VOL. XXVI.] PHILOSOPHICAL TRANSACTIONS. 4/8 



opposite parts, in the same manner as from the superficies of solid crystal ; 

 SO far are they from moving with ease and expedition along the surface of water, 

 as sounds are said to do ; nay, it may be doubted, whether the best polished 

 mirrors would contribute so much to the reflection of sound as of light, seeing 

 an echo is more frequently reflected from the roughest recesses of caves, from 

 desert vallies, and ruinous edifices, rather than from the smoothest and best 

 plastered walls. 



Here I shall attempt to explain, or rather guess at the meaning of the Arch- 

 bishop's acoustic or phonical sphere, after first quoting his words : " I shall 

 here add," says the Archbishop, " a semi-plane of an acoustic or phonical 

 sphere, fig. 12, as an attempt to explain the great principle in this science, 

 which is the progression of sounds ; you are to conceive this rude semi-plane 

 as parallel to the horizon ; for if it be perpendicular to it, I suppose the upper 

 extremity will be no longer circular, but hyperbolical, and the lower part of it 

 suited to a great circle of the earth, so that the whole phonical sphere, if I may 

 so call it, will be a solid hyperbola, standing on a concave spherical base." 



Instead of this scheme I would substitute another, fig. 13, let cgfe be the 

 globe of the earth, and let a sound be produced at a point of its superficies, as 

 c ; this will be propagated every way through the earth itself, as well as through 

 the air, so when it reaches either really (^though perhaps insensibly) or at least 

 Cwere it stronger) would reach on its diffusion through the air a great circle of 

 the earth, described from the pole c, viz. the periphery gbe, it would fill up a 

 certain space, according to the diff'erent facility of its passage, not quite sphe- 

 rical, but unequally extended, and circumscribed by the perimeter of the hyper- 

 bola GLAKE, described about the axis cao perpendicular to the sonorous body 

 c ; nay defined by the superficies of the hyperbolic conoid, generated by the 

 rotation of the hyperbola alg round its axis. Therefore the whole phonical 

 sphere, through which sound is propagated in a given time, will be the solid 

 space comprehended by the hyperbolic conoid gaeb, insisting on gbe a great 

 circle of the earth, and terminated below by the concave hemispherical super- 

 ficies GCEB ; which space cut any where by a plane parallel to the horizon, will 

 give the semicircle lik, such as the Archbishop's figure represents, and which 

 he calls a semi-plane, because it exhibits only one half, the other half not ap- 

 pearing, as lying beyond the vertical hyperbola, which divides in two the pho- 

 nical sphere through its axis. 



But the Archbishop neither intimating the species of the hyperbola, nor the 

 principles on which this doctrine is founded, I propose to find, by the inverse 

 method of investigation, the following particulars. 1. Through what lines so- 

 norous tremours must be diffused, so as to be expanded in a given time into 



VOL. V. 3 P 



