This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1857 Excerpt: ... positions, are subject to the conditions, y constant, and, a2 + /3 = c. (2) Varying the position of the centre of light on the ring, we have, ada + fidfi = 0; (3) and, from the surface equation (1), (rf-Y- + (rv-PSW = o. (4) By combining (3) and (4) we find, "?-#r = 0; and, employing this in combination with (2), P P ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1857 Excerpt: ... positions, are subject to the conditions, y constant, and, a2 + /3 = c. (2) Varying the position of the centre of light on the ring, we have, ada + fidfi = 0; (3) and, from the surface equation (1), (rf-Y- + (rv-PSW = o. (4) By combining (3) and (4) we find, "?-#r = 0; and, employing this in combination with (2), P P When a and j3 are eliminated from the equation (1), it will be reduced to, (yy _ jpp = r-( + y)%yp + ctf, according as the positive or negative sign is employed; and, rejecting the equation yp TjT c = 0, as incompatible with the envelope, we shall obtain, yp + c = + r( + y): (5) or, yp-e = +_ r(f + y): both of which represent the same system of two right cones. Now, if in (1) we write = 0, and i) = 0, rejecting the factor 2, there is the result, and this condition shews that every ray-surface cuts the axis of in two points at distances from the centre of the reflector which are, respectively, ---1--, and-.--3_; these points are, conser-f-c r-c quently, the vertices of the two conical envelopes. To illustrate this geometrically, let c be r, figure 20; and let S be any position of the centre of light upon the luminous ring; AA' that diameter of the reflecting ring which passes through the projection D. Then if SD is produced to S', so that S'D = SD, each of the rays reflected at A and A' will pass through S', and will cut the vertical axis in the two points C and C. Hence, the ray-surface due to each position of the centre of light on the luminous ring meets the axis in these same points C and C, which, consequently, determine in position the vertices of the enveloping cones. A'O A'D' A similar construction being made when c is r, we shall find, OC =--H-; OC = + SL.; the point C bei...
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Add this copy of Investigations in the Theory of Reflected Ray-Surfaces to cart. $56.29, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2016 by Palala Press.
