660 GAUSS’S OBSERVATIONS OF THE 
of 42-8, must be assigned to the means of each corresponding 
pair, as shown in Art. 30. 
29. 
A particularly remarkable and welcome result is afforded by 
the smallness of the values found for e, e', e’, e’, or rather 
immediately for their differences from their means. A sepa- 
rate investigation has given the weight of these determinations 
ae times greater than the weight of ? (+g), consequently 
the mean uncertainty with which they are charged = 60'"5 
a/ se = 20-5; whence it is evident that even the reality of 
any inequalities between e, ¢, e’, el remains wholly doubtful. 
Now as it is highly improbable that in four needles there should 
be constant errors of almost precisely equal amount, we are jus- 
tified in assuming that they have either no constant errors, or, 
at least only such as are wholly insensible; and hence it might 
appear almost superfluous to make use of the capability of re- 
volution of the axles of two of the needles for the purpose of 
further trial. 
For one of the needles, No. 4, this conclusion is actually 
confirmed by some earlier observations. During four days, from 
the 15th to the 19th of May, similarly combined observations 
to the subsequent ones (8th. to the 25th of June) were made 
only with the difference, that each partial result rested on only 
four positions instead of eight: in needle 3 the axle was in the 
same position as in the later observations, but in needle 4 it was 
differently placed, having on the 19th of May been made to 
revolve through nearly a quadrant. The observations arranged 
as in October 23 are as follows :-— 
Observations with Needle 3. 
° “4 o “4 S- 
May 15. | B | 67 41 96 | 67 4453 | 616166 | 
17. B 43 52 45 52 6:20333 
18. A 33 56 39 15 617781 
19. A 36 8 | B77*8 6-19566 | 
Observations with Needle 4. 
| 17. | B | 68 539 36 36 | 5-92034 
| 18). |) -Bo L268. 8 30 36.13 | 594235 
| 1 Ne ie Bg Bia 5947 | 5-94663 
o as Ss. 
May 15. | A | 67 14 38 | 67 47 49 | 5-94332 | 
