MAGNETIC OBSERVATIONS. 123 



north and south, as indicated by the compass card, the point, which we will 

 designate by //, cut by them on the northern or southern horizon, as might be 

 most convenient, was noted. 2. The deflecting magnets were placed in the carriers, 

 one to the east and the other to the west of the compass card, both being at the 

 same distance from the centre of the card, and \vith their similar poles pointing in 

 the same direction. Then, keeping the sight vanes pointed steadily to the object 

 ff, as soon as the compass card ceased to vibrate it was read off by means of the 

 prism attached to the sight vane. Let this reading be designated as A. 3. Each 

 deflecting magnet was reversed, end for end, in its own carrier, and, the sight vanes 

 being still kept directed to the object //, the card was again read. Let this reading 



be designated as B. Then the observed angle of deflection is 



*0 



The dip was obtained by removing the Admiralty Standard Compass with which 

 the deflections had been observed, and putting in its place a dip circle ; the axle 

 of the dipping needle occupying precisely the same position that had previously been 

 occupied by the pivot of the compass card. 



The observations of the deviations of the compasses made during the cruise have 

 been compared with the following theory, which is taken from the English 

 Admiralty Manual of the Deviations of the Compass, edition of 1863. 

 Let 



X, Y, Z, represent the force of the earth's magnetism drawing the north point 

 of the compass needle to the ship's head, to the starboard side and 

 vertically downwards. 

 X\ Y', Z', represent the combined force of the magnetism of the earth and 



ship in the same directions, 

 a, &, c, fZ, e, /, </, 7i, k, represent constant coefficients depending on the amount 



and arrangement of the soft iron of the ship. 



P, Q, R, represent constant coefficients depending on the amount, arrange- 

 ment, and independent magnetism of the hard iron of the ship. 

 H = the horizontal force of the earth. 

 H' the horizontal force of the earth and ship. 

 6 = the dip. 



= azimuth of the ship's head measured eastward from the correct mag- 

 netic north. 



' = azimuth of the ship's head measured from the direction of the dis- 

 turbed needle. 

 8 = ' = the deviation of the compass. 



Then the whole mathematical theory of the deviations of the compass is com- 

 prised in the three following equations : 



X'=X+aX + b F-fc Z+P (1) 



Y'= Y+dX + e Y+/Z + Q (2) 



Z' = Z +gX + hY+ltZ+R (3) 



