MAGNETICAL OBSERVATIONS IN SCOTLAND. 101 



and so forth, there bemg as many equations ^^^^ere are stations 

 of observation. Or if we diminish by an equal amount (71 , tor 

 It ?e^rlh of the observed dips, for th^ c^^^^^^^^^^^^ 

 ing with smaller numbers, and make S = 71 + ^ ^ne^e equa 

 tions become, 



2-047 = 8' + 55.0; -47.y, 



1-995 = 8' + 52.0; -47.y, 



1-885 =8' - 15..r-91.y, 

 and so forth. The sum of the 30 equations, representing the 

 sum of the equations severally multiplied by the coefficient of 



^''^^ + 38-238 = + 30 S* + 4.0- + 56.?/ ... (A) 



Next, multiplying the same equations severally by the respective 



coefficients of x, we have 



+ 112-585= +55 8* + 3025. 0^-2585.. V, 



+ 103-740 = + 52 8' + 2704. A' - 2444. y, 

 _ 28-275 =- 15 8' + 225.0; + 1365.?/, 



and so forth ; the sum of these 30 equations being 



+ 170-00 = +48' + 43084. x + 9660.?/ • • K'^) 



And lastly, multiplying by the coefficients of y, we have 



- 96-209= -47 8' -2585.0; + 2209.?/, 



- 93-765 = - 47 8' - 2444. x + 2209. y, 



- 171-535 = - 91 8' + 1365. X + 8281. y, 



and so forth ; the sum being 



-431-82= + 56 8' + 9660.0; + 7l514.y . • (C) 



The three final equations A, B, C, furnish by eUmination^^^^^^ 

 most probable values of the quantities sought. These are as 

 follows : 



8' = 1°"288, x= + -00557, y=- '00780; 



and from these we obtain the dip at the central station 8 = 71° 

 !^V-T2°-288-72°l7'-3: the angle which the isoclinal line 

 malellL The meridiaii =' - 54° 27' 5 or its direction is from 

 N 54° I7' E. to S. 54° 27' W. ; and the rate of increase of dip 

 iu the normal direction = 0'-575 in each geographical mile, or 

 52-15 geographical miles to each half-degree of dip. 



If now we substitute in the second members of the original 

 equations the previously unknown values of 8, .r, ^"d^, we ob- 

 tain the most probable dip due to the geographical position ot 

 each of the stations of observation ; and, by transposition, the 

 most probable amount of error in each of the observations. 



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