SPEAKING TRUMPET. 161 



aperture A B, it is -bounded in front by a fpherical furface, Theory of the 

 having O, the vertex of the cone D O C, for its centre, and { *™^ DS ti '° m " 

 fublending the plane angle A O B ; in other words, let fuch a 

 furface be defcribed any where in the fruftum ABCD, and, 

 the variable denfity of any one particle of air in contact with 

 it, will be equal to the cotemporary denfity of any other par- 

 ticle in the fame furface. For as foon as the motion is propa- 

 gated into the internal air, the pulfe will expand as far as the 

 fides of the tube will permit: Princip. 4-2.2: after which, the 

 motion will be continued to the oppofite aperture C D, in 

 right angles, 43 ibid, therefore it will be propagated along the 

 lines A D, B C with equal celerities, fuppofe to T and V. — ■ 

 On the plane TV defcribe the furface T N V, in which the 

 denfity of the air is every where equal at any inftant : Now 

 every point of fuch a furface a6ts upon the air externally in 

 eontacl with it, and is re-acted upon by the fame perpendicu- 

 larly to itfelf, in fuch a manner that equal portions of the fur- 

 face (upport equal degrees of preffure. Let U u be an eva- 

 nefcent particle of the curve T N V, draw UR,ai perpen- 

 dicular to N O ; then the fuperficial ring between the planes 

 UK, u k is as U K x Ua; but this ring is as the preffure 

 upon it; which is alfo inverfely as the radius of curvature at 

 U, therefore if U K x U u be conflant, the radius of curva- 

 ture is conftant ; confequently it is equal to O T, and the truth 

 of the propofition is manifeft. 



Art. 3. Let /, be the force of a pulfe in the aperture A B ; 

 and let the internal air of the cone be agitated with an equal 

 and fimilar impuife at the point O ; then the effect thus pro- 

 duced in the trumpet, will be the fame with that of the voice 

 acting at A B, (by Art. 2.) But had the cone been out of the 

 way, the fame force at the difiance O A, would have been 

 uniformly diffufed over the furface of the hemifphere, having 

 O for its centre. 



Art. 4. Put A 0=r ; the variable difiance O T==x ; the ra- 

 dius of an evanefcent circ!e=eZ; the verfed fine of half the 

 angle A O B*=p; 3.1416=c. Then as the force/ is diffufed 

 over the hemifphere whofe radius=±r, in free air by Art. 3* 

 that part of it which refides in an evanefcent point of the fame 



lurface= — —» 

 2 r* 



Vol. X.— March, 1805. M Art, 



