MAGNETIC SURVEY OF GREAT BRITAIN. 121 



clinal line, B the dip observed at a station, of which the latitude 



is \, then is (D — 8) the difference of latitude, and (D — 8) 



r 



^^^ sec X the difference of longitude, between the station and 



r 

 the point which it furnishes for the isoclinal line. 



We have the values of u and r at the central geographical po- 

 sitions in England, Ireland, and Scotland, as derived from obser- 

 vation. If, for a general central station in the British Islands, 

 we take the mean of the central stations in the three countries, 

 viz. lat. 54° 16' N., long. 4° S5' W., we may deduce the values 

 of u and r for that station from equations of the form 



iij = u + a^x + b/i/ 

 r, = r + a,a; + i^y, 



where u, is the angle and r, the rate of increase at one of the 

 three central geographical positions ; a, and b, co-ordinates of 

 distance in longitude and latitude from the general central sta- 

 tion, expressed in geographical miles ; and a; and y coefficients 

 of the change in the values of u and r in each geographical mile, 

 y in the direction of the meridian, and .r in that of the perpen- 

 dicular thereto. The mean results in the three countries will 

 then furnish respectively the three following equations for the 

 value of u ; 



England, 3905' = u — 89 a;- — 98 y 

 Scotland, 3366' = u — 34 ^ + 153 y 

 Ireland, 3632' = u + 123 x ~ 55 y 



The number of stations from which the mean results were ob- 

 tained was, 



In England, 122 1 i • x. f 3 



In Scotland, 46 I o'" nearly m the I 

 In Ireland, 39 J P^^P^^-^ion of ^ ^ 



In combining these equations therefore by the method of 

 least squares, to obtain the most probable values of u, x, and y, 

 we may give the weight of 3 to the English result, and that of 

 unity to each of the two others. 



Pursuing the usual process, we derive u = — 60° 42' ; x = 

 + 0'6 ; y = 4- 2-0 : and we may compute the approximate value 

 of u at any geographical position in the British Islands, by the 

 formula 



« = — 60° 42' + 0-6 a + 2 b, 



