MAGNETIC INCLINATION AT GOTTINGEN. 657 
the poles, both of this and of the other needles, had been often 
changed, and always with the same care and the same magnet- 
bars before any of the observations here given were made. 
He 
After substituting the values of y, y’, y’, y!" in the equations 
(1.), there still remain in those equations thirty-two unknown 
quantities. We then subtract throughout from each other the 
two equations belonging to observations of one and the same 
day, and twenty-four new equations are thus formed, which con- 
tain only the eight unknown quantities a, a’, 2", a!", e, e, el, el". 
The four latter however enter only into the differences between 
each two, so that if we say 
é —e=d' 
el! —e= dq! 
ell! —e= d", 
only seven unknown quantities remain. The coefficients of d', 
d", d" all differ very little from + 1 or —1. For determining 
the values of the seven unknown quantities by means of the 
method of least squares, we may omit, on account of the forma- 
tion of the normal equations relating to 2, 2’, 2", x'", the multi- 
plication by the respective coefficients, so that for the formation 
of the whole seven normal equations simple addition only is re- 
quired. The following normal equations have been found in this 
manner :— 
O= + 4804+ 12:00266 2 — 0:00708 2! + 0:01900 2! 
= — 5806 + 0°01559 # + 12°01005 2’ — 0:00072 2"! 
O = — 3228 + 0:00145 x + 12:00544 2” + 0:04561 a" 
0 = — 5267 + 0:01786 #/— 000489 x" +. 12-00343 a!" 
O=— 297 + 0:02717% +4 011088 2! — 0:04723 a! 
—12d' +44" 
O=— 241 + 0:06326 2+ 0:05839 2!— 0:08085 a" 
—12d"+s8d" 
O=+ 254 — 0°02682 2’— 0:02676 2 + 0°12808 a"! 
+4@748d —12q" 
and hence the values 
ze = — 400! 
a + 484 
at sa OGY 
a" = + 438 
d'=— 22 
