123 



the radicular appendages are tinged blue by solution of iodine, and 

 that he has observed the same effect produced upon the matter con- 

 tained in the summits of the asci, and upon the mucous envelope of 

 the sporidia of several species of Sphceria. It would seem, there- 

 fore, that the absence of starch can no longer be considered as cha- 

 racteristic of the Fungi, and that the existence of that substance in 

 an amorphous state may be considered as satisfactorily proved. 



DESCRIPTION OF THE FIGURES. 

 Fig. 1. Vertical section of the coat of the Fungus, showing the successive layers 



of cells, the innermost of which give off threads into the interior of the 



plant, X 315 diameters. 

 Figs. 2 and 3. Asci with sporidia, X 415. In fig. 3 the sporidia are only partially 



matured. 



Fig. 4. The extremity of a thread showing the mode of origin of the asci, X 315. 

 Fig. 5. Free sporidia, X 415. 



IV. "On the Singular Solutions of Differential Equations." 

 By the Rev. ROBERT CARMICHAEL, Fellow of Trinity Col- 

 lege, Dublin. Communicated by ARTHUR CAYLEY, Esq. 

 Received December 28, 1857. 



(Abstract.) 



The objects contemplated in this paper are the following : 

 1. The reduction to a symmetrical form of the well-known theo- 

 rem by Clairaut for the integration of differential equations in a 



