ON THE GAITSSIAN CONSTANTS FOR THE YEAH 1829. 



15 



assuming tlie numbers marked ?jj and 6^.^.^, under the same super- 

 scription out of the ^'th horizontal line of the Table : — 



,=r . ( -29 -an -36.^,3.. -)+,, . (±^3.^^, . M + .. . N*. 



To facilitate this evaluation, we used the form ^.'=r . M + rr . N", and the 



following logarithms according to the superscriptions under which they 

 stand : 



As a further illustration of these rules,, we give the following example of 

 our reductions. In 1818-5 or for r= — 10-5 were observed 



u X X Y Z 



21° 38', 306° 10', 73-96, 171-92, 1609-74 ; 



hence for S^=M . r+N . rr is obtained 



log Sj,, when standing for 



log a^, 9-5036 n ; log a,, 0-5854 n ; log a^, 0-1365 n ; log a^, 0-7271 n ; 

 log a,, 0-9794 n ; log a,, 0-S963 ; log a., 0-4843 n ; log a,, 9-7474 n. 



log a, 9-5667 ; log h, 9-7393 n ■ log c, 9-8753 ; log d, 9-8359 ; 

 lege, 90332 «; log/, 9-7694 ; log (7, 9-3180 ; log 7i, 9-8149, 

 in BX, according to schedule (3). 



And for 



ax, «a.= -0-12, &a,= +2-12, fa3=-l-03, f?a,= -3-05, 

 f«,= + 4-10, /a„= +2-92, r/a,= -0-63, 7,a,= -0-30; 



-/;fl:J= + 3-35 ; X + gX=77-31=the reduced X. 



therefore 



SX=[rta, + /'a^. . 



* It scarcely needs to be observed that tlie above rule applies verbally to reductions 

 from a year ISOO+^'i to a year 1800+i' (?■, and t standing for any positive or negative 

 numbers whatsoever), if only into d^=T . M+rr . N are introduced 



r^t,-i, M. 



-(87-20. g„-C2^- 22).^,3.3 +S,, 

 > and jS = 



"ws 



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65 



