On the Effect of Local Attraction upon the Plumb-line. 451 



Form four more angles by adding (subtracting if they be negative) 

 tialj oj each of these angles just found to {or from) 45°. 



From the sum of the log-tangents of the first tivo of these anales 

 subtract the sum of the log-tangents of the second two. 



This result, multiplied by Wfeet and by J^, will give the required 



deflection of the plumb-line in seconds of a degree— U being the heio-ht 

 of the Tabular Mass above the sea-level, and its density being taken 

 equal to half the mean density of the earth, which is that of 

 granite. 



The only restriction to be attended to in the application of this 



Rule IS, that the ratio of the height of the attracted station above 



f.r^^". T^.""^ ^^^ horizontal coordinates of the nearest angle 



ne<.lected ' ''' "^"'^ ^^ '"^ '"'''^^ ^^""^ '^' '^"^'^ "^^^ ^^ 



If any part of the attracting mass is nearer to the station than 

 tins. It must be divided into vertical prisms and the attraction of each 

 found ; tor M-hich the author gives a formula in a note 



In the thud part the Rule is applied, for the purpose of illu^tra- 

 tion, to obtain an approximate value of the deflection of the plumb- 

 ine at Burleigh Moor, the north station of the arc under considera- 

 tion situated on the north coast of Yorkshire. The deflection is 

 ound to be 3"-644 to the south. The data upon which this caSa! 

 tion IS based are gathered by the author from the Map which accom- 

 pan.es General Mudge s account of the English Survey, and the 

 heights marked down on that map. 



The deflection at several other stations is deduced from this result 

 of calculation, by using the amplitudes given in Mudge's work, and 

 also in Cap am Yolland's 'Astronomical Observations made with 

 Airy s Zenith Sector,' published in 1852, and by supposing the cur- 

 vature of the meridian to be the mean curvature of the whole o-lobe 

 as laid dovv-n by Mr. Airy in his article on the Figure of the E^arth 

 Thus the deflection at Black Down on the Dorsetshire coast (one of 



o V^ '^"LT^TT''^ ''' ?'P^'^° Yolland's volume), the author finds 

 to be 5 88b to the north, a quantity which tallies well with the de 

 flection assigned to Burleigh Moor on the Yorkshire coast, if the re- 

 lative heigiits of the two coasts are compared, 'i'his affords a satis- 

 factory evidence of the correctness of the principles laid down in the 

 paper; and as the author thinks, makes the subject well worthy the 

 attention of those who are interested in the English Survey and 

 who have It in their power to furnish the most accurate data for the 

 apphcation of the Rule he lays down. The subject is also no le«s 

 important to the mathematician in his investigation of the fi-ure of 

 the earth. e,uic ui 



In a Postscript the author makes the following remarks upon the 

 Astronomer Royal's method of accounting for the large amount of 

 deflection on the Indian arc deduced by the author in his former 

 communication : — 



" Since the above was written, I have had the opportunity of see 

 ing a notice of the communication of the Astronomer Royal on the 



