Sir W. Harris on the Laws and Operation of Electrical Force. 67 



rectangular surface taken as a whole, and the results of the same 

 accumulation upon the same surface divided into two equal and 

 similar portions distant from each other, and endeavours to show, 

 that if as we increase the quantity we also increase the surface and 

 boundary, the intensity does not change. If three or more separated 

 equal spheres, for example, be charged with three or more equal 

 quantities, and be each placed in separate connexion with the electro- 

 meter, the intensity of the whole is not greater than the intensity of 

 one of the parts. A similar result ensues in charging any united 

 number of equal and similar electrical jars. A battery of five equal 

 and similar jars, for example, charged with a given quantity = 1, has 

 the same intensity as a battery of ten equal and similar jars charged 

 with quantity =2 ; so that the intensity of the ten jars taken together 

 is no greater than the intensity of one of the jars taken singly. In 

 accumulating a double quantity upon a given surface divided into 

 two equal and separate parts, the boundaries of each being the same, 

 the intensity varies inversely as the square of the surface. Hence two 

 separate equal parts can receive, taken together under the same elec- 

 trometer indication, twice the quantity which either can receive 

 alone, in which case the charge varies with the surface. Thus if a 

 given quantity be disposed upon two equal and similar jars instead 

 of upon one of the jars only, the intensity upon the two jars will 

 be only one-fourth the intensity of one of them, since the intensity 

 in this case varies with the square of the surface inversely, whilst the 

 quantity upon the two jars under the same electrometer indication 

 will be double the quantity upon one of them only ; in which case 

 the charge varies with the surface, the intensity being constant. If 

 therefore as we increase the number of equal and similar jars we 

 also increase the quantity, the intensity remains the same, and the 

 charge will increase with the number of jars. Taking a given sur- 

 face therefore in equal and divided parts, as for example four equal 

 and similar electrical jars, the intensity is found to vary with the 

 square of the quantity directly (the number of jars remaining the 

 same), and with the square of the surface inversely (the number of 

 jars being increased or diminished) ; hence the charge will vary as 

 the square of the quantity divided by the square of the surface; and 

 we have, calling C the charge, Q the quantity, and S the surface, 



Q 2 



C = ^L; which formula fully represents the phenomenon of a con- 

 S 



stant intensity, attendant upon the charging of equal separated sur- 

 faces with quantities increasing as the surfaces ; as in the case of 

 charging an increasing number of equal electrical jars. Cases, how- 

 ever, may possibly arise in which the intensity varies inversely with 

 the surface, and not inversely with the square of the surface. In 

 such cases, of which the author gives some examples, the above for- 

 mula does not apply. 



9. From these inquiries it is evident, as observed by the early elec- 

 tricians, that conducting bodies do not take up electricity in propor- 

 tion to their surfaces, except under certain relations of surface and 

 boundary. If the breadth of a given surface be indefinitely diminished, 



F2 



