410 Proceedings of the Royal Society of Victoria. 



It is to be noted that as the base of the rt\\ component is irjr 

 the altitudes of its isosceles elements are each 



=^ M = - nir 

 2r 4/- 



its expression in isosceles functions is 



4r l Ir Ir J 



and its harmonic expression is 



4wr r . . ^ , sin3rur'5in3rw/' , ^ ^ 



--{ sinr/x,. sinroj/-(- '^ -f etc. > 



rTT y 3" ) 



Hence the rt\\ component 



^ 2(tanA + tanB) r . . , , sinSrusin 3rw/ 



U r ^ -^^ ^1 \ sinr^sin;oj^ + - *" ^ 



irr^ I 3- 



sinSr/AsinSro)/' 



+ --^5, +etc. j. 



If h be the altitude of either of the giveii triangles, then 



A=:yu,tanA=:(7r — /y.)tanB 

 and the development for the complete wave is , 

 ,. , 'Ih f ■ ■ ^ , sin2asin2a)/ 



, sin3u.sin3oj/ , , 



+ '^ + etc. 



^ 32 -r 



