193 
33 TV. SURFACE PHENOMENA 
may attain a maximum height of as much as 500 feet. As the depth of the explosion is 
increased, the plumes become less marked and also appear later; they may break through 
the dome at the instant when the latter has attained its greatest height, or when it 
is sinking again, or the plumes may not appear until after the dome has disappeared. 
Finally, at great depths, no plumes are formed, but a minute or so after the explosion 
a mass of creamy water pours up to the surface. 
All writers agree that the initial agitation of the surface is produced di- 
rectly by the pressure wave, and that the plumes are thrown up by the exploded gases 
as they escape through the surface. Various theories have been offered, however, as 
to the cause of the dome. 
Hilliar views the dome as an indirect effect of the pressure wave, arising 
from the fact that water can stand only a limited amount of tension. In the process 
of reflection from the surface, the pressure wave first gives to the water a high up- 
ward velocity, then endeavors to jerk it to rest again as tension develops below the 
surface. Bits of the surface may thus be jerked off, forming the initial spray that 
is sometimes observed. The water may also become broken to a depth of several feet, 
and in this case it will retain part of its upward velocity and will rise until 
checked by the action of gravity; a temporary dome of water, filled with bubbles or 
vacuous crevices, will thus be formed. 
The explanation of the dome just described sounds plausible. Upon reflec- 
tion at a free surface, the particle velocity of the water should be doubled. 
Hilliar's report lists 43 domes due to charges fired a long way above the bottom of 
the water. In all cases, calculation shows that the velocity required to project an 
object against gravity to the maximum height of the dome is less by at least 20 per 
cent than twice the calculated maximum velocity due to the reflected pressure wave 
at the surface of the water. 
A final remark may be added concerning the explanation of the great height 
to which the plumes sometimes rise. Hilliar records a height of 140 feet due to 300 
pounds of TNT fired at a depth of 34.5 feet. As the gas approaches the surface, it 
will occupy a volume which, if spherical, might have a diameter of 20 feet. Even if 
this were flattened down to 10 feet, we should have the pressure due to a water head 
of 10 feet transmitted upward through the gas against the last layer of water, a foot 
or so thick, so that this water would experience a momentary acceleration of the order 
of 10g and would be thrown violently upward. It is plausible that actions of this 
kind would be capable of projecting water to the heights observed. 
