(>38 PHILOSOPHICAL TRANSACTIONS. [aNNO 1795. 



Feet. 

 excess and wear ; which add -f 3.542 



The sum of all the degrees shown by the thermometers, was 146051; therefore 



( 54° X 365.9) X -'--; = 5 232 feet, is the correction for the mean heat in 



5 1 -^ 

 which the base was measured above 54°, die temperature to which the chains were re- 

 duced; and this add + 5.232 



Hence these corrections, added to the apparent length, give 36508.835 



Again, for the reduction to the temperature of 62°, viz. for 8° on the brass scale, we 



have 0-»1^37 X 365-9 X 80 ^ ^^.^ ^^^^^ ^^^^^^^^ _ 



12 

 By the tables, the sum of tlie versed sines of the hypotenuses, or the corrections for re- 

 ducing them to tlie plane of the horizon, is 20.916 feet ; and this subtract — 2O.916 



36574..y02 

 The sum of the corrections, for the reduction of the several horizontal lines from tlie 



height of the different hypotenuses above the centre of tlie earth, to the height of Beacon 



Hill above ditto, is 0.501 feet; this add -|- 0.501 



Therefore the apparent length of the base, as reduced to the level of Beacon Hill, 



is 36575.403 



But it will be hereafter shown, that the height of Beacon Hill above the sea is 

 6qo feet nearly, and that of King's Arbour 1 1 8, and of Hampton Poor House 

 86 feet; therefore the height of Beacon Hill above the mean point between 

 King's Arbour and Hampton Poor House, is 588 feet, or ys fathoms. Now as 

 the base thus reduced, may be supposed to have been measured Q6 fathoms far-, 

 ther from the centre of the earth than that on Hounslow Heath, it tnust be re- 

 duced to the same level. Therefore if we take 3481794 fathoms for the mean 

 semi-diameter, and add 98 fathoms to it, we shall get the length by this pro- 

 portion, viz. 3481892 : 3481794 :: 36575.4 : 36574.4, the length of the base 

 nearly. 



The account next enters on the calculation of the sides of the great triangles; 

 and first of the division of the series into different branches. In order to me- 

 thodize the contents of this section, it has been considered as proper to divide 

 the series into different branches, as the triangles of which they are composed 

 seem naturally to resolve themselves into distinct classes. The first branch is 

 that which immediately connects the base of departure on Hounslow Heath, with 

 that of verification on Salisbury Plain, and is bounded by the sides connecting 

 the stations. Hanger Hill, St. Ann's Hill, Bagshot Heath, Highclere, Beacon 

 Hill, and Four Mile Stone on the north, and on the south side by Four Mile 

 Stone, Dean Hill, Butser Hill, Hind Head, Leith Hill, and Banstead. 



The 2d branch, is that which proceeds from the side Hind Head and Leith 

 Hill, to the coast of Sussex and the Isle of Wight, and principally affords the 

 sides which will be hereafter used in finding the distance between Beachy Head 

 and Dunnose. This branch also proceeds westward for the survey of the coast, 

 and is bounded by the sides connecting the stations Leith Hill, Flind Head, 



