MAGNETIC INCLINATION AT GOTTINGEN. 645 
It is here evident that we must reject the second system en- 
tirely, and the upper value of Q in the first system, leaving only 
as admissible the value of Q = 192° 44' 41". It can only be 
ascribed to an accidental mutual compensation of the errors of 
observation, that a really good value of ¢ is combined therewith, 
and that the already considerable deviation of the ratio of the 
_values of = and a from that of the squares of the times of 
vibration (Art. 9.) to which they ought to be proportional, is not 
much greater still. In fact the mere increase of one minute 
in the value of f! (the values of the five other quantities, f, g, h, 
J’, g', remaining the same) produces worthless results, inasmuch 
as calculation conducted according to the above method gives 
two systems of solutions, in which the inclination is respectively 
68° 17!’ 40” and 66° 23! 12", while in both systems the values of 
es 
m’ 
cannot be founded on such combinations. 
13: 
If we now give up the observations in the plane perpendicular 
4, receive opposite signs; a striking proof that calculation 
_to the magnetic meridian, we must either supply their place by 
other data, or we must lay down certain arbitrary suppositions 
which are not rigorously correct, and must be satisfied with the 
degree of exactness in the results which is attainable in this 
manner. Throughout my observations a new datum can be de- 
rived from the times of vibration observed before and after the 
reversal of the poles, the squares of which times may be regarded 
as proportional to the quantities =e f fey . It is true that the 
m’? m 
same apparatus with which the times of vibration are observed 
may also be employed for an immediate determination of the 
quantities ¢ and c', by placing the needle in the stirrup in two 
ways, one with the marked face uppermost, and one with the 
same face beneath, and observing the place of the ends of the 
needle relatively to the graduated arc, and taking account of any 
changes of declination by means of simultaneous observations 
with the unifilar magnetometer. But the apparatus in question 
is not susceptible of such accurate readings as would be requi- 
site for this application, for which it was not designed. If an 
apparatus of the kind were divided with much greater exact- 
