MAGNETIC SURVEY OF GREAT BRITAIN. 91 



Section III.— Ireland. 

 {This Section is by the Rev. H. Lloyd.) 



Before entering into the details connected with this division 

 of our memoir, it will be necessary to make a few remarks upon 

 the principles of the calculation which has been employed in 

 deducing the position of the isoclinal lines from the scattered 

 observations. 



If z denote the dip (or intensity) at any station of observa- 

 tion ; s!q that at some near station, which is taken as the origin 

 of co-ordinates ; and x and 1/ the actual distances (in geogra- 

 phical miles) between the stations, estimated on the parallel of 

 latitude and on the meridian, respectively, — or the co-ordinates 

 of position of the first station referred to the latter as an origin ; 

 then I have shown*, (Fifth Report, p. 151) that the relation 

 of these quantities is expressed approximately by the equation 



SI- Zo = Mx + l<li/; (1) 



in which M and N represent the increase of the dip (or inten- 

 sity), corresponding to each geographical mile of distance in 

 the two directions. 



In employing this equation in the calculation of the isoclinal 

 and isodynamic lines, I had taken one of the stations of ob- 

 servation — namely, Dublin — as the origin of co-ordinates : ob- 

 servation, therefore, gave the values of z and Zq, and the equa- 

 tions of condition thus obtained were combined, by the method 

 of least squares, so as to give the most probable values of M 

 and N. In a subsequent application of this method, (Sixth 

 Report, p. 99) Major Sabine adopted a better course, and 

 took an arbitrary station, with an unknown dip and intensity, 

 as the origin. Zq was thus unknown, as well as M and N ; and 

 the resulting equations gave not only the most probable values 

 of the increase of the dip (or intensity) in the two directions, 

 but likewise that of its absolute amount at some one station. 



Let this latter quantity be denoted by L, i. e. let ^g = L in 

 the preceding equation ; then each observation will furnish an 

 equation of concfition of the form 



L + Mx + Ny = s. (2) 



Combining these equations by the method of least squares, we 

 have the three following final equations : 



* The notation here used is somewhat different from that employed in the 

 Report. The variation can cause no embaiTassment to the reader. 



