ON THE THEORIES OP ELBTATION AND EARTHQUAKES. 91 
methods might also be adopted for the determination of C. Suppose for 
instance two points were known, at which the vibratory Avave arrived at the 
same instant, then, if we bisected the line joining these two points, and drew 
another line perpendicular to it through the point of bisection, the latter 
line would pass tliroughC, assuming always the spherical form of the general 
vibratory wave. In some cases also, as in those of earthquakes iu the neigh¬ 
bourhood of insulated, volcanos, circumstances may indicate, antecedently to 
any instrumental observations, the approximate position of the point in 
question. 
C being determined, the determination of the depth CO of the centre of 
disturbance^ by the formula (/3.} (art. 18) would require the values of the 
horizontal velocity (v) of the wave, and of its absolute velocity (\'). For 
the determination of f>, two instruments would be ncee*ssary merely to record 
the exact times of the initial shock at two places, which ought to be situated 
as nearly as should be convenient ou the same Hue through C. They ought 
to be too near C, because tlie variation of horizontal velocity would there 
he very rapid; nor ought they to Im so far removed from that point tliat the 
angle d (fig. 13 ) should approximate too near to a right angle, because the 
difference between v and V would then bo «o stuaJl that a small error in the 
detei^nation of either would vitiate the result given by the formula. 
} . ® already indicated (art. 40) how the absolute velocity of jiropagation 
(V) might be detennined if we could ascertain the. coefficients of elasticity 
of a number of rocks similar to Umsc which inny be presumed to constitute 
the portions of the earth’s crust tliroiigb which earthquake vil)ralion 8 arc 
propagated. And here I would again remark on the insufficiency of attend- 
mg only to the coefficient of finear expansion; tliat of cubicol expansion 
wujt also be determined. We might also determine V by observing tho 
“oruontal velocity at such a distance from ihft origin of the motioUt that the 
orizoHtal anil absolute velocities of propagation might be considered as 
approximately equal, and in tho present imperfect state of our knowledge 
jwpecting the velocity with which vibratory motions are propagated through 
“bd masses, this would probably be th <3 best way of detcriiiiuiug the quau- 
btym question. ^ J ^ e i 
■ ® aurrouadiijg an active volcano, it is probable that a sensitive 
wo *oi]lil detect a great number of slight earthquake sliocks which 
UW pass entirely unnoticed witliout Home special moans of observation; 
* ’ “®'‘^over, the volcano should be an insulated one, like Vesuvius for 
jjf., P should have a ca.so in which, as already rcmarkcel, the position 
know^ alwve denoted by C, might he considei’etl as very approximately 
lain 1 ^*® shocks to originate in the interior of tho volcanic moun- 
• ^nen a region will naturally suggest itself as one in which wo should 
.OUrillMtriinii.nflll nKanrvofin... >>.<] ...w.nn.,* nv/.Arfnin thp. CanO- 
mpnt. 'i j — ‘‘hratorj'wave, the only csscfilial requisite./. ...v - - 
initini should note accurately Me tJirtnM of the 
deton t«’spceli'*e stations chosen as almvc Tiieulione<l for the 
reouuW^.L^” ^ without the above assumption, it would also bo 
should imlicHte the horizoitial directim of the 
nw-nu .* 1 ^!!'"?* requisite belong?. I beUevc, to several instru- 
of vib,! • ^ invented ; in fact, the determination of the horizontal direction 
lute d^'l* ** ^ much more simple problem than that of the abso- 
neecssaX t‘ ""‘I amplitude of vibration would not bo at all 
consfnw’I ^ T that any self-registering instrument has yet been 
''ilh the power of recording the exact instant of a shock. With- 
, ' *• 
• ‘ 
r 
