1374 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1954 



ability of a single-contact open. Such a performance, however, has never 

 been observed in practice where an improvement of only 10 : 1 is usually 

 more tj^pical. A study of the mechanisms involved has revealed that only 

 a very small number of opens are obtained due to the simultaneous oc- 

 currence of opens on both members of a twin contact. The majority of 

 opens, however, occur by having an open in one member of a twin con- 

 tact which persists long enough to allow the occurrence of an open on the 

 other member. By expressing this physical process in mathematical 

 terms it was possible to develop a theory of performance of tmn contacts 

 in terms of the characteristics of single contacts. 



NOTATION 



d Diameter of dust particle 



/ Fractions of opens in single contacts cleared after A^ operations 



/^ The asymptotic value of / corresponding to A^ = oo 



n Average number of operations required to clear an open on a 



single contact 



r Distance of particle from center of circular open contact zone 



To Radius of "open zone" 



s Fraction of the twin contacts that are half open at any time, 



S = S„ + Sn 



s^ Fraction of twin contacts that are permanently half open 



Sn Fraction of t\\'in contacts that are temporaril}' half open 



w Alechanical wipe 



X Average displacement of a dust particle per contact operation 



F Contact force 



N Number of contact operations 



Ps Probability of occurrence of a single-contact open in opens/con- 

 tact operation 



Pt Probability of occurrence of a twin-contact open in opens/contact 

 operation 



X Total displacement distance to clear an open 



a = (2 - P.)(l - /J 



^ = nf^Ps(2 - P.) 



6 Angle of displacement 



if Slope of contact surface irregularity 



PRESENTATION OF THEORY 



Outline and Assumptions 



Consider a large group of t\\Tin contacts each constituting a pair of 

 identical and entirely independent single contacts. After a period of 



