202 
MR. J. ZELENY ON THE VELOCITY OF THE IONS 
sponds to the inclination of the paths of the ions represented by bh of fig. 3, 
T corresponds to dh, and W to eh. As the paths change from eh to dh, the 
diminution in the number of ions reaching D is equal to about twice the number 
that are getting to D in the latter case (AVe = 3 Td). If, therefore, the rate of 
diminution remained unchanged until ions just ceased to reach D, the change in 
potential required for this would be just a half of the change from eh to dh or 
from dh to bh. Thus in the curve it is seen that by prolonging WT it reaches 
the axis at c, half way between b and d. This corresponds to a potential which 
would be required for an ion starting from c (fig. 3) the middle point of the beam 
of rays bd, in order to have it just reach the juncture h in the inner cylinder. 
It is evident that the points T and U are not very sharply defined on an experi¬ 
mental curve, and hence cannot he determined as accurately as the point c, and so 
in jmactice the potential A of formula (9) has always been determined in this 
latter way. Evidently the value of X which is to be used with this value of 
A has to be measured from the middle of the beam of the rays where they cross 
the inner cylinder to the middle of the juncture h, as all ions reaching the middle 
point are drawn to D. The width of this juncture was only - 05 centim. The 
width of the beam of rays was used as small as possible, and in most cases was 
'2 centim., this being a small part of the total distance X. 
4. In considerinp - the distribution of the ions between the two cylinders while the 
O «/ 
conduction is going on, it is seen from the lower part of fig. 3 that supposing the 
external tube to be positive, the negative ions starting from s will describe a path 
somewhat like sw, so that all of the negative ions will be confined to the space 
wmnts. Similarly the positive ions starting from rn will describe the path mh, 
and all of the positive ions will be confined to the space hunts. In the space 
where these two overlap, i.e., omnts , both kinds of ions will be present and recom¬ 
bination will take place, the number of ions per cubic centim. diminishing, there¬ 
fore, as we go from sm to o. 
The space oivm will he occupied by negative ions alone, and ohs by positive ions alone. 
ivm will usually be shorter than hs, because as a rule the negative ions travel the 
faster in the same electric field. 
5. Of the ions starting from m towards h all will not follow the path mh, but 
some, due to the motions assigned to them by the kinetic theory of gases, will 
diffuse to either side so that the distribution, along the path, of the ions which 
started from m will lie between the two dotted lines mr and mp. This effect will 
produce a distortion in such a curve as that shown in fig. 4, and to bring all of the 
ions to the part B of the inner cylinder will require a greater force than would be 
necessary if there were no diffusion. The effect of this disturbance upon the value 
of the ionic velocity obtained in the manner described is to give a result that is 
too small because the potential A obtained is too large. Moreover the amount of 
the diffusion depends upon the time required for the ions to travel between the two 
