ON THE GAUSSIAN CONSTANTS I'OK THE YEAR 1829. 



11 



tiou. The values attributed to p had therefore to be assumed with at least 



an additional regard to this circumstance. 



Now, as for the conditional equations themselves, between a^ a, . . . . a, for 



1843-5, and the empiric data hitherto recorded for the same year or for the 



period 1829-58, it appears, first, that these equations for the " ff or increments 



of declination from 1829-58" had once more to be formed according to 



schedule (1) (of A, or "equations for 1811"). In this schedule we had again 



a • 29 



to make 51= -, but this time with k= -. — — . 



K u) . sm 1 



As for the two values of? and U that are recorded under number 13, we have 

 employed for M the said schedule (1), and in it have taken «= — with 



..= 1 and for li the schedule (2) (of A, or "equations for 1811"), 



0) . sin 1'' 



%' 1 



after substitution of n=— with k= ^-^', and then, finally, all the 



K ID . sm i 



recorded values of gX, ^Y, and cZ were set in equations, according to the 



following schedules (3), (4), and (5), which we had derived for the purpose. 



With 



rt= +siu u, f?= +sin 2u, _ry= —sin 2u . cos 2X, 



6==— cos«. cosX, <?=— cos2j6. cosX, 7i=— sin2t{ . sin2X, 



c= — cosrt . sinX, /= — cos2« . sin X, 



there is 

 «=gX=« .a^ + i. a.., + c . a,^ + d . a^ + e. a,+f. a,,+g . a^ + h . ^c^; 



r with 



a=0, d=0, ^= + 2sinM.sin2X, 



6= + sinX, f= + COSH, sin X, ^=— 2 sin it . cos 2 X, 



c= — cosX, /=— COSit. cosX, 



is 

 n=2Y=rt . a^ + h. cc.^ + c . cc, + d . a^ + e . cc,+f . a^+ff ■ a, + h . a,; 



(3) ..{ 



(4) 



V 



(5) 



.^ 



and then 



rwith 

 a= + 2 cos II, d= + (3 . cos= u—1), i/= + 3 sin' u . cos 2X, 



j= + 2sintt. cosX, c= + | . sin2it . cos X, 7i= + 3 .sin'w. sin2X, 

 c==+2sin?tsinX, /= +| . sin 2m . sinX, 



there is again 



C. Evaluation of the annual Increments a„ a, a, of the Gaussian constants 



Q^'\ g^'\ ^"' /"' -9^ '' ^^ '' 5'^^' ^""^ ^^^^ •^*"' ^'^^^^ ^Ipochs, and Re- 

 ductions made, by the help of these increments, of magnetic Observations 

 from different dates to 1829. 

 The heretofore described means had now supplied us for 1811 with eighty- 



