_a_^2 _b_ = _a_ tan _e_ + ————————————, 4H cos^2 _e_
H being the height due to the velocity of projection. Whence
___________________ 2H ± √4H(H + _b_) - _a_^2 Tan _e_ = ——————————————————————————. _a_
_a_^2 _g_ V^2 = ———————————————————————————————. 2 cos^2 _e_ (_b_ - _a_ tan _e_)
For the back motion or subnormal wave in the direction C O,
___________________ 2H ± √4H(H + _b_) - _a_^2 Tan _e_ = ——————————————————————————. _a_
_a_^2 _g_ V^2 = ———————————————————————————————. 2 cos^2 _e_ (_b_ + _a_ tan _e_)
A serious error which may enter into calculations of this description when practically applied has been pointed out when speaking of columns as seismometers. It was then shown that such bodies before being overthrown may often be caused to rock, and therefore that their final overthrow may not have any direct connection with the impulse of the succeeding shock.
Another point to which attention must be drawn respecting the above calculations is that if there was no friction or adherence between the projected body and its pedestal, in consequence of its inertia it would be left behind by the forward motion of the shock, and simply drop at the foot of its support. In the case of frictional adherence it would be carried forward by the velocity acquired before this adherence was broken, and thrown in a direction _opposite_ to that given in the figure—that is to say, in the direction of the shock.[14]
_The Absolute Intensity of the Force exerted by an Earthquake._—No doubt it has occurred to many who have experienced an earthquake that the power which gave birth to such a disturbance must have been enormously great. The estimates which we shall make of the absolute amount of energy represented by an earthquake cannot, on account of the nature of the factors with which we deal, be regarded as accurate. They may, however, be of assistance in forming estimates of quantities about which we have at present no conception. One method of obtaining the result we seek is that which was employed by Mallet in his calculations respecting the Neapolitan earthquake. Although disbelieving in the general increment of temperature as we descend in the earth at an average rate of 1° F. for every fifty or sixty feet of descent, for want of better means. Mallet assumes this law to be true, and, knowing from a variety of observations the depth of various parts of the cavity from which the disturbance sprang, he calculates the temperatures of this cavity in various parts as due to its depth beneath the surface. Next, it is assumed that steam was suddenly admitted into this cavity, which might exert the greatest possible pressure due to the maximum temperature. This was calculated as being about 684 atmospheres.