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to be a position of such ordinate indefinitelynear to HF ; then through F draw Frparallel to CD ; and put the absciss CH—x, the ordinate HF=?/, the arc CF=zthe angle CFH=<p, the measure of theconstant tension at the vertex, as explainedby art. 6. and 7.=c, and the measure ofthe tension at F=£, and the specific gravityof the chain per linear unit—g.

Then by art. 6. and 7. will the tensionat C —eg, that at F=£g, and the weight ofthe part CF of the chain = zg : also thethree sides r F, F f and fr of the nascentrectilineal triangle r¥ f will be respectivelyrepresented by x, z, and y. Now, thechain having assumed the form ACB, itis immaterial whether the part CF be con-sidered flexible or rigid. On the lattersupposition it is kept at rest by the threefollowing forces ; viz. the tension at Cacting in the horizontal direction of rf\that at F acting in the direction of thetangent at the point F, or of the indefinitelysmall arc Ff ; and the weight of CF, act-ing in the vertical direction of rF. Andsince we have shown that these forces are