designed to accommodate Spectators and Auditors 

 Fig. 3. 



135 



first anterior point ; join Al, 

 and let it cut the vertical line 

 through 2 in x^ the portion 

 downwards x^l= \\ feet ; then 

 I is the point found. Join Pd ; 

 make x^h — \\\ join A A,', and 

 make a-^ i = 1;^ ; join Ai, and 

 make x-^ h= \\, and so on ; fy 

 g; h, i, k, I, are the places found 

 which the heads of the spectators will occupy, and shew the 

 elevation to be given to the seats successively. 



If the simple process we have described be accurately per- 

 formed, the points which indicate the place of the spectators 

 will lie in the branches of a very beautiful curve which may 

 be termed the equal-seeing or cqual-hearmg curve, the iseido- 

 mal or isacoustic curve. This curve will be of the annexed 



Fijr. 4. 



form ; — A being the place of the speaker, and the heads of the 

 spectators being placed on the line A m n continued as far as 

 the voice of a man can reach, XAX being the axis of the 

 curve and Ay its parameter. 



This curve has two branches on opposite sides of A, shewing 

 that if the building extend behind the speaker, or if the spec- 

 tacle be visible or the sound audible on every side, the same 

 may be continued all round. From the property of this 

 curve it follows, that if two straight lines be drawn to any pairs 

 of points of it that are at equal horizontal distances, these lines 

 will intercept the same parts of the vertical lines through these 

 points. By means of this curve the position of seats in a 



