Page:Great Neapolitan Earthquake of 1857 Vol 2.djvu/383

318 the coefficient of compression, be known, then the total compression may be obtained, and the temperature due to the pressure producing it. In this way, a new method would present itself, through the medium of seismology, for attempting the ascertainment of temperatures, at depths that can never be reached eaperimentally.

The vis vivâ of the wave, is constant throughout its transit, (assuming elasticity perfect,) and = $1⁄2$ $$M\ a^2$$; $$M$$ being the mass of material, in any spherical couche, or in simultaneous wave motion, and equal to twice the "work done," in compressing, the originating sphere of impulse, whose radius is $$o\ t$$. Hence, we can express, the work of the wave, in foot pounds, and, finally, transmuting the mechanical effort, by the aid of Joules' thermodynamic unit ($$\mathit J$$ = 772) into heat; we can determine, the expenditure of volcanic or hypogeal heat, necessary to the production of the earthquake; or as there are 11,000,000 foot pounds of absolute dynamic energy, in the combustion of a pound of coal, we can compare the value, of the "shock power," in "cheval vapeurs," or with any other measure of power, we please.

Unfortunately, we are as yet without some of the numerical data necessary, to enable us to attempt putting such a calculation into form.

The only experiments that have been made, upon the compressibility of limestone, are those of Tredgold ('Phil. Mag.,' vol. lvi. p. 290), who deduced the coefficient, by the use of Dr. Young's formulæ, from experiments on flexure, and obtained, for primary limestone, the modulus of elasticity = 2,520,000 lbs. for the base of an inch square.

The compression due to each ton pressure upon a prism of a foot long = $$L$$, is, therefore = 0·000446 feet = $$\mathit l$$, a