84 
REPORT—J847. 
real velocity of propagation at points near to C, but approximates 
real velocity at points remote from C. 
Let CP as above determined =a ; then 
CO=acot.fl 
V 
This would appear to be the simplest formula for the determination of CO. 
A formula may also be obtained independently of the previous determina¬ 
tion of the point C. For let v' be the horizontal velocity of the wave at a 
point distant a' from C ; then 
CO=a'^. 
•v« 
a'—a=Co| 
V 
L V* V'ru_V«}. 
determine CO in (Grins of the differenco of the distances of P ami 
1 trom C. This forniula might be useful when V and P' are known to be 
nearly on the samo line of horizontal propagation; for in that case we 
nii^ht substitute the distance PP' for This would be the case in 
finl? I r o/C’ would be least accurately determined by the me- 
thod before indicated (art. 42), if wo had to use observations at P and P'; 
e augePCI being small, a small error in tJie determination of the 
inTbp nil!-? propagation would make a comparatively large error 
I nT of those directions! 
direct distancp'oP^n'^f'if also to indicate a formula for determining the 
the vihmfm depending on the retardation of the wave in which 
normal rrfv’'? "-ith reference to the wave in which they are 
V will bp oro'tL velocity of the latter wave, that of the former; 
the waves off, f respective Umes in which 
arrivals of tL t O to I, and T the observed interval between the 
arrivals ot the two waves at I-*. 'i’hen 
OP=V,<„ 
OP=V,i„ 
/,W, = T; 
\v, vj 
-T V,V, 
OP=:T. 
V.-V. 
vibration is &®^og'caI formations through which the 
approxima JyTnoC %r‘> ^ 
quire an instrumpiw nf determination of T would 
ference in the nature of accuracy and i^nsibility to detect the diP 
taneously from O Th/* h-\ *° die two waves proceeding simui- 
of the cLiZo sufficiently great to allow 
and the position of C found • ^ OP being thus determined, 
diateiy kLwn JfU stuid Lp ?f O wiU be imme 
•w aves can he fruoueutlv „,nf d ' ‘I’® existence of these tw^ 
u*ay probably be lound morP^m-t!'""*' tccogniswi, the determination of T 
tal velocity of the w ave ' “^"venient than that of the horUon- 
