662 GAUSS’S OBSERVATIONS OF THE 
Determinations of Inclination. 
1842. May 15. | 67 3928 || Junels, | 67 41 6 
17. 
41 06 22. 37 58 
18. 40 45 23. 40 4 
19, 40 47 25, 39 47 
20. 40 18 July 6. 41 0 
21. 39 26 7. 40 30 
22. 39 36 8. 40 4 
24. 39 2 9. 39 34 
31. 39 47 re 40 1 
June 2. 37 27 f MLB 39 44 
4. 37 15 ie 39 4 
5. 40 52 20. 39 22 
8. 43 43 Aug. I. 39 57 
9. 37 51 rf 40 26 
11. 37 14 Sept. 23. 40 54 
16. 37 42 
The mean of these thirty-one determinations, without con- 
sidering any difference of weight, is 
67° 39! 44", 
and may be regarded as corresponding to the 21st of June. The 
mean of the twenty-four determinations only which are com- 
prised between the 20th of May and the 20th of July, rhe 
to the middle period of the 19th of June, and is 
ay Aaa 1 le Le 
31. 
The differences of the inclinations on the thirty-one several 
days of observation from their mean, are compounded of the still 
remaining influence of the errors of observation, and of the real 
inequalities of the inclination itself. It is true that these com- 
ponent parts cannot be separated for single days, but with so nu- 
merous a series the estimation of a mean value of the actual 
fluctuations may well be attempted. With this view I have first 
reduced the inclinations to the 21st of June, assuming a regular 
annual diminution of 3 minutes, and have have then added to- 
gether the squares of the differences from the mean value ; the 
sum is 220184", which divided by 30 gives 7339""5 as the square 
of the mean error to which we should be liable, in taking at 
hazard any one of those thirty-one inclinations and regarding it 
as valid for the mean epoch of observation. If we wish to take 
into account the unequal weight of the three groups of observa- 
tions, and call the mean error of the four first observations m’, 
that of the three last m'', and that of the other twenty-four m, 
and the mean fluctuation of the inclination itself M, we may 
