706 PHILOSOPHICAL TRANSACTIONS. [aNNO 1775. 



north or south side of the hill, and those observed at the east or west end of it, 

 after allowing for the difference of latitude answering to the distance of the pa- 

 rallels of latitude passing through the two stations, will show the quantity of the 

 attraction at the north or south station. But the experiment may be made to 

 more advantage on a hill like Schehallien, which is steep both on the north and 

 south sides, by making the two observations of the stars on both sides ; for the 

 plumb-line being attracted contrary ways at the two stations, the apparent zenith 

 distances of stars will be affected contrary ways; those which were increased at 

 the one station being diminished at the other, and consequently their difference 

 will be affected by the sum of the two contrary attractions of the hill. On the 

 south side of the hill, the plumb-line being carried northward at its lower extre- 

 mity, will occasion the apparent zenith, which is in the direction of the plumb- 

 line, continued backwards, to be carried southward, and consequently to approach 

 the equator; and therefore the latitude of the place will appear too small by the 

 quantity of the attraction; the distance of the equator from the zenith being 

 equal to the latitude of the place. The contrary happens on the north side of 

 the hill; the lower extremity of the plumb-line, being there carried southward, 

 will occasion the apparent zenith to be carried northward, or from the equator ; 

 and the latitude of the place will appear too great by the quantity of the attrac- 

 tion. Thus the less latitude appearing too small by the attraction on the south 

 side, and the greater latitude appearing too great by the attraction on the north 

 side, the difference of the latitudes will appear too great by the sum of the two 

 contrary attractions ; if therefore there is an attraction of the hill, the difference 

 of latitude by the celestial observations ought to come out greater than what an- 

 swers to the distance of the two stations measured trigonometrically, according 

 to the length of a degree of latitude in that parallel, and the observed difference 

 of latitude subtracted from the difference of latitude inferred from the terrestrial 

 operations, will give the sum of the two contrary attractions of the hill. To 

 ascertain the distance between the parallels of latitude passing through the two 

 stations on contrary sides of the hill, a base must be measured in some level spot 

 near the hill, and connected with the two stations by a chain of triangles, the 

 direction of whose sides, with respect to the meridian, should be settled by astro- 

 nomical observations. 



If it be required, as it ought to be, not only to know the attraction of the 

 hill, but also from it the proportion of the density of the matter of the hill to 

 the mean density of the earth; then a survey must be made of the hill, to as- 

 certain its dimensions and figure, from which a calculation may be made, how 

 much the hill ought to attract, if its density was equal to the mean density of 

 the earth ; it is evident, that the proportion of the actual attraction of the hill, 

 to that computed in this manner, will be the proportion of the density of the hill 

 to the mean density of the earth. 



