110 SIXTH REPORT 1836. 



and r = the coefficient which determines the rate of increase 

 of the force in the normal direction ; and if we put as before 

 r cos u = X, r sin u = y, and / = 1 + /', we have tliree series 

 of equations, analogous to those in the dip calculations ; each 

 series in the present instance consisting of 23 equations. Sum- 

 ming each series we obtain the three final equations as follows : 



+ '7158=+ 23/'- 158 .r+ 154y . . (A) 



— 2-7180 :^ - 158/' + 31892 A' + 87672/ • • (B) 



- 1-251 = + 154/' + 8767^' + 633343/ . . (C) 



From which we obtain by elimination, 



^ = + -00010705 ; y =. — -00011186 ; 

 7< = — 46° 15'-5 ; r — -0001548; and/' = -0326. 



The intensity at the central position is consequently 1-0326 to 

 unity in London. The isodynamic line passing through it 

 makes an angle of 46° 15'-5 with the meridian ; and lines corre- 

 sponding to differences of intensity amounting to -005 are at 

 intervals apart of 32*29 geographical miles. These are the 

 results of the statical method. 



II. Intensity. 

 § 2. jBz/ the Method of Horizontal Vibrations. 



These observations were made in the well-known apparatus 

 of M. Hansteen. The cylinders employed were two, belonging 

 to Professor Lloyd, which had been extensively used by us both 

 in the Irish magnetical observations, and are described in the 

 report of those observations as L (a) and L (Z»). The method 

 of observing which I pursued in Scotland is precisely similar to 

 the description given in that Report ; and nothing further in 

 respect to it appears necessary to be added here, except that the 

 same silk suspension was preserved throughout ; the same chro- 

 nometer, of small and very steady rate, always employed ; and 

 that the coefficient for temperature for both cylinders is -00025. 

 The column of " corrected time" in the subjoined Tables is the 

 time of vibration reduced by this coefficient to a standard tem- 

 perature of 60°. 



