43 



If the constant be zero we have 



k-x= ~ (seci// + tan;//)y (scc>// - tani//)f/^ 14 



from which, with equation 11 if re is known as a function 

 of;// the equation to the convohite can always be found. 

 Again, from equation l-i 



X — L, — — / 



s -/ 



where the clashes are differentials with regard to x, and 

 where s is measured along the curve (V). And if PV^ = A 

 we obtain from this last equation 



X + r} = s 15 



Hence supposing N the free end of the string to be fastened 

 to a ring which can slide along Ox, we obtain a geometrical 

 construction for the convolute in tliis case also. 



MICEOSCOPICAL AND NATURAL HISTOEY SECTION. 



January 19, 1885. 



Dr. Alcock, President of the Section, in the chair. 



Mr. Hyde showed specimens of the wing3 of the following- 

 insects, mounted dry between glass-plates, for the purpose of 

 exhibition in the magic lantern. 



1. Dragon Fly. 



2. Grasshopper. 



3. Ditiscus Marginalis. 



He also showed some interesting drawino-s of insects on 

 ground glass for the magic lantern. 



The Peesident exhibited some specimens of Everlastino- 

 flowers, and made some remarks upon them. 



