Royal Institution, 299 



The deflection due to x is therefore Wepq, where the proper 

 values of jo and q must be taken according to the relative posi- 

 tion of a, b, and x. 



If a, b, /, x represent the number of the respective pieces, 

 reckoning from the beginning and calling the first joint 0, the 

 second joint and the piece opposite 1, &c, and if L be the length 

 of each piece, and the extensibility of each piece == e, then the 

 deflection of b due to W at a will be, by summation of series, 



= lWeV.?^Zp {2b(l-a)-(b- a Y + l\. 



This is the deflection due to the yielding of all the horizontal 

 pieces. The greater the number of pieces, the less is the import- 

 ance of the last term. 



Let the inclination of the pieces of the web be a, then the 



force on a piece between and a is W y-. — , or 

 r / sin a 



I— a , 



when x<a } 



and 

 Also 



»'= 7—: — when xxi. 

 I sin a. 



q'= j~i — when x<b. 

 2 / sin a 



q f = r~. — when x > b. 

 I sin a 



If e' be the extensibility of a piece of the web, we have to sum 

 MV^e'p'q 1 to get the deflection due to the yielding of the web, 



W ~ a(L-b)\l + 2(b-a)\. 



la. * * 



sin' 



LI. Proceedings of Learned Societies. 



ROYAL INSTITUTION OF GREAT BRITAIN. 



Feb. 12, "i^VN the Synthesis of Organic Bodies." By J. Alfred 

 1864. V^J Wanklyn, Esq., Professor of Chemistry, London 

 Institution. 



On this tray you will see a collection of well-known substances. 

 Compare these substances with one another, and you will be struck 

 with their dissimilarities. Some are solids and crystalline and brittle, 

 others are liquids which are more fluid than water. Some are without 

 colour ; others are highly coloured, and are used for dyeing. Some 



