...284 I-Í+ ,,. . .- 1 <?» / d*u\du therefore -_J , J» , and d^Hence • • L. ; Л^ЛЧ* ./ , ¿V The chord of curvature passing through the origin...320). Hence the chord of curvature through the origin • f ,d U(U+d •u dffi. 324. If fy be the angle which the tangent at any point of a curve makes with...

...necessary, passes through the pole, is obtained by multiplying 2p by the cosine of the angle included between the radius vector and the normal to the curve at the point ; but if r is the radius vector, and p the perpendicular let fall from the pole on the tangent to the...

...(„ + 35,) The chord of curvature passing through the origin will be obtained by multiplying 2/э by the cosine of the angle between the radius vector...320.) Hence the chord of curvature through the origin dx' dx* dx dx* a/ d"u\ ' II~ ^JuZ I V СЬ" / 324 If ^ be the angle which the tangent at the point...

...= V 1 dp f , d*u\ du therefore — 3 -v~ = [ M + -^» I -^ . , dp and -f- = — Hence p — — d' The chord of curvature passing through the origin....the chord of curvature through the origin 324. If ^r be the angle which the tangent at the point (x, y] of a curve makes with the axis of x, we have...

...du therefore ~=M . 3 , d?u and Hence P=~~ The chord of curvature passing through the origin will bo obtained by multiplying 2p by the cosine of the angle...the chord of curvature through the origin 324. If ty be the angle which the tangent at the point (x, y] of a curve makes with the axis of x, we have...

...efwN du f \ do J The chord of curvature passing through the origin will be obtained by multiplying 2/j by the cosine of the angle between the radius vector...the chord of curvature through the origin 324. If i^ be the angle which the tangent at the point (x, y) of a curve makes with the axis of x, we have...

...,, dr l du By Art. 321 t> = r = ~*By Art. 284 f . * „„ , . d*u\ du therefore Hence и + м'[м + The chord of curvature passing through the origin...origin 324. If i/r be the angle which the tangent at the point (x, y) of a curve makes with the axis of x, we have , dx therefore -=*- = dy dfy dx3 dx dx*...

...a small surface s at a distant point P was expressed by ks, and it appeared that k was independent of the angle between the radius vector and the normal to the wave-front. But this only proves that at the central disc, the cosine of that angle being sensibly...

...wave normal is equal to the refractive index /i. It can be seen from the construction of fig. 8.8 that the angle between the radius vector and the normal to the curve is then the same as the angle a between the wave normal and the ray direction. It is to be noticed...