VOL. LXXXV.] PHILOSOPHICAL TRANSACTIONS. 643 



great plank in Mr. Ramsden's shop, Fahrenheit's thermometer was at 55°, but 

 the temperature is omitted when those points in the plank were transferred from 

 the brass standard. The " original points" must be those alluded to in the 

 General's account of the Hounslow Heath base, which were fixed in the plank 

 from the brass standard in the temperature of 63° ; but it is probable that Gen. 

 Roy supposed them to have been transferred in 62°, and through mistake sub- 

 tracted the sum of the first 2 corrections in page 131, instead of their difference, 

 which in that case would have been the true correction for the contraction of the 

 chain. The error however is about 33 inches : for since the chain in the tem- 

 perature of 55° was equal to 100 feet of the brass standard in that of 63°, it fol- 

 lows, from the table of expansions in the General's account of the Hounslow 

 Heath base, that its length in 53'*-fV was equal to 100 feet of the brass standard 

 in 62°; and therefore 53°-jV is the temperature to which the measurement 

 by the chain should be reduced. Now the apparent length being 258.36736 

 chains, and 68290.5 the sum of all the degrees shown by the thermometers in 

 the table, page 134, we have (285.36736 X 53-ji^ — ^~^) X .00763 inches 



= 12.8 inches, the contraction below 53°-rV; this, with the other corrections 

 applied to the apparent length, give 28535 feet 8 inches, instead of 28532 feet 

 11 inches. 



To determine the distance from Hollingbourn Hill to Fairlight Down from 

 this base (28535.66 feet) by means of the fewest triangles, we suppose, accord- 

 ing to General Roy, that the observed angle at Hollingbourn Hill, between 

 Allington Knoll and Fairlight Down, was 48°56'3l".5, and reduce it to 48' 

 56' 30" for computation ; then from the 24th, 23d, and 22d triangles, and the 

 triangle Hollingbourn Hill 48° 56' 30", Allington Knoll 88° 25' 44", Fairlight 

 Down 42° 37' 46", we get 141759.6 feet for the distance of Hollingbourn Hill 

 and Fairlight Down. 



The distance of those stations as deduced from the other base (27404.7) is 

 141748.5 ; hence 27404.7 : 27404.2 :: 141748.5 : 141746 feet nearly, their 

 distance from the mean of the measurements on Hounslow Heath; therefore the 

 mean distance resulting from both bases is 141753 feet nearly. Now with this 

 distance, and the 13th, 12lh, and Uth triangles, we shall find the distance from 

 Hollingbourn Hill to Botley Hill 150071 feet; and the angle at Hollingbourn 

 Hill, between Botley Hill and Fairlight Down 88° 27' 0".25 ; these will give the 

 distance from Botley Hill to Fairlight Down, 204275.5 feet. 



To determine this line from our triangles, we have 92632.2 and II7190.4 

 feet for the distances of Botley Hill and Ditchling Beacon from Leith Hill ; also 

 102132.4 and 98513.7 feet for the distances of Ditchling Beacon and Fairlight 

 Down from Beachy Head ; from these, with the included angles at Leith Hill 



4n 2 



