MAGNETIC OBSERVATIONS. 



211 



Hence, the general equations for the determination of the deviations of this 

 compass are 



AT ,= X — 0.0396 X — 0.0000 Y — 0.0022 Z — 0.322 — 0.00027 / 



y fe= y — 0.0000 x — 0.2324 y — 0.0058 z — 0.038 + 0.00034 / 



Z' *= Z + o. 1 140 X + 0.0098 Y — 0.0509 Z — 0.392 + 0.00363 / 



The constants p, Q, fi, are the resolved values of the hard iron magnetism of the 

 ship; and in order to show as clearly as possible how it varied during the cruise, 

 at the positions occupied by the two compasses under discussion, the following table 

 is appended. The columns headed "F" contain the values of the total hard iron 

 force, computed by means of the formula 



F=V P 2 + Q 2 + R 2 



Date. 





Admiralty Standard Compass. 



After Azimuth Compass 







>. 



Q- 



S. 



F 



P. 



Q. 



X. 



F. 



November 1, 

 June 23, 



1865 

 1S66 



+ 0.425 

 + O.205 



+ O.006 



— 0.043 



+ 0.166 



+ 0.327 



0.456 

 0.388 



— O.322 



-°-3S5 



— 0.038 

 + 0.042 



— 0.392 



+ 0.457 



0.509 

 o-S99 



Thus it appears that in the interval between November 1, 1865, and June 23, 1866, 

 the total hard iron force had decreased fifteen per centum at the position of the 

 Admiralty Standard Compass, while it had increased eighteen per centum at the 

 position of the After Azimuth Compass; and in both cases the changes in the 

 direction of the force were very great. On the whole, the so-called permanent 

 and sub-permanent magnetism of the Monadnock seem to have been in a very 

 unstable condition. 



There were some places where observations of the deviations of the compasses 

 were obtained on a number of points less than thirty-two, because the ship could 

 not be made to swing completely around. In order to deduce from these observa- 

 tions the corresponding values of the coefficients A t , B u G v D,, E x , we remark that 

 each observed deviation furnishes an equation of condition of the form 



= — 8 -f A l + B l sin i + (7, cos £ + D l sin 2£ -f E l cos 2£ 

 and from all the equations thus obtained the values of the coefficients must be 

 found by the method of least squares. As all the compasses were observed simul- 

 taneously; the deviations at each place are given on the same points in the case of 

 each compass. Hence, although the absolute terms in the equations of condition 

 will be different, the numerical coefficients of the unknown quantities A u //,, C„ 

 Di, i7„ will be identical for all the compasses at any one station. Advantage has 

 been taken of this circumstance in forming the following table, which gives the 

 equations of condition for all the compasses at Ceara. The absolute terms of the 

 equations of condition belonging to any compass will be found in the column 

 headed with the name of that compass, while the coefficients of the remaining terms 

 of the equations will be found in the columns headed J„ /?„ Ci, D,, E,. For 

 example, the first equation of condition for the Admiralty Standard Compass is 

 = _ 170 -f- .4, + 0.195 B, + 0.981 <7, + 0.383 D, + 0.924 E,. 



