Barhiv's Essay on Magnetic At traclion, 135 



of the ball and compass, the distance between the two being al- 

 ways the same. From these it was discovered, that while the 

 longitude was zero, the tangents of the angles of deviation were 

 proportional to the sine of the double latitude ; and while the 

 latitude was constant, the tangents were proportional to the co- 

 sine of the longitude: so that in r11 cases, while the distance 

 and mass were constant, the deviation was expressed by the for- 

 mula tan. J = A (sin. 2x. cos I.) 

 where J denotes the angle of deviation; A the latitude, and I 

 the longitude, on the ideal sphere above mentioned ; and A a 

 constant coefficient to be determined by experiment. 



The next object of the author was to ascertain the law as re- 

 spects the distance: and here again he was equally successful : 

 the results showing in the most unexceptionable manner, that all 

 other things being the same, the tangents of deviation were in- 

 versely proportional to the cubes of the distances. It still re- 

 mained to determine the Ihw as regards the mass; and with this 

 view, balls of different diameters were emploved, from which it 

 seemed to follow, that the tangents of deviation were propor- 

 tional to the masses, as to the cubes of the diameters. 



Mr. Barlow appears in the first instance to have adopted this 

 concluiion, and to have considered his experiments on regular 

 bodies as completed ; when out of mere accident, or curiosity, he 

 made trials with certain shells of iron of the same diameter as his 

 balls, from which results were obtained as singular as they were 

 unexpected ; viz. that the balls and shells of the same diameter 

 gave the same deviation ; so that it appeared that the latter was 

 independent of the mass, and had only reference to the quantity 

 of surface. This led to several experiments on iron plates, each 

 2. foot square, but of various thicknesses ; from which it is made 

 manifest, that after the thickness of the iron surpasses a certain 

 quantity, (about ^-'^th of an inch) no addition of power is gained 

 by an increase of thickness; in fact, thi\t magnetism like electri- 

 city resides wholly in the surface. 



Introducing all these circumstancen, tlic general formula for 

 e; pressing the quantity of deviation becomes 



I>3 . 



tan. A — —.-- (sm. 2 A. cos /.) 



where D uenotcs the diameter of the ball ; o the distance, and 

 X', X and /, the same as before. 



All these experiments, it will be observed, were performed on 

 regular masses of iron, and it might still be douljtful whether 

 tbey would be found to obtain on irregular masses. With a view 

 to this determination, Mr. Barlow commenced a long course of 

 •xperimcnt* on a ?4-pounder, mounted upon what is termed a 



I 4 traversing 



