10 ations of the comet of 1807 
4. That the sum of the positive errors in the observed latitudes in 
the observations made in October should be equal to the sum of the 
negative ones. That is, 
x(2*)4x($°4(81)... x(42)=0. 
5. The four preceding eqiting having been fulfilled, ‘the fifth is 
that the sum of all the errors in the longitudes and latitudes taken pos- 
itively should be a minimum. 
In applying the four first of these conditions to the inane of equa- 
tions A, they furnished four equations between d, ¢, p, n, i, by means 
of which I exterminated d, ¢, n,i from the equations A. | Thus the 
equations ~(*)-++«(#)4x() . +. +(55)=0, found by Kaige a 
equations x(*)+~(*). + ton ®=0 and x(#*)w(#*)... --x(4*)=0,* gives 
for the sum of all the €quations~,-..... 
O= 11030 * d+27248 *t—12941 “p—66.8 n—15086 “E4742 
by dividing by—27248, z 
O=—0°40480 * d—#40'47498 * p4+0*24398 +n 
| +0°55366*i—0-02723. (1) 
By multiplying this equation successively by the coefficients of ¢ in 
_ the equations A, I obtained a system of equations B, in which the co- 
eflicients of ¢ were equal and of a contrary sign to those of the system 
A, and by adding together the corresponding equations of the systems 
A and B, I obtained the equations C independent of ¢, of this form : 
x)= —316 +d+130 * p4+239> earch EE i+38 
x(?)=—317* d-¢138" rae: na 24 988 eee) 
&e. &e. 
The sum of the first twenty eight of these equations gives, in putting 
x@)ta() ++ te *)=0, . as 
-..* T took the sum of the two equations instead of the second of them from the 
circumstance of having previously calculated the sum ofall the equations A, 
