Fisr. 3. 



Sig. Quirino Majorana on the Contact Theory. 259 



with which we are dealing - , let us assume that in the case of 



the quartz fibre and the plate only two elements each of area 



A attract each other. In fig. 3 Q 



represents the quartz fibre, and L is the 



point of the zinc disk at which we 



assume the attracting area to exist. In 



consequence of the attraction OQ is 



deflected to OE. If P is the weight 



of the quartz fibre, and I its length, 



and if EL=# and QL = «, the force 



acting on the end E along EL is 



P(a—x)/2l. This supposes the quartz 



fibre to be rigid and hinged at its upper 



end. For equilibrium this force must 



be equal to the attraction between the two hypothetical areas 



considered. Wherefore 



or 



P(«-; 

 21 



(a—x)x 2 = 



V 2 A 



Sttx 2 ' 



Y 2 Al 

 4ttP' 



In order that this equation may be possible, it is necessary 

 that the greatest value which the left-hand side can have for 

 a given value of a, when x varies, must be greater than the 

 right-hand side, which is constant ; hence, differentiating with 

 respect to x and equating to zero, 



2x (a — x) — x 2 — ; whence x = 



3 



We have, therefore, 



4a 3 



2T' 



V 2 A/ 

 4ttP' 



If, however, we equate the two expressions, we obtain 



,3_ 



27 V 2 AZ 

 IGtt" P 



In this case the distance a is that corresponding to the 

 instant at which, on causing the plate to approach the fibre, 

 the latter suddenly rushes towards the plate. 



From the preceding expression we have 



16 



27 



, 1U U J. 



U2 



