1839] Terrestrial Magnetic Fcrce in Southern India. 243 



On comparing each of these with its several constituent values, we find 

 tliat the mean error at a single station is 6% 33" ; from which we should 

 conclude, that the latitude of the magnetic equator, derived from the 

 first 9 stations, as far as error of obsei-vation goes, is probably not above 

 2 or 3 minutes in error: and the same may be said of the result from 13, 

 and of that from 1 1 obsei^ations. Hence we are free to infer that the 

 discordance which exists between these three values, as compared with 

 the longitude, is without the liniit of error of observations; and since no 

 simple value of inclination of the isoclinal lines would reconcile both 

 the longitudes and latitudes, we are left to conclude, either that the 

 isoclinal lines (arising from local causes) are undulating, or that we have 

 assumed an erroneous theory. 



Having come to this conclusion, we will now proceed with the obser- 

 vations at these three groups of stations, to obtain values for the inclina- 

 tion of the isoclinal lines to the meridian {9) \ and the rate of variation (r) 

 corresponding to a variation (of one minute for instance) in the latitude. 

 For this purpose, let \ and fx represent resj-ectively the longitude and 

 latitude of any principal station (O) to which we wish to refer a group 

 of observations; and \ and fi^ the same for any one of the other sta- 

 tions. Let P represent the pole of the earth: P O the meridian of the 

 said principal station, and P Q the meridian of any one of the stations 

 which we wish to refer to 0. From Q let fall Q R perpendicular to P O ; 

 or, since R O and R Q will in no case exceed \\ or 2 degrees, we may, 

 for sinij licily sake, make R O a parallel of latitude; vhen 



R O = A = \-\. 

 and R Q = B = /*,) cos \, 



Let O S represent an isoclined line, making the single O S P —0 

 with the meridian, and draw =z perpendicular to it ; then we get 



p — (B. cos 6 -Y P^. sin 6) nearly. 



Now, within the limited range of each group of stations, we may safely 

 allow, that the dip varies as the distance — that r remains constant ; — 

 hence 



t—c, =: rp 



or B — =z r cos 6.B -\- r sin 6. A ; where, substituting x, and ?/, for 

 the term>s r. sin 6 & r. cos $^ and restoring the values of A & B, 

 c-S, z=z {fx—fjL^ cos X -\- (X— \ ) y. 



The stations proper to be chosen for principal stations, are evidently 

 those which are situated in the middle of the group, or such as we 

 have already obtained ; where 



