162 SPEAKING TRUMPET. 



Theory ,>f the Art. b. Th« magnitude of the fur face TNV = 2cp^: 



(peaking trum- but the f orce f [s , diffufed over this fegment by Art. 3. con- 



fequently thai part of it which is confined to an evancfcent 



fpace a = 



r * 2cpx r 



Art. 6. Since the fpherica! fur face T N V is convex to the 

 plane C N D (Art. 2.) the agitation of the air in the latter 

 will commence at the centre N, and extend thence by the ap- 

 plication of fucceffive circles of the fphere T N V to equal 

 circles of the plane C D, having N for their centre ; which 

 operation will continue until T and V fali upon C and D. — 

 Now as C N D is in contact with unconfined air, each point 

 of it, upon being ftruck, will become a centre, from which a 

 pulfe will radiate freely. (Princip. +2.2.) 



Art. 7. Let P be fuch a phyfical point, and let its area = a ; 

 then if an evanefeent plane zzq be drawn through P perpen- 

 dicular to O P or x, the force imprefled upon it by the trum- 

 pet will be — - (Art. 5) but the fame force is imparted at 



the fame time to the equal phyfical point P in the plane. 

 (Art. 1.) 



Art. 8. Let L be the place of an ear, in O N produced, or 

 more properly of a minute fphere of air. Put N P =y ; PL 

 = zv. Now the pulfe proceeding from P will have due effect 

 upon the point L (Manc/i. Mem. v. V. p. 662. cor. 1) ; which 



effect is as - (Arts. 6 and 7): hence we have (by 



2 cp x 2 iv* J 



f fd* fq fqd* . , r 



Art. 4) as— : J — - : : — - ' ■ : ' , -> for the force 



' r 2 2 r 2 2cpx 2 w* 4>cp$*tt>* 



acting upon the fphere L having d for its radius, Rut the num. 



2 c yy f 

 ber of points which ad together =3 — ~ (Art. 6.) j confe- 



, 2 fd* y y' 



quentlv their united forces zz — '-± — • (Art. \ ,) 



^ J 4px z iv* 



Art. 9. PutLN=g; N O = e ; OC — a; CL~b; and 



fd* 



the correci fluent of the preceding expreflion is 



$Xpg 2 —pe' 



drawn into the hyp. log. of —7-' when g and e are unequal. 



But if C D bifeft O L ; put C.N = k, and the coneft fluent 

 fd* k* 



becomes 



4pg a b x Art. }0. 



