Mathematical Questions and Solutions, from the Educational Times. Volume 34

Mathematical Questions and Solutions, from the Educational Times. Volume 34

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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. 1881 edition. Excerpt: ... or impossible) formed by the three links and the line of centres shall be equal to zero. Professor Sylvester states that Roberts' two cases of inverse conical 3-bar motion are special cases of unicursal 3-bar motion. Solution by Samuel Roberts, M.A. Professor Cayley has shown Mathematical Society's Proceedings, Vol. IV., pp. 109, 110) that the condition specified in the question is sufficient, and notices the cases of reduction of order. To show the necessity of the condition, I consider that in general the curves described by points rigidly connected with the traversing bar, have a one-to-one correspondence, and have therefore the same deficiency. We may therefore regard a point on the traversing bar as describing the locus, and since the extremities of the links which rotate describe exceptional loci, we will suppose the describing point different from these. The locus described is evidently symmetrical about the line of centres. Moreover, since the circular points are triple points, and there are three double points on the line of centres, we must, in order to have a unicursal curve, have on this line a contact of two branches whoBe common tangent is perpendicular to the line of centres. Por we cannot have four double points ou the line of centres identically, nor one double point finitely distant from that line; since, then, there would be another double point on the other side of it. Now, taking A as origin, and the line of centres as the axis of x (see figure), we have x = a cos p + 6 + K) cos e, y = a sin tp + (i + K) sin 6, x = ccos ty + K cosefd, y = c sin ii + K sin fl; 6381. (By Dr. Hopkinson, F.R.S.)--A heavy wire of uniform section is carried on a series of supports in the same horizontal plane, Lr being the bending moment...show more

Product details

  • Paperback | 34 pages
  • 189 x 246 x 2mm | 82g
  • Rarebooksclub.com
  • United States
  • English
  • black & white illustrations
  • 1236790189
  • 9781236790187