300 Mr. A. P. Chattock on the Electrification 



Now the field (/) measured by the attraction of a plate on a 

 needle-point is the average number of lines of force per square 

 centimetre of the point-surface, and takes no account of the 

 manner in which they are distributed over it. (This is because 

 the point is so small that the lines have room to become uniformly 

 spread out before they reach the plate.) Hence it follows 

 that, for different dispositions of the chains, the measured 

 values of/ may be very different, and yet the number of lines 

 of force running through each chain be the constant number 

 corresponding to ionic charge on its atoms. /, in fact, for a 

 given amount of induction per chain, depends both on the 

 length and on the closeness of the chains. Great length or 

 great closeness, or both, means that the greater part of the 

 lines proceeding from the point have been absorbed by the 

 chains, hardly any passing in between them. Id this case 

 / is practically proportional to the number of chains per square 

 centimetre and is independent of their lengths. On the other 

 hand, very short chains, or very few to the square centimetre, 

 or both, mean that /is sensibly independent of their closeness, 

 but is now dependent on their length; being inversely pro- 

 portional thereto so long as it is not very great compared with 

 the radius of curvature of the point. Between these two 

 extremes / depends both on length and on closeness of the 

 chains — varying in an inverse manner with the former, and in 

 a direct manner with the latter. 



Now both length and closeness of the chains increase with 

 increase of gas-pressure. Hence there must be some pressure 

 A above which / is sensibly proportional to the closeness of 

 the chains only, and some lower pressure B below which it 

 is inversely proportional to the chain-lengths only. In the 

 neighbourhood of A increase of pressure will affect / chiefly 

 by the resulting alteration of the closeness, and will therefore 

 increase /. Near B it will have the opposite effect, as increase 

 in the length of the chains means a decrease of /. Hence 

 between A and B there must be some pressure for which / is 

 a minimum. This point is of course well known to exist*, 

 though I was unable to obtain a sufficiently good vacuum 

 with my apparatus to reach it. If, however, / be expressed 

 in terms of some power («) of the pressure, n will be at the 

 minimum point, and positive and increasing as the pressure rises 

 from there. This increase is shown well in Table III. (calculated 

 from Table II. for positive discharge only — the negative is 

 too uncertain). Here n x is calculated from the values of/ 

 corresponding to 76 and 40 centim. of mercury, and n 2 for 

 40 and 20 centim. n 2 is in every case less than n v 

 * Rontgen, Wiedemann's Electricitat, vol. iv. § 582. 



