also that for p = 0 we must dPhave -T— = 1; for as p tends to vanish, the length of an element perpendicular to the radius tends to become pdw. Hence the first integral is Jo) (1 - -^ ) . This may be written in a more convenient form as follows:Let 6 be the angle which any radius vector makes with… … CURVES TRACED ON SURFACES. 357 dP6 in passing to a consecutive point; hence dO — — j- dco. The integral just found is therefore dco + dO, which integrated asecond time is (o-{- 6 — 0\ where co is the angle between thetwo extreme radii vectores which we consider, and 6\ 6^ arethe corresponding…
Geometry, Analytic · Surfaces
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