Terrestrial Magnetic Intensity. 259 



coordinates of the place ; a being reckoned in minutes of lati- 

 tude, b in minutes of longitude, c in hundreds of feet of eleva- 

 tion. It is convenient to assume some station as a point of 

 reference, and write for a, b 9 and c, the differences of the co- 

 ordinates merely, and for I the difference of intensities. Let 

 a' 9 b\ c\ and I' represent these quantities for the fundamental 

 station, and then for any other the expression will be 



(a-a')x + (p-V)y + (c-c') z = I-I' 



and by a combination of all the equations of similar form 

 which the observations furnish, we are to deduce the most 

 probable values of x 9 y, and z, the coefficients of variation in 

 each direction. If, further, we wish to have the most probable 

 absolute value of the horizontal intensity at the fundamental 

 station before mentioned, it must clearly be deduced from the 

 whole mass of the observations, and not from the observation 

 made there alone. Let us suppose, then, that the intensity at 

 the fundamental station requires a small correction, 8 I', we 

 shall write I' + flF instead of I' in the preceding expression, 

 considering 8 Y as another unknown quantity, which will give 

 us a series of equations (for the different points of observation) 

 of the form 



(a-a')j? +- (b-V)y+ (c-c) z = I-I'-*I' (2.) 



or using the letters with subscript numerals instead of a — a\ 

 &c, and putting all the unknowns on the left hand, we shall 

 have a series of equations of condition of the form 



a \ x + hy + c i z + 8I ' = Ii 1/q > 



a * + b 2 y + c*» + 81' = I 2 J W 



&c. 



from which the most probable values of x, y, z, and 8T are to 



be deduced by the method of least squares. 



29. The observations contained in Table VII. include two 

 groups of observations, to which we mean to apply the me- 

 thod in question. One of these includes the alpine observa- 

 tions made in August, September, and October 1832; the 

 other a short series in the Pyrenees, made almost entirely 

 with reference to the effect of height in 1 835. The remaining 

 observations must be considered for the present as isolated. 

 They are important, however, as fixing the relative horizontal 

 intensities at Paris, Edinburgh, Brussels, Heidelberg, and 

 some points of less note. The admirable coincidence of the 

 Edinburgh observations made in different years gives great 

 confidence in the accuracy of the determination of '8402 for 

 the horizontal intensity, that at Paris being = 1 ; both needles 



2 L2 



