170

Then if g represents the weight of alinear unit of CG or FH, and CG be put= cand FH=£, the absolute tension ofthe curve at the vertex will be representedby eg, and that at F by tg.

Again, put CF=x, EF =y, CF=;z andthe l. CFE = <p.

Then I f—z, F r — cc and fr —y.

And since the thickness at F is to that atC as FH : CG i.e. as t : c, and the weightof homogeneous materials are in the com-pound ratio of their lengths and thick-nesses, the weight of CG is to that of F f(considered as of uniform thickness) as CGx CG : : Ff x FH, i. e. c* : zt.

But the weight of C G=cg .\ c 1 : tz :: eg :

~ = the weight of Ff ; consequently

f t (~) = ~-f l tz = the weight of the wholestring CF.

Whence, the tension at C, the tensionat F, and the weight of CF, being to eachother as rf, Ff and Fr, we have eg, tg, and

--F* tz to each other as y, z, and cc, that is,