cr
the remotest particle moved, while the chord is moving from If toD; durmg which time the chord, having an accelerated motionwill cause the particles to-Approach each other with an acceleratedmotion likewise; and because those accelerated approaches beginat A, and reach to E, in the time the chord is going from B toD, therefore • the distance A B will be less than B C, and thisless than C D, and that less than -D E, and the distance E E willbegm to diminish when the string is arrived at the site ADC, andthe particles A, B, C, D, E, E, &c. will have the arrangementrepresented m the second line. But now the chord, having ac-quired the situation A D C, will be no farther accelerated, but onne contrary retarded, as it will now go on from D to E; hence theparades of air before it will all go on forward till the chord comes,? aR ^ '-he particle A to its situation in the third line; but sincethe force upon A begins to abate, as the string begins to move fromiJ, the elastic force now between A and B will, by acting bothways, continue to accelerate the motion of B, and retard that ofA. | bus the distance B C will still diminish, till B comes to lieequi-distant between A and C; and C will be accelerated till it beequi-distant between B and D, and so on. So that, as the acce-leration is continued forwards, the distances will diminish tow-ards-c R,1( l> by the time the chord is arrived at E, the particles E Ewill be at their nearest distance. And, since the motion of A iscontinually retarded, it will lose what before it had gained in thesame time, and will therefore now lie at the same distance from B,as at first nearly. So that the particle from A to G will have thesituations as represented in the third line. The chord now return-ing from E to D, gives liberty to the repulsive power between Aand B to separate them to a greater distance than thev have at pre-sent. By tliis means all the other intervals, B C, C D, D E, t E,will increase, and become successively greater than the naturaldistance; hut that excess will be less in each, till you come to F G,which will he equal to the natural distance at present between Aand B. The motion at the same time continuing in all the particlesfrom H to N, they will all move forwards, and the present con-tracted interval between Ii and I will succeed between all the rest,till it arrives at the particle N, when the interval M N will be thesame as at present is II I. And those particles beyond N to Swill, by the preceding ones, be put intp the same respective dis-tances, as those have between G and N, but in an inverse order.
_ uic suuauqn >1 u w, nm going on 10 .v a w
a retarded motion, the velocity of the contiguous particle A wilalso be retarded, and becomes less than that of B; upon whichthe distance between them will he lessened, and the more so, athe string approaches to B. Hence all the intervals, now dilateibeyond their natural state, will, by degrees contract; but gradually slower till you come to E, where the present largest intervabetween A and B will be found between E and G, and that tie.tween A and B will have acquired its natural extent, when tinchord is arrived at B. Then, likewise, the particles from G to b.will acquire the same situation as those now have between A and G.and from N to S, the same as is now seen between G and N ; amfrom S forwards the same as is now before the particle N, thpoint S being at this moment the middle point ot condensationall which is clearly seen in the fifth line ot the figure. '1 bus thcondensation which begins at A, by the first part of the vibratiorwas propagated to G bv the second, from thence to N by ththird, and, lastly, to S by the fourth part of the whole motion ithe string in going and returning; and this extent of air, thus ag
■ fated by the chord in going and returning, is called by Sir IsaaiNewton a win e, or pulse of air. In which wave the particles froiA to N are in a dilated state, and from N to X in a contracted ccondensed state; which two parts of the wave, answer to the coicave and convex, or low and high part of a watvy wave. Asti;chord goes on to make another vibration, it will not only continuto agitate the air, at present in motion, but will spvead’the puls;lion of the air as much fart her, and by the same degrees as beforeand the like will happen after every complete vibration of tl
■ string., r ljius the air being a fluid body, and the impression maton any one part affecting all the particles alike around it, it is plaithose pulses will be propagated' in every direction all around iconcentric aerial shells, or spherical waves of air. That the moticof the pulses in an elastic medium is analogous to that of wavigenerated in the surface of stagnant water, is evident, when v
