718 PHILOSOPHICAL TRANSACTIONS. [aNNO 1775^ 



which exceed 300, shall have been computed ; but, as from the agreement of 

 these results together, as well as from the small differences that are usually 

 found in observations made within a few days of one another, we may presume, 

 that the result from the whole will not differ materially from that deduced above 

 from 40 observations, I thought I had better take this opportunity of gratifying 

 the impatience of the society in presenting them with these my first computa- 

 tions, before their summer recess, than delay giving them any account at all of 

 this experiment, till I had leisure to complete the whole of my calculations. 



I am now to show, what the distance is between the parallels of latitude pas- 

 sing through the '2 stations of the observatory in feet, according to the trigono- 

 metrical mensuration ; and thence, what the difference of latitude ought to have 

 been, if the hill had been away, or had exerted no sensible attraction. This de- 

 pends on the enumeration of several particulars. The length of the base mea- 

 sured in the meadow of Rannoch, was 5897.119 feet, according to the state of 

 the brass standard, when the thermometer was at 40° ; but, to reduce it to an- 

 swer to the state of the brass standard in the heat of 6'1°, we must subtract 

 16.721 feet; we should also subtract further 0.327, for the diminution which 

 the brass standard has suffered by wear, and there remains 5880.071 feet for the 

 true length of the base in Rannoch. See Phil. Trans, vol. 58, p. 313, 324, 

 326. Hence, with the help of the angles taken with the theodolite at the ends 

 of the base in Rannoch, and at the west cairn, the horizontal distance between 

 the east and west cairns comes out 4047.4 feet. Nearly the same result comes 

 out from the base measured on the south side of the hill, though with less ex- 

 actness ; this, when all corrections are made, is 3011.684 feet, whence the dis- 

 tance of the 2 cairns should come out 4058 feet, or about 10 feet longer than 

 results from the base in Rannoch. But I prefer the deduction from the base in 

 Rannoch as most to be depended on. Hence, by the calculation of the 2 trian- 

 gles formed by the 2 cairns and the two stations of the observatory, the distance 

 between the parallels of latitude passing through the 2 stations comes out 

 4364.4 feet, which, according to M. Bouguer's table of the length of a degree 

 in this latitude of 56° 40', at the rate of 101.64 English feet to one second, an- 

 swers to an arc of the meridian of 42'.94. The other series of triangles carried 

 across the hill, gives the same distance of the parallels only 10 feet less, and 

 consequently the arc of the meridian only ^ig- of a second less. Thus the dif- 

 ference of latitude found by the astronomical observations, cOmes out greater 

 than the difference of latitude answering to the distance of the parallels, the 

 forpner being 54".6, the latter only 42". g4. The difference 11 ".6 is to be attri- 

 bvlted to the sum of the 2 contrary attractions of the hill. 



The attraction of the hill, computed in a rough manner, on supposition of 

 its density being equal to the mean density of the earth, and the force of at- 



