504 Prof. Fleming and Mr. Clinton on the 



Therefore the capacity of a very elongated ellipsoid of 

 revolution of which a is the major and b the minor semiaxis 

 is given bv 



c= 2a ■ 

 2 loge %a[b 



If therefore we can consider a thin circular-sectioned wire of 

 diameter d and length I as an ellipsoid, we have its capacity 

 in electrostatic units given by the formula 



C (in E.S. units) = ^ 7,,-., 



2 log e 21/ d 



where I and d are of course measured in centimetres. To 

 reduce a capacity expressed in electrostatic units to micro- 

 farads we have to divide by 9 X 10°. and therefore to convert 

 capacity expressed in electrostatic units to the same expressed 

 in micro-microfarads, we have to multiply by 1-^ or to increase 

 by about 11 per cent. 



Hence expressed in micro-microfarads the above capacity 

 is : — 



C (in M.M.Fds.)= •- , QAO *,,. . -^ 



v ; 2x 2-303 x 9 x 10° x log 1Q 2l/d 



= I 



" 4'14541og 10 2/AT 



An approximate formula for the capacity of a telegraph-wire 

 is also easily found. If an infinitely long filamentary wire is 

 uniformly charged with electricity so that it has q electro- 

 static units of charge per centimetre of length, then from the 

 analogy with the case of an infinitely long straight current, it 

 is easy to show that the force due to the filament at any point 

 distant r centimetres from it, is '2<]/r. Hence if the potential 

 at this point is V we have 



_dV _ 2q 

 dr r 



or Y=— Zqlogr + Ct, 



where Ct is the constant of integration. 



If we have two very long straight circular-sectioned wires 

 suspended in air parallel to one another, at a distance D, 

 the diameter of each wire being 2r, and r/D being a small 

 quantity, then it is easy to calculate the capacity of the 

 condenser formed of these wires, if we assume them to be so 

 far apart that the electrical charge on each remains uniformly 

 distributed round the surface of each wire. Let one wire 



