656 GAUSS’S OBSERVATIONS OF THE 
fered with; then the mean must be taken of the equations be- 
longing to the same group (if several come into one group), and 
then again the mean of these partial means must be taken ; then 
by making the means so resulting equal to each other, the equa- 
tion by which y is determined is obtained. I subjoin in illustra- 
tion the abbreviated calculation for needle 1, in which I have 
employed for this olject, in addition to the above 12 observa- 
tions, three others *, made on the 1st and 7th of August and the 
23rd of September. During the whole interval the needle was 
magnetised nine times, so that it was in ten different conditions, 
five belonging to each position of the poles. 
Needle 1. Ba North Pole. Needle 1. A a North Pole. 
ety= c-y= 
4 “4 “i “ 
May 20. eas May 21. — 6531 _ gos 
24. +871 i 22. — 592 f — 
31. ago} F June 2. i oat ee 
June 5. : + 675 4, — 734 f — 
July 8 + 739 July 6. he aml ares 
4711$4 723 7. — 608 
Aug. 1 + 720 Aug. 1, — 720| _ 752 
4 584 pans 7 — 785 
Sept. 23 + 528 } on Sept. 23 (OMe tS ge 
Meance+y=-+ 859 Mean c — y = — 680 
whence y = + 769". The non-abbreviated calculation gave 
for B a North Pole, c = + 859 + 0:00102 x — 1°00290 y 
for A a North Pole, ce = — 680 + 0°00082 2 + 0°99915 y, 
whence 
y = | 769" + 0:00097 «. 
In like manner we find for the other three needles, 
y! = + 456"— 0:00192 a! 
y! = — 101 + 0:00134 2” 
y= +1107 + 0:00224 a", 
The fluctuations in the values of ¢ extend with needle 1 to 143 
minutes, with needles 2 and 3 to 4} minutes, and with needle 4 
to 10 minutes. Lest any particular importance should be at- 
tached to the circumstance that the widest result with needle 1 
appears on the first day of observation, it should be noticed that 
* The observation of the 23rd of September is that which was employed above 
as an example, Art.9—22. The observations of the 1st and 7th of August are 
given in Art. 30. 
