47-* PHILOSOPHICAL TRANSACTIONS. (^ANNO 1 /OQ- 



such a hyperbola. 2. The variation of density to be supposed at different 

 heights of the air, to give sound a direction (supposing the common law of re- 

 fraction of light) in those lines ; and 3. The law of refraction, which sonorous 

 tremours forming such curves, do observe, supposing the variation of the den- 

 sity of the air, as most philosophers and mathematicians allow, and as is con- 

 sonant to experiments, to be in the ratio of the weight of the incumbent at- 

 mosphere. 



For which, let us consider that the sonorous body c, fig. 14, communicates 

 its tremours every way, in the directions en, cm, ch ; or at least in the direc- 

 tion of the lines wherein the impulse was given to the body on its restitution, 

 repelling the air, and protruding it by frequent oscillations, by which it undu- 

 lates, and is solicited to a tremulous motion in the same direction. Let there- 

 fore these tremours be supposed, in a very small time, to reach the points n, m, 

 h, and from thence after any given time to be propagated together, the first 

 tremour to the point n, the second to m, and the third to h ; and again, after 

 any other given time, to be propagated together, the first to g, the second to l, 

 and the third to a. Now I denominate the lines en, ng, cm, ml, ch, ha, in 

 which each tremour is successively diffused by the sonorous rays ; and the lines 

 nmh, nmh, gla, which the above sonorous rays, and all the other intermediate 

 synchronal rays, reach in any given time at once, the sonorous waves. And 

 indeed it is plain, that in a medium entirely uniform, when the cause ceases, 

 that diverts the sonorous tremours from their direction into this or the other 

 course, the sonorous rays always proceed in right lines, or move directly the 

 shortest way from one point to another, and form waves entirely circular, and 

 concentrical to the sonorous body ; because, when they find no greater difficulty 

 iQ their passage in one place than in another, they will reach equal distances in 

 any given time ; and each ray will intersect its wave perpendicularly, and each 

 wave be concentrical and similar, as appears from the elements. 

 tfi'But in a medium of a difform density, as our air, in which it varies accord- 

 ing to its different altitude (for here we do not now consider the vicissitudes of 

 heat, cold, moisture, and dryness, which cannot be reduced to any certain law) 

 the ray cha alone passing perpendicularly through all the lamella, or superficies 

 of air, concentrical to the earth, will be unrefracted and proceed in a right 

 line ; while the other rays impinging obliquely on the same superficies, will be 

 continually refracted at each point, and inflected into the curves cmML, cnNG ; 

 and according to the various facility of their passage, be propagated in any 

 given time to different distances ; wherefore the points a, l, g, or h, m, n, which 

 the sound emitted in the direction of any ray shall reach in the same time, will 

 be unequally distant from the sonorous body c ; and therefore the waves alg. 



