374 OBSERVATIONS ON THE MAGNETIC DIP AND DECLINATION. 
The object of these observations was to test the accuracy of form of the axles of the 
needles, the freedom of the dip-circle from magnetism and ferruginous matter, and to 
ascertain the true dip from the observations made with the plane of the dip-circle, both 
in and out of the magnetic meridian. ; 
In this table, column ten shows the equivalent dip for the plane of the magnetic meri- 
dian, deduced from each azimuthal observation, by the formula 
Cotan. 6 
Cotati. = Coun 6 
In which @ represents the azimuth observed in, 0’ the dip observed in said azimuth, and 
§ the equivalent dip when reduced to the plane of the magnetic meridian. 
The several values of 6, thus deduced, are compared directly with the dip as it was 
actually observed in the plane of the magnetic meridian, by means of ninety-six obser- 
vations on the two needles, which give 76° 40’.419 for the dip. 
Inasmuch, however, as a very small error of observation at a large azimuth, (say at 
60°, 70°, or 80° from the plane of the magnetic meridian,) would make a great difference 
in the value of § as derived from computation, and thus show a discrepancy due, not to 
the form of the axle or to magnetism in the circle, but to the error of reading the needle 
combined with any small error that might exist in the division of the azimuthal circle, 
or in setting the vernier to the stated azimuth, it has been thought proper to institute 
likewise a comparison between the dips, as actually observed in the various azimuths, 
and the computed azimuthal dips, assuming 4 to be equal to the dip actually observed in 
the plane of the magnetic meridian. 
Hence, 0’ observed, column seven, is compared directly with 8”, column eight, com- 
puted by transposing the terms of the formula so as to make 
Cotan. 6” = Cotan. 3, Cosin 6. 
Column nine shows the difference in minutes and decimals of minutes, + or —, be- 
tween 8’ and 8” for each azimuth observed in, and the quantities in this ninth column are 
considered as exhibiting a truer index of the accuracy of form of the axles of the needles 
than would be derived from a comparison of the several deduced values of 5 contained in 
column ten. 
