440 



V. " On the Effect of Local Attraction upon the Plumb-line at 

 stations on the English Arc of the Meridian, between Dun- 

 nose and Burleigh Moor ; and a Method of computing its 

 Amount." By the Venerable Archdeacon PRATT. Com- 

 municated by the Rev. J. CHALLIS, F.R.S. Received June 

 5, 1855. 



The author states that in a former communication he had pointed 

 out a method for calculating the deflection of the plumb-line at sta- 

 tions on the Indian arc, caused by the attraction of the Himalayas 

 and of the vast regions beyond, with a view to the correction of the 

 astronomical amplitudes of the measured subdivisions of the arc 

 before they are applied to the determination of the ellipticity of the 

 earth. 



The same subject is taken up in the present paper, but in refer- 

 ence to the English arc between Dunnose and Burleigh Moor ; and 

 a different method of calculating the attraction is given. 



The paper consists of three parts. In the first, the ellipticity of 

 the English arc is calculated without taking account of attraction. 

 The arc is divided into five parts, and the lengths and amplitudes 

 assigned to them in Mudge's Trigonometrical Survey of England, 

 vols. ii. and iii., are made the basis of the calculation. These por- 

 tions of the arc are compared two and two, and ten values of the 



ellipticity thence deduced ; the mean of which is - . The 



, . 43'8687 



ten values, of which this is the mean, differ considerably among each 

 other, indicating that there is some disturbing cause, like local at- 

 traction, affecting the plumb-line, and therefore the apparent lati- 

 tudes. The variations of the observed amplitudes are then dis- 

 cussed ; and the necessity of calculating the local attraction pointed 

 out. 



In the second part a formula is obtained for calculating the at- 

 traction. The method is different from that given by the author in his 

 first communication. The curvature of the earth is neglected, as 

 this would have no sensible effect on the results in the British Isles. 

 The attracting mass is divided into a number of smaller masses 

 standing on rectangular bases at the sea-level, and the height of each 



