Surface of a Needle-Point discharging in Air. 271 



This means tbat if we calculate / from P, the total resolved 

 pull on the point, and assume p 2 uniform, /„ will be 7 per cent, 

 too high; whereas if we assume the sine law it will be 9 per 

 cent, too high ; always supposing of course that the values 

 of k obtained above are correct. 



Actually, however, they are too high for the following two 

 reasons : — 



1. The 400 cm. sec. -1 taken for V represents the specific 

 velocity of fully formed ions. If the C ion* do not at once 

 reach their full size, V will be greater than 400 and k 

 proportionately less. 



2. A still stronger reason for reducing k is the fact that in 

 actual discharge the surrounding gas is not kept out ot the 

 discharge cone as has hitheitobeen assumed. It is of course 

 really quite free to flow in laterally, and so to prevent the 

 pressure from falling in the region of the point to anything 

 like the extent the above values of k suggest. Instead of 

 producing a slope of pressure, the drag of the ions must be 

 mainly converted into motion of the gas, and the resulting 

 momentum thus transmitted to the plate rather than to the 

 point. 



It seems clear, therefore, that as the error in/ due to the 

 suction of the C ions is probably not much more than 

 9 per cent, without either of these reductions, it will be safe 

 to neglect it altogether when they are taken into account. 



Consider now the electrical effect of the discharge. 



The ionizing layer is traversed by bothB and C ions. The 

 B ions are densest at the side of the layer next the point, and 

 the C ions at its other side. The ionizing field will therefore 

 contain lines of force due to both B and C ions, none of which 

 are measured by the pull ; and the field calculated in terms 

 of the pull is consequently too small. 



It is probable, however, that the ions are swept away so 

 quickly that their lines of force form a negligibly small 

 part of the field at the point. Let t be the thickness of 

 the ionizing layer and t the average density of the charge 

 on the B ions, close to the metal : 



C 1 



^"o 2 /oV 



and 47tt£ is that part of the field at the metal which is due 

 to the B ions if f is the average value of r through the 

 distance t. 



The distribution of t through i is of course unknown, but 



