124 . D. Boboulieff— Dissipation of Electricity in Gases. 
3 
@) = —31R7 ap 
and cis the distance between the centers of the ball and the 
atom ; the equation (2) is obtained by disregarding higher powers 
: : r r 
of the fractions, as for instance aT and oR 
allowable only in case (c— R) is much greater than r. 
us now see what will be the effect of such a force on the 
duration of the interval between two consecutive concussions. 
To this end let the velocities be wu and u; the distances of the 
center of the atom from the center of the electrified conductor at 
the beginning and the end of the interval be cy and c; then 
we consider the living forces we fin 
*r/ 
w—Uu = Q (= ~ =). 
m\e e, 
which is 
t ¢= cy ni where (=,;!,;,; of a millimeter, or the 
average length of the path between the concussions of two 
atoms;* and nis an abstract number of such value that the 
eee . 
ratio — represents a small fraction, so that we can put 
1 4nl 
Lae ae 
o 
thus we have 
4Q?r’nl 
(3) v—u~= oie =. 
The quantity m, the mass of the atom, can be expressed thus: 
prin a 
“Ng” Ng’ (1+ at)760’ 
where P is the weight of the unit of volume of the gas; N is 
the number of atoms in said volume; 6=0-001293 milligram 
is the weight of one cubic millimeter of air at 0° C. and 760™; 
is the actual pressure of the gas: ¢ is the temperature; @ 1s 
the density of the gas as compared with air; g=9800™" is the 
force of gravity expressed as a velocity per second. 
urthermore,+ 
1 1 
ee See 
where A is the mean distance between the atoms; p is the radius 
of action of the atoms. If now we indicate by A= iaR? the 
density of the electricity, i.e, the quantity belonging to one 
* Clausius, Abhandlungen, II, p. 325. 
+ Clausius, Abhandlungen, II, p. 272. 
