92 
llEPORT^lb47. 
out this requisite, however, no instrument can have tlie slightest valne for 
the purposes here eontomplated. 
In the methods above suggested, the horizontal direction of propagation 
is alone required; but if V, and could be determined with sufficient accu¬ 
racy by means of the coeffieiente of linear and cubical expansion, the formula 
(c.) (art. 4S) w'ould give immediately the position of O by a single observa¬ 
tion, provided our instrunient could determine the time denoted by T, and 
the absolute direction of propagation of the wave within the earth. This 
direction will coincide with tJiat of the nonnal vibrations of tlie wave arriviog 
first at any point within the earth; but it should be observed that the par¬ 
ticles situated at the surface will not generally vibrato in the same direcdon 
as those within the vibrating muss. Consequently, supposing w# had an in¬ 
strument with the above-mentioned rtquisites, it would be necessary, for Iha 
object here proposed, to place it at a certain depth below the surface of die 
earth; and here again the interference of the wave reflected back frofu the 
surface into the interior inas.s with the incident wave, would render the ob¬ 
servations useless, unless the instrument were jdaced at a sufficient depth. 
Let this depth ~h^ ami let 0 denote tlic angle of incidence, as in figure IS: 
then it is easily shown that the interval of time between the arrival of tk 
incident and reflected waves at the point of observation . . - - , 
since tlin sounds usually resulting from these vibration.s are ro/i//»uous sow/fs, 
80 many vibrations must take place in ii second, that if the insminieiU were 
placed, for instance, in a mine at the depth of a few hundred feet, scwral 
complete vibrations of the incident wave might be completed at the point of 
observation before the arrival of the reflected wave; and if the instrument 
sliould bo capable of recording the absolute direction of these initial vibra- 
lons, independently of the subsequent ones due to the combined eflecU of 
tne two waves, the absolute direefion of propagation of the wave in the in- 
termr of the terrestrial niass would be detennined as required, 
ir, ♦ of this method would consist in its requiring only a single 
s rumen a observation; but the exactness with which the observation 
must be made, and the few localities in which Uio instrument could be placed 
depth, must necessarily render the method comparatively 
Soneral detennination of the depths of volcanic foci. I ha^ 
w«tiM j bt-mf dUcusaiun of it to indicate the precautions which 
j adoption of any methrxl depending on the deter” 
SnT of vibration within the vibrating mass. Tie 
will nrnb 11 '•’^'catcd, ilepcnding on the /inrizonal fiirection of vibratiocj 
of cLifiiWp^® nnwcfliuiple in application, and far more dfsei-ving 
absZt. 5 . - ® however; that the determination of the 
Toc-S t! nt of vibration, if it was found practicable in any one 
on acemm^^ be highly interesting 
of ^ <‘’tporunental knowledge it wouM afford of the characters 
marked through solid media. Itraayalsohere- 
detS,,Sn ‘ ^kis purpose avail ourselves of siinn*^ 
mllht nUnT vibrating nms these latter 
in ® r*“i ^ affording interesting tests of theoW; and, moreover, 
tiofs the-wnnw '^ff ?■'* horizontal parts of tlm superficial vibra- 
oarthauak'’^««-^ ns a knowledge of one of the csseoHal elements of 
dislmsitinc prA ^ rctevcncc to their disturbing awl 
their influiicc ^ surface and subjected W 
