170 



might be determined within the hemispheres in which all the force 

 may be conceived to be collected, and to be the same as if proceeding 

 from every point of the hemisphere. If Z=the distance of either 

 point, qq' taken within the hemisphere, r= radius, and = distance 

 between the near or what may be termed the touching points of the 



spheres, then we have Z= ^ > an ^ if A = the surface, we 



have F GC > x y. When both hemispheres are equal, and distance 



=a variable, then we have also Foe , . q.y Th e autnor m a f r - 



mer paper had applied these formulae to the limited induction of a 

 sphere of an inch radius ; he now extends the inquiry to spheres 

 varying from an inch to 5 inches or more in diameter, and finds the 

 results conformable to the formulae. He gives a table containing 

 the results of a series of experiments with four spheres whose areas 

 regularly increased, and the radii of which were from 1 to 2 inches 

 in diameter. These were examined by the electrical balance. They 

 were first placed with the points q q, or centres of force as calculated 

 for each at a constant distance of 1*1 of an inch, in which case the 

 weights requisite to balance the force with a given number of mea- 

 sures of electricity were as the opposed areas, thus confirming the 

 preceding results deduced with plane surfaces ; when the distances 

 were varied, the force varied as the squares of the distances between 



the centres of force, or according to the formula Fee , , ~ y 



"With the view of further verifying these results, a set of plane 

 circular plates in pairs, each pair equal in area to the areas of the 

 respective hemispheres of the spheres, were submitted to experiment 

 at the same constant distance 1*1, so as to cut the points qq', or 

 centres of force of the spheres ; the attractive forces were found pre- 

 cisely the same as that of the opposed spheres to which the particular 

 plates belonged. 



The author has examined at various times and with very rigid at- 

 tention, the several conditions under which electrical attractive force 

 conforms to the law of force as deduced by Cavendish and Coulomb, 

 and other eminent philosophers, and he finds this law true only for 

 charged and neutral conductors of large inductive capacity ; if either 

 of the attracting surfaces have a narrow or limited susceptibility of 



