Mr. Laming on the prmarj/ Forces of Eledticiti/, 489 



6. The law by which electrical are united to common atoms 

 becomes therefore an important object of investigation ; and 

 if we be not immediately led to it we may derive from obser- 

 vation such a ratio as at least corresponds most exactly with 

 all the facts. This ratio may be thus announced : if any num- 

 ber of equal quantities into which we may suppose the electrical 

 equivalent to be divided be denoted by numbers increasing in 

 arithmetical progression^ then the forces of these quantities on 

 the common nucleus will be expressed by numbers increasing 

 in a certain geometrical progression, as in the scheme below : 



Quantities 1st. 2nd. 3rd. 4th. 5th. 6th. &c. 



Forces 1. 3. 5. 7. 9. 11. &c. 



for instance, if the abstraction of one part of electricity from 

 a common nucleus be resisted by an unit of force, the abs- 

 traction of a second part will be opposed by three units of 

 force ; a third part by five units, and so on. How this ratio is 

 obtained will appear on comparing it, and the doctrine of 

 the definite nature of the electrical attraction, with the known 

 results of experiment. 



7. Let the point A, in the annexed figure, be an insulated 

 body charged with a given excess of elec- Y'w, 1. 

 tricity ; then as the attraction of electri- 

 city is definite it will act on an equivalent 

 of matter, wherever it may be founds with 

 a force determined by the law of Coulomb. [ [ ^ ^^^^]^y]f 

 Suppose B to be a comparatively large 

 mass of matter in its natural state of elec- 

 trical saturation, or equilibrium, and un- ^"^ 

 insulated ; then an equivalent of common matter in B will be 

 acted on electrically in two directions; first, by the plus elec- 

 tricity in A, and again by the electricity possessed by itself; 

 now as each of these forces is to the other a retarding force, 

 whenever they are in equilibrio, either may, of course, be ex- 

 pressed in the terms of the other. 



Let the circular lines c d ef represent portions of sphe- 

 rical surfaces increasing in distance in arithmetical progres- 

 sion from the point A ; and suppose B to be placed success- 

 ively on all these lines; then if while on y it be acted upon 

 by an unit of force, at e it will, according to the law of 

 Coulomb, be under the influence of IJ units of force, tit d 

 under four units of force, and at c of sixteen units; and as 

 the quantity of common matter in B acted upon is constant 

 at all distances, being the equivalent of the constant quantity 

 of plus electricity in A, these numbers without alteration will 

 express the forces by which the plus charge and the minus 

 matter tend to come together ; or in other words, the quan- 



