322 THE FIGURES OF EQUILIBRIUM OF A LIQUID MASS 
* 
And afterwards, in speaking of a vein received at a very small distance from 
the orifice on a thick solid body: 
‘Tn this case, as well as when the vein is entire, we observe that the grave and high 
octaves, the fifth and the sharp minor thirdsof the sound in question—that is, of unison— 
also influence, though in a less degree, the state of the vein.” 
And again, in reference to the modifications experienced, under the influence 
of the consonance due to the impact against a stretched membrane, by a vein 
withdrawn from every other extraneous influence : 
‘Analogous results are obtained when, with a stringed instrument, different sounds are 
produced in the vicinity of the reservoir, but one of the sounds always exerts upon the vein 
a greater influence than all the others.” 
Do these passages signify that besides unison it is only the grave octave and 
fifth, the minor third, the superfluous fourth, and the shrill octave which modify 
the state of the vein? That is little probable, for then, instead of saying, 
“there are sounds which do not act in any manner,” &c., Savart would have 
said, all the other sounds which precede them are without influence, &c. Must we 
interpret these passages as admitting that the sounds therein specified are the 
most active after unison, and that, among the remaining tones of the gamut, 
some are simply less efficacious, while others absolutely exert no influence ! 
But in that case, can we believe that Savart would have thus expressed himself? 
We remark, moreover, that the superfluous fourth mentioned in the first pas- 
sage is omitted in the second. 
These vague ‘statements show that Savart had but little studied the influence 
of other sounds than unison, at least under the circumstances which we are 
considering, and it appears to us that there could no more be deduced therefrom 
the existence of any disagreement between our theoretical conclusions and the 
facts, than that of an absolute accordance. Fortunately Savart contrived after- 
wards to augment the energy of action of the vibrations produced by the instru- 
ment, and then the effects, such as he describes them, must be regarded as 
wholly conformable with our conclusions, as will presently be seen. 
§ 15. To finish what regards the influence of a sound excited at a distance : 
and different from unison, we have still to account for the facts of No. 10 of § 3. 
We shall proceed to show that these facts, excepting the last, depend on a more 
general principle, which may be stated in the following manner: if the vibra- 
tions of the instrument are sufliciently energetic in relation to those occasioned 
by the impact of the isolated masses, and if at the same time the interval of the 
two sounds is not too great, the sound of the vein may be brought to unison 
with that of the instrunfent. We observe that these circumstances are those 
of the number cited: in effect, when the vein falls on a body which can only 
render a determinate sound, such as a diapason, if we suppose for an instant 
that it undergoes no modification in the number of the isolated masses¢ the 
vibrations due to the impact of these masses will be generally of another period 
than those of the body struck, and consequently they can only proceed from 
the circumstance that each time a mass reaches that body the air is driven from 
between them, then returns, to be expelled anew on the arrival of the following 
mass, and so on in succession; but the sonorous waves produced in this manner 
" are necessarily very weak relatively to those produced by the vibrations of ihe 
body struck ; besides, we have it in our power, by varying either the discharge 
or the diameter of the orifice, to diminish as much as we please the interval of 
the two sounds. 
The vibrations of the instrument, (or, in the case before us, of the body im- 
pinged upon,) transmitted by the air to the vessel and the liquid, not having 
the same duration with the transits of the incipient constrictions and dilata- 
tions due to the configurative forces, there is, as has been shown, (§ 12,) a varia- 
ble conflict between these two kinds of action; but, if the two sounds do not 
