On the Biology of Stereum hirsutum, Fr. 285 



most interesting examples (from the point of view of application to 

 mathematical physics) are the equations 



or, with the notation of the memoir, 



a + fc + c = 0, 



a + b + c = — k?v • 



and the theory is applied to these equations in detail. Solutions, 

 which are believed to be new, are obtained for both of them ; each 

 solution involves two explicit arbitrary functional forms, and the 

 argument of each of these arbitrary functions itself involves an 

 arbitrary element ; but in each case the solution is not that of the 

 widest possible generality which the equation is known to possess. 

 To quote one result : a solution of the equation 



a+ 6-f- c = 



can be stated as follows : — 



Let p, q, r denote three arbitrary functions of u subject solely to 

 the condition 



jtr + 2 3 + r 2 = ; 



let u be determined as a function of x, y, z by means of the equation 



au — xp(u) +yc[(u) +2r(?0> 

 where a is a constant, and let v denote 



G(u) 



H(m) + 



a — xp'(u)—yq'(u)—zr'(u) ' 



where G and H are distinct arbitrary functions : then v satisfies the 

 equation 



a + 6 + c = v 2 u = 0. 



u On the Biology of Stereum hirsutum, Fr." By H. MARSHALL 

 Ward, D.Sc., F.R.S., Professor of Botany in the University 

 of Cambridge. Received November 23, — Read December 

 16, 1897. 



(Abstract.) 



The author has cultivated the mycelium of this fungus obtained 

 from spores, on sterilised wood, and after several months the cultures 

 doveloped yellow bosses which proved to be the hymenophores bearing 

 the basidia. This fungus has not hitherto been made to produce 



x 2 



