QUADRANT AL EFFECT EXPLAINED. 143 



direction. Resolve this into horizontal and vertical 

 directions. The effect of the vertical part will be, 

 to produce a series of vertical linear magnets, each of 

 which has its center at the same height as the compass- 

 needle ; and these produce no effect on the compass. 

 The horizontal part remains, which is in the direction 

 of the magnetic meridian, and is proportional to the 

 horizontal force. 



Now this horizontal induction does really produce a 

 series of linear meridional magnets, as shewn in the first 

 diagram : and the clothing of the surface will really be 

 such as is shewn there. But we may resolve the induc- 

 tion into two, one parallel to the length of the mass as 

 in the second diagram, and one transversal to that length 

 as in the third diagram : and their energies will be 

 respectively proportional to cosine azimuth of axis of 

 mass, and sine of the same azimuth. The linear mag- 

 netic needles which they will produce, and the magnetic 

 clothings, are shewn in the second and third diagrams. 

 The aggregate of actions in the second diagram will be 

 represented by that of one magnet, radial to the compass, 

 whose entire action (as already said) is proportional to 

 cosine azimuth : but the resolved part of this tending 

 to give rotation to the needle receives the factor sine 

 azimuth, so that its force tending to deflect the needle 

 may be represented by 



A x cosine azimuth x sine azimuth. 

 The aggregate of actions in the third diagram will be 



