The Principles of Fluxions; Designed for the Use of Students in the University

The Principles of Fluxions; Designed for the Use of Students in the University

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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. 1812 edition. Excerpt: ...2, the attraction becomes unity; therefore the attraction is the same at all distances' PO. Prop. XXXlV. let the attractive force of a corpuscle at Y to each particle vary inversely as the square of the distance; to find the attraction of P to the cone P AC 70. fey the last article, the attraction of P to the circle sr is as 1--=1-----; the attraction therefore rs FA. to every section sr is the same; hence, the attraction Hence, for similar cones, r-being constant, the attraction varies as the length. Prop. XXXV. If a corpuscle be situated at P in the axis SQ of a cylinder, to find its attraction to the cylinder, supposing the attractive force to each particle to vary inversely as the square of the distance. 71. Put RF=a, PR=#, then PF=Va2+pl; and by Art. 69. the attraction of P towards the circle EF OC is as 1-----; hence, the fluxion of the attrac, whose fluent is a: --becomes PQ--PB, and. when x--PS, it becomes PS--PC; and as we want the attraction of P to the solid between these two values of x, their difference SQ + PB--PC is as the attraction required. If the length be infinite, then PC = PS; therefore SQ--PC= SQ--PS =--PQ, and the attraction ber conies as PB--PQ. If the density d of the sphere should vary, then the... da2 attraction will vary as---, If the corpuscle be at the surface of the sphere, then a = 6, and the attraction varies as da. Since the quantity of matter m varies as da3, the at traction varies as--. Now if the sphere were evanescent in magnitude, with the same quantity of matter, the attraction would be the same, it being independent of a. Hence, the attraction of a corpuscle to a sphere is just the same as if all the matter of the sphere were collected into its centre On SECOND, THIRD, &c. FLUXIONS. Prop. XXXVII more

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  • Paperback | 30 pages
  • 189 x 246 x 2mm | 73g
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236565061
  • 9781236565068