702 



The author has not recomputed the total attraction of all the dis- 

 turbing masses, but has merely given in this postscript a computation 

 of the meridional component of the attraction of the table-land alone. 

 In accordance with the new information, the height of the table-land 

 is assumed to be uniform, and to be equal to 2|- miles above the level 

 of Kaliana, that is, about 15,000 feet above the sea-level. The 

 resulting northern deflections are as follows : 



At Kaliana 19"'85 



AtKalianpur .... 10"- 28 

 At Damargida .... 4"'29 



Hence the errors produced in the astronomical amplitudes will be 

 9"'57 and 5"'99, which much exceed the errors (5"*236 and 3"'791) 

 brought to light by the survey, on the assumption that the ellipticity 

 of the Indian arc is the mean ellipticity of the whole earth ; and the 

 discrepancy will be still further increased when the attraction of the 

 nearer masses is also taken into account. 



The new information regarding the nature of the country north of 

 the Himalayas does not, it thus appears, relieve the subject of its 

 difficulties ; and no geodetic calculations can be of service in the 

 problem of the figure of the earth, nor indeed in mapping the country 

 with extreme precision, till these perplexities are removed by the 

 deflection being found and allowed for. 



March 24/A, 1859. 



Sir BENJAMIN C. BRODIE, Bart., President, in the Chair. 

 The following communications were read : 



I. " On the Conic of Five-pointic Contact at any point of a Plane 

 Curve." By A. CAYLEY, Esq., F.R.S. Received March 1, 



1859. 



(Abstract.) 



The tangent is a line passing through two consecutive points of a 

 plane curve, and we may in like manner consider the conic which 

 passes through five consecutive points of a plane curve ; and as there 

 are certain singular points, viz. the points of inflexion, where three 

 consecutive points of the curve lie in a line, so there are singular 



