CHAP. 3TV.] THE BRACED ARCH. 259 



From the table, a and h and P being known, H and y can be 

 found for the successive positions of P at 0.1, 0.2, etc., of a, or 



the half span, by multiplying P ^ by the tabular number for 



ill 



H, and h by the tabular number for y. 



%d. CIRCULAR AKO. For a circular arc we have for the equa- 

 tion of the locus cdeik [Fig. 91], 



1 + B/c 



where K = - ,, I being the moment of inertia of the constant 

 A/- 2 ' 



cross-section, A its area, and r the radius of the circle : also 

 where 



(sin* a sin* )3) (a 3 sin a cos a + 2 a cos* a) 

 sin a [sin 2 a sin 2 /3 + 2 cos a (c'os /3 cos a) 2 cos a (a sin a j3 sin /3)]' 



a being the angle subtended at centre by the half span, and 



__ 2 cos a (a sin a ft sin ft) 



~ sin 2 a sin 2 ft + 2 cos a (cos ft cos a a sin a + ft sin $)' 



_ 2 a cos 2 a 



2 (a 3 sin a cos a + 2 a cos 2 a)' 



or, approximately, 



A= 2 * 6 * 



1 K. IK. ^4 



j* ^P _ p _ 



~ 4 a 4 ~~ 64 A 45 

 where /S is the angle from crown to weight. 



= the square of the radius of gyration, or, approximately 



A. 



the square of the half depth, hence K = - - approximately. 



