relation. The potential required to produce this discharge is much less
than that required to produce a spark of length l between parallel
plates; thus from Chattock's experiments to produce the point discharge
when l = .5 cm. in air at atmospheric pressure requires a potential
difference of about 3800 volts when the pointed electrode is positive,
while to produce a spark at the same distance between plane electrodes
would require a potential difference of about 15,000 volts. Chattock
showed that with the same pointed electrode the value of the electric
intensity at the point was the same whatever the distance of the point
from the plane. The value of the electric intensity depended upon the
sharpness of the point. When the end of the pointed electrode is a
hemisphere of radius a, Chattock showed that for the same gas at the
same pressure the electric intensity f when discharge takes place is
roughly proportioned to a^-0.8. The value of the electric intensity at
the pointed electrode is much greater than its value at a plane
electrode for long sparks; but we must remember that at a distance from
a pointed electrode equal to a small multiple of the radius of curvature
of its extremity the electric intensity falls very far below that
required to produce discharge in a uniform field, so that the discharge
from a pointed electrode ought to be compared with a spark whose length
is comparable with the radius of curvature of the point. For such short
sparks the electric intensity is very high. The electric intensity
required to produce the discharge from a gas diminishes as the pressure
of the gas diminishes, but not nearly so rapidly as the electric
intensity for long sparks. Here again the discharge from a point is
comparable with short sparks, which, as we have seen, are much less
sensitive to pressure changes than longer ones. The minimum potential at
which the electricity streams from the point does not depend upon the
material of which the point is made; it varies, however, considerably
with the nature of the gas. The following are the results of some
experiments on this point. Those in the first two columns are due to
Rontgen, those in the third and fourth to Precht:--

+------+-----------------------------+--------------------+
| |Discharge Potential. Point +.| Pressure 760. |
| Gas. +--------------+--------------+----------+---------+
| | Pressure 205.| Pressure 110.| Point +. | Point -.|
+-