658 GAUSS’S OBSERVATIONS OF THE 
d'=— 23 
Instead of the three latter, by making 
diete+el + el) =e, 
we may write 
See 
é =—I11l +¢ 
e§’ = —12 + 
ev = +12 +6, 
where the part in common (z) is evidently not determinable front 
the data at our disposal. The substitution of the values found 
for x, e, x’, e, &c. in the equations I. (already freed from y, y’, 
&c.) now gives us, omitting «, the following inclinations :— 
| Needle. Needle. 
° 4 “4 ° 4 tka 
May 20. 1 67 41 25 2 67 39 12 
21. wes 39 21 oe 39 31 
} 22 39 51 39 22 
24 37 43 40 21 
3l. nee 40 17 ms 39 17 
June 2. as 36 39 ua 38 16 
4 ea 37 31 ae 37 «(0 
5 41 56 39 48 
8 3 44 12 4 43 14 
9 37 27 38 15 
lI 36 27 38 «(1 
16 37 «6 38 17 
18 41 12 40 48 
22. 38 5 37 51 
23 . 40 6 40 2 
iy was 39 45 tes 39 49 
July 6. 1 40 42 3 41 17 
7 tai 41 ll ce 39 49 
8 39 «(5 41 3 
9 39 12 39 57 
17 2 39 55 4 40 7 
18 39 56 39 31 
19 39 35 38 32 
20. 39 43 39 #1 
28. 
The differences between the two determinations of the inclina- 
tion on each day must now give us the measure of the uncer- 
tainty of the observations themselves. The greatest difference 
(on the 24th of May) amounts to 2! 38", and the sum of the 
squares of all the twenty-four differences, taking, the second as 
unity, is 124389. From the principles of the calculus of proba- 
bilities, it is easy to deduce, that if we give equal weight to the 
