— a ec, A 
— 
— 
MAGNETIC INCLINATION AT GOTTINGEN. 655 
i + e instead of 7, so that e expresses any supposed constant * 
error of needle 1, the presumptive constant error of needles 2, 
3, 4 being expressed by e! e” el". 
In this manner the 48 equations I. contain in all 36 unknown 
quantities, namely, the inclinations on the 24 days of observation, 
and the 12 quantities xz, y, e, z', y', e, 2, &c. But first we must 
remark, that the members which contain y, y’, y", y" have all only 
very small coefficients, and that in the abbreviated calculation 
they are altogether wanting: the greatest of these 48 coefficients 
is 000289 in the instance above quoted. If however it is desired 
to take account of so small an influence, amounting only to a few 
- seconds, the values of these y, y’, y", y! must first have been other- 
wise deduced, in which however roughly approximate values will 
suffice for the object. 
26. 
For this deduction we have at our command the equations II. 
But if we consider that in the 12 equations of this division 
which relate to one needle, the letter ¢ represents unequal values, 
its value being liable to alteration every time the poles are re- 
versed by means of the bar-magnets, we shall easily perceive that 
it is impossible to eliminate this ¢ out of the equations, and that 
we are therefore necessitated to call to our aid a somewhat pre- 
carious hypothesis. Mine is the followmg. As with all the 
fluctuations of c, supposing the same manner of touch in chan- 
ging the poles to be always adhered to, a mean value of ¢ will 
result, I assume that the mean value is the same for the two po- 
sitions of the poles. It is true that if the number of changes in 
the poles has been but small, only a very imperfect compensation 
can be expected, and the value of y deduced in this manner will 
have but little certainty ; but this uncertainty cannot be avoided 
in any way, unless we obtain the values of c by means of a spe- 
cial apparatus (Art.17). In order to use this principle, those 
equations II. with each needle which relate to B a north pole, 
must first be separated from those in which A was a north pole ; 
then both sets must be resolved into as many groups as the 
number of times when the magnetism of the needle was inter- 
* The reader need hardly be reminded that such an error, which, supposing 
it to be real, must be ascribed to a deviation of the axle from the cylindrical 
form, is only constant so long as it is the same part of the axle that rests upon 
the planes, and therefore that with quite a different inclination, the error in 
question might have quite a different value. 
VOL. III. PART XII. Oe 
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