A Treatise on the Cycloid and All Forms of Cycloidal Curves, and of the Use of Such Curves in Dealing with the Motions of Planets, Comets, &C. and of Matter Projected from the Sun

A Treatise on the Cycloid and All Forms of Cycloidal Curves, and of the Use of Such Curves in Dealing with the Motions of Planets, Comets, &C. and of Matter Projected from the Sun

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1878 edition. Excerpt: ...by DO. Hence as T'DT rolls on the circle Q'D Q, the point 0 regarded as rigidly attached to T' O T, the tangent to circle Q'DQ of radius F, at D, will trace out a spiral of Archimedes in which the linear velocity of the moving point along the revolving radius is equal to F. angular velocity of the latter. PROP.---The axis of a planet's shadow in space is a spiral of Archimedes. The spiral of Archimedes is interesting as the path along which the centre of a planet's shadow (the earth's for example) may be regarded as constantly travelling outwards with the velocity of light. This is easily seen if we suppose the earth and its shadow momentarily reduced to rest, and, with the sun as pole, imagine a radius vector carried from an initial position coinciding with the earth and retrograding through the various portions of the shadow. Let V be the velocity of the earth in her orbit, D her distance from the sun, and therefore% her angular velocity about the sun. Also let L be the velocity of light. Then if our radius vector, carried back through an angle 0, corre sponding to the earth's motion in time t, is equal to r, we have%t = 0, or t=-?6;andr=Lt=% Wherefore, since the radius vector varies as the vectorial angle, the corresponding point of the shadow's axis (which was at the earth at time t before the epoch we are considering) lies on a spiral of Archimedes. We have in fact L, the velocity of light, for the velocity along the radius vector (v in the preceding demonstra tion), when the angular velocity about the sun is taken... V equal to the earth's angular velocity in her orbit, or 15 (corresponding to w in preceding demonstration). The radius F of the fixed circle by which this...show more

Product details

  • Paperback | 56 pages
  • 189 x 246 x 3mm | 118g
  • Rarebooksclub.com
  • United States
  • English
  • black & white illustrations
  • 1236740688
  • 9781236740687