Barus — D isplacemen t In terferom eter. 73 



corresponding to a displacement — AN 11 , the mean of the equa- 

 tions, AJV = £(AiV x + AN"), after reduction becomes 

 Mg AN D* (1+2 A/Z>) 2 



I r 2 V, 



= V 



the corrected equation required, reducing to the above case 

 when A = 0. The correction factor is thus \/F— (1 + 2A/D) 2 

 and was computed in an auxiliary table. 



It is now easy to discuss the conditions of equilibrium, for 

 the forces X are given by the equations (second member 

 referring to the pendulum and third member to the electrical 

 forces) 



Mg A N r* 1 



x= r~ - v > v * j* (1+2 A/uf 



Hence, if AN = A, h = 0, the condition under which the disk 

 just moves, without interruption, from the guard ring to the 

 condenser plates, i. <?., the limiting value of the potential 

 products, ( V x V 3 ) for stable positions of the disk, since 



■4A/Z> 



dA~ I ~\ "» v * JU* (1 



+ 2 A/ By 

 are (in electrostatic units) 



/Viz \ Mg & (l + 8A/2>) ' 



\ V > V * )- M r 2 A/D 



Assuming V x = 250 volts, the forces ^TTfor the pendulum and 

 the electric field were also computed. 



If now, we insert the value of V 3 from the above equation 

 and reduce 



— 6 A/D = l or -A=D/6 



Hence the value of V~ s which corresponds to tangency is 



y^Mgl? { ,\ /„\, , Mgl>> 



#(-*) (*) 



I V x r> \ V \V -^ I V 1 r 2 



or V 3 = 145 volts, above which charge the disk passes contin- 

 uously from guard ring to plate. 



If the suspension is provided with a horizontal micrometer 

 by which it can be shifted as a whole from k to k 1 taking the 

 needle with it, k may "be eliminated. But the expression is 

 not simple. 



The idiostatic method needs a corresponding correction, and 

 if A 2 is neglected in comparison with D, 



2 Mg D* / \ 



—fc- AN=V 3 2 (l + 4A/Z>j 



-As the new factor is practically k or constant, V 2 is linear 

 with AiV. If, as above indicated, the suspension is provided 



