REPORT 1873. 



there were formed forty-two conditional or primary equations to schedule 

 (1), and then just as many to schedule (2). 



With (jj for the horizontal intensity, d for the declination, 



56 



and K= : — —, there had to be calculated for the a measured 



to . sin 1° 



by degrees of are : — 

 a = — siuK . sine?, 



6= +cos?t . cos \ . sincZ-f-sinX . cosd, 

 c— -\-cosii, . sin X . sin d — cos \ . cos d, 

 d= — sin2({ . sind, 



c= -f cos 2u . cos X . sin d-\- cos u . sin X . cos d, 

 f= + cos 2u . sin X . sin d — cos u . cos X . cos d, 

 [I— -fsin 2if . cos 2\ . sin d-\-2 . sin u . sin 2\ . cos d, 

 h=.-\- sin 2u . sin 2X . sin d — 2 . sin u . cos 2X . cos d, 



and then formed as primary equations, to which the sough t- 

 for a, .... a^ had to answer as nearly as possible, 



n— - =a.)x^ + h.a, + c.ac.^ + d.a.^ + e.oc-+f.cc^+[/.c(.J + h.a^. 



(1) 



(2) 



< 



r 



The t or sixty years' inclination-increments being measured 



by degrees of arc, with i for the inclination, <>• = , there 



w.sinl° 



had to be evaluated : — 



a = — sin u . sin i . cos i . cos fi!-|-2 cos ^(, . cos^ i, 



6=(cos %(■ . cos d . cos X — sin . d . sin X) . sin i . cos i 

 -\-2 .sinu . cos X . cos° i, 



c=(cos it . cos d . sin X + sin d . cos X) sin i . cos i 

 -{■ 2 . sin 11 . sin X . cos'^ i, 



d= — sin . 2m . cosfZ . sini . cosi-f-(3 . cos^it— 1) . cos'^i', 



f =(cos 2m . cos X . cos d — cos u . sinX . sin d) sin i . cos i 

 '^ -1-|- . sin 2m . cos X . eos^ /, 



y"=(cos 2m . sin X . cos c?-|-cos m . cos X . sin X) . sin i . cos i 

 -\- ^ . sin 2u , sin X . cos'^ i, 



g={sm2u . cos2X . coscZ — 2sinit . sin2X . sinr?) . sin?' . cos* 

 -|- 3 . sin' It . cos 2X . cos' i, 



7i = (sin2M . sin2X . cos(?-(-2sin w . cos2X . sind) . sin i . eosi 

 + 3 . sin' M . sin 2X . cos' i, 



and then to be formed as primaiy equations, to which the 

 «;.... a^ had to answer as nearly as possible, 



n= - =a.tx.^ + h.a, + c.a^ + d.a^ + e.a.+f.a^+g.a. + h.ag. 



The forty-two numerical values of a and i which we have used in the 

 primary equations to the preceding schedules (1) and (2) are shown in the 



