616 Dimensions of the Cathode Images. 



For aluminium in hydrogen n=2, i.e., in this case the 

 current -density is proportional to the square of the pressure. 

 For surfaces of any shape equation (4) may be written 



= constant, (5) 



f . D n ^ ' 



where./ stands for the area covered by the glow. 



6. Relations connecting the thickness of the canal-ray layer, 

 the cathode dark space, and the negative glow layer with the 

 pressure and cur rent -density. — If the thickness of any of the 

 above layers be denoted by d, and the pressure by p, then, so 

 long as the cathode is not completely covered by the glow, 



p . d= constant, 



i. e., the thickness of the first three layers is inversely propor- 

 tional to the pressure* '. 



If the cathode is completely covered by the glow, the 

 thickness of the canal-ray layer increases with increasing 

 current, rapidly at first, then more slowly. The thickness of 

 the cathode dark space decreases with increasing current, 

 rapidly at first, then approaching asymptotically a minimum. 

 The drop of potential Y at the cathode was, within the range 

 of the present measurements, found to increase nearly in 

 proportion to the current f. 



7. Relations connecting the luminous intensity of the glow 

 with the current and pressure when the cathode is not completely 

 covered. — So long as the glow does not completely cover the 

 cathode, and the current remains constant, the quantity of 

 light sent out hy the glow is constant, and entirely independent 

 of the pressure (the intensity was determined by a photographic 

 method). Since, as shown above, the area covered by the 

 glow is directly proportional to the current, we may also 

 state the above proposition as follows : — 



The total intensity of the glow per unit of current remains 

 the same at all pressures, so long as the cathode is not entirely 

 covered. 



If, the cathode not being completely covered, the current 

 be varied while the pressure is maintained constant, the 

 intensity of the glow is directly proportional to the current. 

 Now since the current-density is directly proportional to the 

 pressure, it follows that the intensity of the glow per unit of 

 area is directly proportional to the current-density . 



* In this connexion, reference may be made to the experiments of 

 H. Ebert, Wied. Ann. lxix. p. 200, 1899; H. Ebert and P. Ewers, 

 Drude's Ann. x. p. 72, 1903, and O. Lehmann, Verh. cles natunoiss. 

 Vereins zu Karlsruhe, xv. 1902. 



t A similar result was found by Herr G. C. Schmidt. Ann. d. Physik, 

 i. p. 640, 1900, while recently Herr F. Stark (Ann. d. Phys. xii. p. 1, 1903) 

 has found that the relation connecting V and i is not a linear one. 



