640 GAUSS’S OBSERVATIONS OF THE 
8 = mcos(L + ¢ —?2) + gsin(L — Q) 
__m cos (Q + i— Cc) 
cos (L + Q) 
_ gcos(Q +i— ¢) 
™~ gin(L +c — %)~ 
II, For V = V° + 180°, 
sin (L + ¢ + i) = —4 cos (L + Q) 
= —mcos(L +c +i) +qsin(L + Q) 
m cos (Q — c — i) 
cos (L + Q) 
_ 7008 (Q —c—t?) 
sin (L + ¢ + 7%) ° 
III. In accordance therewith, for V = V° + 90°, and V = V® 
+ 270°; 
sinicos(L + ce) =— = cos (L + Q) 
8 = msinisin (L + c) + gsin(L + Q) 
msin 7 sin(Q—c) 
cos (L + Q) 
_ qgsin (Q—¢) 
~ cos (L + c¢)° 
Our example gives for the two latter cases, instead of equal 
values of L, inequalities of 3! 3" and 2! 8" respectively, attribu- 
table partly to accidental errors of observation, and partly to the 
concurrence of several circumstances ; namely, a small uncer- 
tainty as to the magnetic meridian at the commencement, and 
the possible change of the magnetic declination, and there- 
fore of the value of V®, in the course of the observations,—in a 
small excentricity of the horizontal circle, for which, in the ab- 
sence of two readings, there is no check ; and finally, because the 
axle can only be made imperfectly rectangular to the plane of 
the circle in raising it and lowering it by means of the Y’s. All 
these circumstances are rendered as harmless as possible by 
taking the means of the two positions thus :— 
For Banorth pole . . L=89° 51! 49". 
For Aanorth ple . . L=90 10 48. 
However, by reason of these circumstances the results, in a 
position normal to the magnetic meridian, will always deserve 
