646 GAUSS’S OBSERVATIONS OF THE 
ness, and carefully and immoveably fixed, and if the readings 
were taken with microscopes, it would no doubt be possible to 
determine c and ¢’ directly, with all the accuracy that could be 
desired; we should then have even a datum more than necessary, 
so that by suitable arrangements the accuracy of the results 
could be further increased. 
At present I supply the place of the datum which is wanting 
by supposing the magnetic axis of the needle not to be changed 
by the reversal of the poles, or that ¢’ =c. This assumption 
has been made by all observers who have attempted to determine 
the inclination by a more rigorous calculation than by the for- 
mula otherwise in general employment,i = 3(f+g9+/'+ 9); 
and we certainly have reason to expect that the assumption will 
not be likely to be much in error if the change of poles is always 
performed with great care, with the same bar-magnets, and with 
the needle in the same position in a suitably constructed groove. 
However, my own experience shows that, in spite of these pre- 
cautions, differences which are not inconsiderable may arise in 
the position of the magnetic axis, and clear indications of the 
same may often be traced in the figures of other observers. (For 
example, Erman’s observations of the 13th of October 1829, 
treated according to his own propositions, give the deviation of 
the magnetic axis of one needle 36’ 24”, whilst at other times it 
appears to have been very small.) Fortunately, under the circum- 
stances which take place here, even a considerable degree of in- 
correctness in the assumption in question can have only a very 
small influence on the result. 
18. 
According to these positions the solution of the problem is 
given in the following manner. I combine with the equation (7.) 
already employed, viz.— 
cosi.sin(2e+f—g) _ # 
sin (f+ 9) mt 
those which follow in a similar manner shalt and (5.), putting 
.sin(Q— c); 
therein c in lieu of c’, and 44 instead of —2 ; 
m ml 
cos 7. sin (2¢+f'—g') _ _vYG 
sin (f! +9) 
thus 
