describe the computations made from them.* 



First is given a synopsis of the horizontal and vertical angles that mere observed 

 at the principal points in making the survey about Schihallien. — These angles are 

 very numerous, and occupy many pages. 



Then are particularly described the two principal bases which were accurately 

 measured, as foundations on which every thing else must depend: these were 

 one on the south side of the hill, and the other on the north. And first of the 



* This very curious and important paper, containing a full account of all the measures and calcu- 

 lations, here drawn up by Dr. H. at the desire of the ii. s., concerning a problem at tlie very tirst 

 consequence in physics, viz. to determine the mean density and mass of the whole globe of the earth, 

 being necessarily very long, extending through full 100 pages of the original, we must content our- 

 selves with an abstract only of the principles, and the novel metliods of calculation, witli tlie chief 

 results of the whole. t i, 



