442 



In the third part the Rule is applied, for the purpose of illustra- 

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

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

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

 found to be 3"* 644 to the south. The data upon which this calcula- 

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

 panies General Madge'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 Captain 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 globe 

 as laid down by Mr. Airy in his article on the Figure of the Earth. 

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

 the places mentioned in Captain Yolland's volume), the author finds 

 to be 5"'886 to the north, a quantity which tallies well with the de- 

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

 lative heights of the two coasts are compared. This 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 

 application of the Rule he lays down. The subject is also no less 

 important to the mathematician in his investigation of the figure of 

 the earth. 



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 

 Density of Table-lands supposed to be supported by a dense fluid or 

 semi-fluid mass ; and the use he makes of his suggestions to remove 

 the discrepancy, pointed out in my first communication, between the 

 values of the deflection of the plumb-line in India, as determined by 

 calculating the attraction of the Himalayas, and as indicated by the 

 results of the Great Trigonometrical Survey. The following diffi- 



