■452 Injiiiencc of Atasses of Irnn 



To determine the deviations produced when a dipping needle 

 is substituted for the compass at C, it will be merely neeessary" 

 • _to resolve the forces (3) and (4) into two others which are in the 

 'nieridian, and respectively parallel and perpendicular to the di- 

 rection of the dip. 

 „ ■ iJiit the force (3) when estimated in the direction AO is equi- 

 valent to 



V And when estimated in the direction GO is equivalent to 



\i ' ■■■ "*i% ■'■*•■'- '""'^ 'P- ''"" !'■ '■"'' i 



•"'Therefore the total force in the direction at right angks to NO 

 i§ as,\-r •; 



'^ ~^ ^^^ (? i .sin k. cos d -f- cos k. cosi. sin d ^ . 

 And in the direction N O the force is evidently as 

 •' ' ■ ^,.[3cos^^-l(. . 



Hence we have for the equation that determines the deviation 5' 

 m'. sin S'= — . \ cos f (sin k. cos^-j-cos k. cos i. sin dj.o^y: 



~(3cas»<f-l) sin^).? 

 Or reclucing as before, ' 



. ^ if cos i8. (siti Tc. ch^ d +rn5 k. ro? ;'. fin d) 

 triH 6 ssA . T . 



Or Mibstituting for (sin kMos d + cos k. cos /. sin d) its equal 

 sin ^. sin /, 



-/ A' s;ti I. sip ^0 ... 



tan6=;— • - — (9) 



From which we may derive, as before, the approximate expression 



. \.f A' sin /. sin'Jip. /ia\ 



tanS=— • —- — (10) 



Having given the deviations in the horizontal plane, those in 

 the vertical tnay be deduced very readily from them; for A= 7— ^;; 

 whence by substituting in (8) and (9), and equating the resuke, 



tan S'= tan S. cos d. '■ = tan 3. cos d. tan /. 



CIS / 



As the dip at London is 70° 30' this equation will become for 

 that place, 



tan S' = .o33S tan ;. tan 8. " " '' ■ 



From which expression we learn that 3' will be less than S from 



/ = to / = 71° 32'. And as we know from our^xpressions 



(S) and (0) that the maximum value of 5 is to that of t' as 



1 f9 3333; \Ve may conclude that ^he deviations j)roduced iothe 



vertical 