consider that the condensation of the parts of the elastic medium isin lieu of the elevation of the water; the elastic force effects thesame in the medium, as gravity does in the water, and the densestpart of the pulses corresponds to the highest part of the waves.Thus, let A B C (Fig. 3.) represent the sonorous body ; by thetremulous motion of its parts, it will agitate the am contiguous toevery point, as A, where it will be condensed to a certain smalldistance, and make a pulse or wave of air, in the manner as hasbeen already shewn. The first wave or pulse will, by its-elasticpower in expanding itself, produce a second, that a third, and soon; till the impressed motion be diffused through too large aquantity of air, to he any longer sensible. The quantity of mo-tion, produced by each tremor of the sonorous body, being com-municated successively to large portions ot air, the part thereof,which each particle will acquire, will constantly decrease. Thisdecrement of the motion will lie as the increment of the numberof particles, which is as the superficies of the spherical shell; andsince all superficies are as the squares of their diameters, or semi-diameters, therefore the force in the particles of the wave or shellat D is to that in the particles of the shell at E, as A I‘ 2 to A D-,that is, the force of sound decreases as the squares ot the distancesincrease. It is plain the distance to which sounds may be heard,will he proportional to the magnitude, or intensity, of the strokemade on the tremulous body emitting the sound; tor, the greaterthat stroke is, the greater will be the agitation of the parts of thesonorous body, and, of course, the greater will be the force withwhich they will strike the particles of air. Easily, the greater theforce is upon the air, the more closely will it be condensed andexpanded; hence the greater will be the stroke at any given di -tance on the drum of the ear, and, consequently, the greater willhe the distance at which the agitation of the air will he sensible.The experiments are numerous by which it lias been found, thatsound is audible to the distance of fifty, sixty, or eighty miles:hut Dr. Ilearn, physician to the king of Sweden , tells us, that atthe bombardment at liolmia, A. D. H55S, the sound was heard totlie distance of thirty Swedish miles, which make 180 of ours.And in the fight between England and Holland, A. D. 1672, thenoise of the guns was heard even in Wales , which cannot be lessthan 200 miles. With regard to the velocity of Sound, Newtonhas determined it by a very intricate calculation, to be in propor-tion to the thickness of the parts of the air and the distance of theseparts from each other; proving that each part moves like a pendu-lum ; from whence he infers, that if the density of the atmos-phere were the same every where as on the surface of the earth, apendulum reaching from its highest surface down to that of theearth, would ascertain, by its vibrations, the proportion of the ve-locity. And he shows, that the velocity of each pulse would asmuch exceed that of such a pendulum, swinging with one com-plete vibration, as the circumference of a circle exceeds the dia-meter. From all this lie calculates that the motion of sound shouldbe 1088 feet in a second. But since the atmo-pliere consists not ofpure air, but lias an admixture of vapours of a different elasticityand tone; these vapours will not participate of the motion of pureair, by which sound is propagated; in like manner as an elasticstring, if struck, will not move another very near it, unless it beunder tiie same degree of tension, and of the same tone. There-fore the quantity of air producing sound must be diminished inproportion to (lie quantity of vapour, in a given space; in whichSir Isaac supposes the air is to the vapour as 10 to 1. Whence theair and vapour together in a given space is to the pure air as 11 to10. But the velocity of the pulses will increase m the suhdupli-cate ratio of the diminished quantity of matter, that is, in thesubduplicate ratio of 11 to 10, or in the entire ratio of 21 to 20,(as lie has shewn, Princip. Prop. 48. lib. II.) Therefore, if. wesay, as 20 : 21 : : 1088 : 1142; we find that the real velocity ofsound is at the rate of 1142 feet per second. The truth and ac-curacy of this theory have been sufficiently confirmed by experi-ments, particularly those made by the Key. Dr. Derham. Thedifferent estimates’made of the velocity of sound by several emi-nent philosophers are, as in the table following;
Feet per second.
The honourable Mr. Roberts.1300
The honourable Mr. Boyle.1200
Mr. Walker. 1338
Mersennus.1474
The academy at Florence.1 G*
Feet