7l6 PHILOSOPHICAL TKANSACTIONS. [aNN0 1775. 



render it impossible to do any thing more that season. It became therefore 

 necessary to finish this astronomical campaign, leaving the theodolite in the care 

 of Mr. Menzies, to complete what little remained to be done the next season. 



I have thus described the plan which was adopted for the operations on Sche- 

 hallien, and the manner in which it was carried into execution ; it only remains 

 to give the result of computations made on those operations for deducing the 

 effect of the attraction of the mountain. The operations themselves at large 

 shall be communicated at another opportunity. 



I had caused the arch of the sector to be divided by fine points, according to 

 anew and arbitrary division adapted to the method of continual bisection. One 

 8th part of the radius of the instrument was found by 3 bisections, and applied 

 as a chord to the arch from the middle on each side, intercepting each way 

 7° 9' 59".917. These spaces were each divided by points into 128 parts, by 

 continual bisection ; therefore one division will contain 3' '2l".56\854. Hence 

 the number of degrees and minutes, answering to any number of divisions, may 

 easily be found. Twenty-four additional parts were also set off, taken from the 

 former, and added at the 128th division on each side, to fill up the whole extent 

 of the arch, which thus consisted of 152 divisions on each side of the centre, 

 answering to an angle of 8° 30' 37".4, which was therefore the greatest angle 

 the instrument was capable of measuring. To find the value of the parts of the 

 micrometer in seconds, I measured the distance of the points on the limb, by 5 

 at a time, by means of the plumb-line, in parts of the micrometer from O to 1 28, 

 on each side of the middle or point marked O on the arch. By a mean of all 

 these measures, one division of the arch, or 3' 2l".562, came out equal to 4 

 revolutions and 34.8272 parts of the micrometer, 41 of which make one revo- 

 lution; and therefore one partis equal to l".0137545, and 41, or one revolution, 

 is equal to 41".5639345. Hence the value of any number of revolutions and 

 parts of the micrometer may be easily found. At all observations of the same 

 star, whether on the north or south side of the hill, I brought the same point 

 of the arch, namely, that which agreed nearest with the zenith distance of the 

 star, under the plumb-line, so that the difference of the apparent zenith dis 

 tances of the same star, on contrary sides of the hill, is given in parts of the 

 micrometer, and has no reference to the divisions of the instrument, whether 

 they be equal or unequal ; and, the parts of the micrometer screw being per- 

 fectly equal, as I had formerly satisfied myself by measuring the interval of 2 

 given points on the arch with different parts of the screw, that difference of ap- 

 parent zenith distances may be perfectly relied on, as far as depends on the in- 

 strument, provided the bisection of the star by the wire in the telescope, and 

 that of the point on the arch by the plumb-line, were accurately performed. 

 As the plane of the instrument was placed both east and west, at both stations of 



