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. 1823 Excerpt: ...but just R touch it; hence, v=--T. Now by the Table, to Art. 466, it appears that R sr may be represented by 2. 8'. 2, r being represented by 57. 17'. 45. Hence, i=,8209 the sine of 55. 11', within which distance must the node be from conjunction, in order that there may be an eclipse. 431. Draw Iv perpendicular to BN; ...
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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. 1823 Excerpt: ...but just R touch it; hence, v=--T. Now by the Table, to Art. 466, it appears that R sr may be represented by 2. 8'. 2, r being represented by 57. 17'. 45. Hence, i=,8209 the sine of 55. 11', within which distance must the node be from conjunction, in order that there may be an eclipse. 431. Draw Iv perpendicular to BN; then in the right angled triangle /ct', if we know Ic and the angle vie (the complement of cIN), we shall know cv the distance from the middle of the eclipse to the conjunction of the satellite. The supposition that mt is a straight line, produces no error of any consequence. 432. Hitherto we have supposed the section of the shadow of Jupiter to be a circle; but as Jupiter is a spheroid, and not a sphere, and the plane of its equator very nearly coincides with its orbit, we should consider the section of the shadow as an ellipse and not a circle, the major axis of which is nearly coincident with the orbit. M. de la Lande therefore proposes the following correction. Let AFBG be the section, supposed to be a Fig. circle, AxBz the elliptical section of the shadow, and draw nm parallel, and nc mc perpendicular to Ix. Let nc be half the duration; then, upon supposition that the section was circular, the same half duration would be represented by mc; so that the distance Ic before computed: the true distance Vol. i. i i y/li--d; consequently yr, x v--dx=vsr, therefore s=jp x--- JE, r and d being expressed by B t r and d' in time. M. de la Lande puts Zr: ZF:: 13: 14, and therefore s=--x-;--. To find the inclination 14 vr of the orbit of the fourth satellite upon this supposition, M. Wargentin supposed the limit of the distance of the node from conjunction to be 55. 11'. 10; and upon supposition of a circular section, he found ..
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