64 Proceedings of the Royal Society of Victoria. 



in which the coefficients of db, db\ d^, and dji' being equated to 

 zero give us, 



Eliminating A, B, and C from any two sets of three of these 

 equations we get the two relations 



which show that b'>'2b and <Sb 

 and y8'>2;8and<3/3. 



Letb' = $h, f3' = i](S, p=ub, 

 and equations I. can be put in the forms 



U=2};-^^-^ j 



(II. 



?/ + 2' '^~ ti + '. 



Su + i 2// +31" 





by means of which the equation of the losses 

 a/ fil 



becomes 



Cin + 4)(3//^ + &u + 2) ^^ /I jjj 



?/-^(2?^ + 3)(/r + 6?^ + 6) ""QK' ^ '' 

 from which « (the one positive root) can be determined by trial 

 when s/I/QK is known. ^ and r] are found from ti by equations IL, 

 and so the shapes of window and tongue and their relative sizes 

 are determined. 



The i-elation | wn.,C^=^^., 

 can now be reduced to 



