232 REPORT — 1861. 



In Table XII. the load on the unit of surface (1 square inch) at which the 

 elastic limit of the rock is passed, and that at which it is finally crushed, 

 together with the modulus of cohesion or resistance to compression, are also 

 given, and will be useful to the engineer and architect. In the last column, 

 the value of my own modification of Poncelet's coetficient T, (la force vive 

 de rupture) is calculated in foot pounds, and represents the relative work 

 done at fracture in eacli case. 



To apply the results thus obtained to those of experimental wave-trans- 

 mission at Holyhead. 



Poisson has shown (Traite de Mecanique, vol. ii. p. 319) that the velocity 

 of wave-transmission (sound) in longitudinal vibrations of elastic prisms is 



V^=^ (I.) 



P 



When g has its usual relation to gravity, I and p are the .length and weight 



of the prism, and 9=^. A being a weight that is capable of elongating the 

 c 



prism by an amount=c/, or extending it to the length 



/(Ix^). 

 Substituting, we have 



w 



but A : W : : ^ : 1, W being the weight capable of doubling the length of the 

 prism. Therefore 



Y2_ghvh_ff[L_^ 

 pS I 



orV=v/^ (II.) 



So that L being the modulus of elasticity of the solid, expressed in feet, the 

 velocity of wave-transmission through it, if absolutely homogeneous and 

 unbroken, is 



V=5-674\/L (III.) 



Where, owing to want of homogeneity, or to shattering, or other such con- 

 dition, as found in natural rock, the experimental value of V difiTers from 

 the above theoretic one, we may still express the former by the same 

 general form of equation — 



V'=a \/l; (IV.) 



in which the coefficient a. expresses the ratio to g that the actual or experi- 

 mental bears to the theoretic (or maximum possible) velocity of wave-trans- 

 mission. 



In the slate- and quartz-rocks of Holyhead, I ascertained the mean lowest 

 velocity of wave-transmission (for small explosions or impulses) to be 1089 

 feet per second (omitting decimals), the mean highest velocity 1352 feet 

 per second, and the general mtan velocity from all, 1220 feet per second. 



Applying Eq. IV. to these numbers, and adopting the values of L given 

 in Table XII. (mean of Nos. 9 and 10), we obtain 



V 

 a=: — =; ; 



and for the three preceding velocities, a has the following values : — 



