Velocity of Transmission of Disturbances through Sea-water. 521 



Determination of the Isothermal Resiliences. 



With regard to Eg, Professor Tait has kindly supplied us with 

 information. He gives formulas for the compressibility of fresh 

 water and of sea- water at low pressures and high pressures. The 

 compressibility, as given by him, is a function of the pressure and the 

 temperature, and thus for a pressure which varies rapidly from a low 

 value to such a great value as one or three tons weight per square 

 inch, the compressibility would be a variable quantity. It did not 

 appear at first whether his formula for moderately low pressures, or 

 the formula for such pressures as from one to three tons per square 

 inch, was to be used to get E<?, the reciprocal of the compressibility. 

 The further uncertainty as to the effect of viscosity is not allowed for 

 in finding the theoretical velocity. With a view to settle which of 

 Tait's formulas was to be adopted, it was remarked that for an incom- 

 pressible uniform liquid, subject to impulsive pressures, the equation 

 to determine the impulsive pressure at any point is (Lamb, p. 12) — 



And hence, for an impulsive pressure uniformly distributed over a 

 sphere, the impulsive pressure at a point outside the sphere would be 

 inversely proportional to the distance at that point from the centre of 

 sphere. 



It seems desirable to determine the function -sr of x, y, z, and t, which 

 will satisfy given boundary conditions and the equation 



dp dPur d 2 ^ _ n 



Tt + d^ + df + d^ ~ ' 



arising from the equation of continuity combined with the equations 

 of impulses, when a relation is assumed between p and nr. If it is 

 supposed that impulsive pressure is subject to the laws of ordinary 

 pressure, such a relation as that given by Van der Waals might 

 perhaps be taken, or one of Tait's relations giving the compressibility 

 as a function of pressure and temperature. 



Supposing that the above consideration approximately applies to 

 sea- water, it was further concluded, by the method of Berthelot in 

 discussing the experiments of Sarrau and Vieille, that in our case the 

 initial pressure on the walls of the case containing the explosive was 

 in each case (guncotton and dynamite) about 8000 kilograms weight 

 per sq. cm. This agreement between the initial pressure due to gun- 

 cotton and that due to dynamite is accounted for by the density of 

 charge being rather different in the two cases. Supposing this 

 pressure uniformly distributed over a sphere of 1 foot diameter, 



