T 
78 
REPORT-1847* 
S8. Vibrations propagated alony a solid Bar .—Tlie next ease I shall 
consider is that of a long solid bar, as one calculated to elucidate the more 
complicated case of vibrator)* waves diverging in all directions through a 
solid substance. If a bar, of which the transverse section is the same in 
every part, and of which the dfmsity is unifomi, be acted on for an instant 
by a force of siitficient intensity applied parallel to the axis, and uniformly 
on every point of its terminal section (supposoil to Ih? perpendicular toib 
^is), a wave will be propagated alorrg the bar very nearly similar to those 
already described os propagated along tubes filled with perfectly elsiUc or 
common fluid. But a solid bar admits also of a different kind of vibratioa. 
In the case just stated, the dij*ectiou of vibration is longiUidinaty or parallel 
to the axis of the bar*; whereas, In the case 1 now allude to, the direction 
ofvibration is Iratm^se, or perpendicular to the axis, ami analogous to the 
Quinary transverse vibrations of a musical string, though not identical with 
them. As in the small transverse vibrations of the string the tension of the 
string suffers no sensible variation, so tlie transverse vibrations of a solid bar 
do not produce those alternations of conflensatidn and dilataliim which iie- 
cessanly attend longitudinal vibrations. Conseqtiently the elasticities called 
in o ^ctioii in the propagation of longitudinal and of transverse vihrationi 
are of different kinds. In the former case the elasticity depends upon the 
lorcG which any element of the substance is cajiable of exerting to recowr 
Its natural vohmie, when corajircsscd or dilated by the direct action of pres¬ 
sure or tension; wdicrena, in the other case, the elasticity called forthde- 
pends on the force whicJi an element is capable of cxitrtinc to recover its 
unconstrained/om when distorted from tliat form without any alteration of 
nnoo?! ^ former rose the compressing or diluting forces are sup- 
posed to act tiormaUg on the surface of the element; in the latter case the 
W M h? tanyentiaUy on its surface. Thus suppose the 
f^^ctongulaf pamllclepipt'd, and that we take a very smaU 
It ^ parallel to those of the bar, as an elemeot, 
namuS.T* vibrations will distort such an element into a 
tliis dSf nn u rcctaiigulor, nor is it difficult to underetand that 
If such a Hinta ^ 1 , place Without changing the volume of the eleincDt. 
caSd o d . . 1"" at one part of the bar, it will be communi. 
watioti nf whini *%i*^**^f* *n succession by tronsversc vibrations, tlie props- 
Srendy stated avactly similar to those 
bctw1rn”£ -assigns ageneral relation, for aU solid bodies, 
certain exuorimciif^ X Jcinds of elasticity above mentioned, and 
tudinal vibrations woni I produced by transverse and longi- 
ments are opposed to^t ‘ 
elusions to rest on an „r,y, * •"* 1 therefore, not to allow our con¬ 
ns two constants to b theory, but to consider these two coefficients 
I umy heretmfe substances, by experimact. 
transverse vibration-.; ift 1 w the coefficients of* elasticity for 
V« denote the vp]noir ^ ^‘^“K'tudinal ones. Hence, if and 
vilrations respoctivcly?V^J]^^^e*g^^^^^^^ 
n the particles at one extremity of tlie bar be disturbed by a ibme acting 
for the clupidation iittendwh* ThV snim^ m*i}t 1 e ***' X “ sufficient opproximitioa 
mentioned afterwardt. ’® ‘“derstooci of the transverse nbntioia 
I’liistitfit, voi. yiii., and TSarPoYySniqurvoS.^^ Elaatiynea, in the M^nJoirrt de 
