ON THE GAUSSIAN CONSTANTS FOR THE YEAR 1829. 13 



1)}' the occurrence of ^)=1 in every one of the eighty-four termed sums [ ]; 

 •whereas in the computations for 1843--5 we had to substitute in the sums 

 [ ], no^y unity, now another number for the p's of the seventy-four terms, 

 according to the empirical values for that year, as above mentioned under "B. 



On the Equations for 1843-5." 



'Now the numerical values for the final equations (6) have been found to 

 be : — 



For the year 1811. 



[«,/]= + 3-970, [ab]= -4-900, [«c]= + 10-685, [w?]= + 0-235, 

 [rtc]= -1-3-200, [«/]= -1-0-109, [a^]= -0-353, [«/;]= +4-971, 



[«,*]= -8-541. 



[&6]= + 68-229, [6c]= + 3-758, [bd]= +2-881, [Je]= -0-408, 

 [6/]= + l-90G, [6^]= -3-264, [67i]= + 5-044, [6n]= -15-069. 



[fc]= + 62-186, [cf?]=-2-742, [ce]=+2-290, [cf]= + l-95i, 

 [er/]= -6-771, [c7i]=- 11-994, [crt]= -32-370. 



[fW]= +23-994, [c?e]= -0-455, [f?/]= -2-493, [f7r/]= -3-006, 

 [f?A]= -3-110, [f7)i]= -8-427. 



[ee]= +16-280, [?/]= +0-699, [«i/]= -0-414, [eA]= + 7-918, 

 [«i]= -15-486. 



[//]= + 13-402, [/i/]=-6-608, [/A]=-l-268, [>]= + 13-745. 



[f/5f]= + 138-801, [r/7i]= + 5-350, [(/)i]= -44-715. 



[hh]= + 134-080, [hn']= - 6-073. 



For the year 1843-5. 



[«f<p]= + 67-883, [«6p]= +12-989, [ac2;]= + 9-091, [rt(^j>]= + 8-784, 

 [fff^]= + 20-978, [r/^9]= +2-959, [«(7i3]= +0-407, [rt7t2j]= + 8-036, 

 [«n23]= + 64-265. 



[%]= + 75-782, [6cp]= +2-961, [6r7j>]= -3-325, [6ep]= + 0-198, 

 [6/>]=-l-578, [652.>]= + 31-818, [%9]= + 5-062, [7»«^]= -23-362. 



[cc:2J]= + 71-859, [cf7p]=- 3-574, [cfw]=+3-691, [r/)>]= +3-067, 

 [cr/_^j]= -3-337, [c7(j.7]= +23-278, [«i2:>]= + 25-870. 



[f7f7^]= + 42-260, \dcp]^ + 7-160, [dfp']= + 8-076, [%ij]= + 2-040, 

 [J7i2j]= -1-781, [(%:.]= -29-599. 



[<?f^]= + 43-335, [c/p]=- 0-359, [er/^j]= + 10-268, [J//>]= + 6-543, 

 [g„p]=_ 7-862. 



[//p]= + 37-446, [%]=-5-698, r/;tp]= + 8-145, [/«^]= -12-456. 



[^r/i']= + 154-637, [r/7*j9]=- 5-424, [r/njj]^: -59-602. 



[/J(p]= + 122-981, [/iHij]= - 18'439. 



