640 



Dr. A. M. Tyndall on the Critical 



The point was normal to the plate, and the distance between 

 them readily adjustable. The tube was made airtight, and 

 connexion made by a flexible glass joint to pump and 

 manometer. The mechanical force on the point was mea- 

 sured by placing the whole apparatus on a tilting-table, and 

 finding the tilt required to keep the end of the point always 

 on the cross-wire. The distance between point and plate 

 was always greater than a few diameters o£ the point. 

 Under these conditions it has previously been shown that the 

 critical field is independent of the position of the plate. 



Townsend's theorem applied to the critical field may be 

 stated thus: — If X is the critical field at a pressure^ at a 

 point of radius a and X' is the critical field at a pressure p' 

 at a point of radius a', then Xa = XV when ap = a / p f . Now 

 the product of field and radius of point is directly proportional 

 to the root of the mechanical force on the point, so that if 

 F and F' are the corresponding values of the latter, then 

 -y/F should equal V / F / when ap = a'p'. This may be tested 

 by taking the results for two points a = 0'02S cm. and 

 a =0*054 cm.; the values of p and p f in mm. and of ^/F 

 and ^F' in arbitrary units are shown in Table I. It will 

 be seen that the agreement between them for a given sign of 

 discharge is very striking indeed. 



Table I. 





Positive Point. 



Negative Point. 



V- 



y. 



VF. 



Vf. 



Vf. 



vp. 



760 



395 



2-80 



2-78 



275 



2-80 



650 



338 



2-58 



253 



. 249 



2-53 



550 



286 



2-28 



2-28 



225 



2-28 



450 



234 



202 



202 



1-98 



202 



350 



182 



1-72 



1-72 



1-70 



1-72 



250 



129 



1-40 



1-37 



1-39 



1-38 



150 



78 



1-05 



1-02 



102 



103 



80 



42 



•78 



•76 



•67 



•67 



50 



26 



•65 



•61 



•50 



•50 



35 



18 



•57 



•52 



•40 



•39 



The absolute values of X may be obtained from the 



