QUADRANTAL EFFECT IS INDEPENDENT OF LOCALITY.147 



ing force depends only on the amount of magnetism 

 produced by induction: and the amount of induction 

 depends only on the terrestrial horizontal force which 

 produces it : and therefore the deviating force is pro- 

 portional to the terrestrial horizontal force : and there- 

 fore the fraction exhibited above is independent of the 

 terrestrial horizontal force : and, in a given position of 

 a mass of iron with respect to the compass, the deviation 

 produced is the same in all parts of the earth. 



68. General investigation of the disturbance produced 

 by a mass of iron symmetrical with respect to a vertical 

 plane passing through the compass-axis (as an iron-built 

 ship) subject to terrestrial induction. 



It is supposed here that, by the action of terres- 

 trial magnetism, every particle of iron is converted 

 into a small magnet whose direction is parallel to the 

 local direction of the dipping-needle, and whose in- 

 tensity is proportional to the local total intensity of 

 terrestrial magnetism ; the poles of the small magnet 

 being in the same positions as those of the dipping- 

 needle, or opposite to those of a magnet representing 

 local terrestrial action. For convenience of language, 

 we shall use terms applicable to a ship : but the results 

 apply equally to any other masses of iron possessing 

 the symmetry above-mentioned. 



Let the center of the compass be the origin of 

 co-ordinates ; let A be the azimuth of the ship's head, 

 measured from the magnetic north towards the east ; a 

 the azimuth of any particle measured from the ship's 



102 



