MAGNETIC EFFECT OF SYMMETRICAL IRON. 149 

 And the attraction in the direction of z is 



z( 7 sinS , x cos S 4- z sin 



j m 1_Z_ _ + 



ft* I 



(It is supposed here that the compass is so small that 

 no sensible error will be produced in the small terms of 

 these expressions, by adopting for the red end of the 

 needle the values of x, y, z, which correctly apply to its 

 center.) 



The repulsions of the red end of the small magnet 

 on the red end of the compass are the same, with no 

 change but in the sign of I. 



The true forces upon' the red end of the needle, or 

 the excesses of the attractions over the repulsions, 

 putting H for terrestrial horizontal force or /cos 8, and 

 V for terrestrial vertical force or / sin S, are 



6lm. xz 

 mx 



my 



These are the forces produced by a single particle 

 upon the red pole of the compass-needle. To find the 

 forces which all the iron of the entire ship produces 

 upon that pole, we must take the sum of each of the 

 factors of H or V through the whole ship. And for this 



