The Analytical Theory of Heat |
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Page xix
... integral 8 PAGE • 333 dq 0 9 sin q cos qx is 1 , · 338 339 · if we give to x a value included between 1 and -1 . The definite integral has a nul value , if x is not included between 1 and -1 . · • 349. Application to the case in which ...
... integral 8 PAGE • 333 dq 0 9 sin q cos qx is 1 , · 338 339 · if we give to x a value included between 1 and -1 . The definite integral has a nul value , if x is not included between 1 and -1 . · • 349. Application to the case in which ...
Page xx
... integral of the equation dv d2v d2v d2v = + + dt dx dys dz2 solves the proposed problem . It cannot have a more extended integral ; it is derived also from the particular value or from this : v = e - n1t cos NX , v = dv dv which both ...
... integral of the equation dv d2v d2v d2v = + + dt dx dys dz2 solves the proposed problem . It cannot have a more extended integral ; it is derived also from the particular value or from this : v = e - n1t cos NX , v = dv dv which both ...
Page xxi
... INTEGRALS . PAGE 385 • 387 392 396. First integral ( a ) of the equation = dv dt dx2 d2v ( a ) . This integral expresses 396 398 • the movement of heat in a ring 397. Second integral ( 3 ) of the same equation ( a ) . It expresses the ...
... INTEGRALS . PAGE 385 • 387 392 396. First integral ( a ) of the equation = dv dt dx2 d2v ( a ) . This integral expresses 396 398 • the movement of heat in a ring 397. Second integral ( 3 ) of the same equation ( a ) . It expresses the ...
Page xxii
Jean-Baptiste-Joseph Fourier Alexander Freeman. ART . PAGE 411. Integral of equation ( e ) of vibrating elastic surfaces 412 . Second form of the integral . 413. Use of the same theorem to obtain the integrals , by summing the series ...
Jean-Baptiste-Joseph Fourier Alexander Freeman. ART . PAGE 411. Integral of equation ( e ) of vibrating elastic surfaces 412 . Second form of the integral . 413. Use of the same theorem to obtain the integrals , by summing the series ...
Page 57
... integral from x = 0 to xx , we shall have the quantity of heat lost through the part of the surface included between the source of heat and the section made at the distance x . Denoting the first integral by C , whose value is constant ...
... integral from x = 0 to xx , we shall have the quantity of heat lost through the part of the surface included between the source of heat and the section made at the distance x . Denoting the first integral by C , whose value is constant ...
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a₁ abscissa action actual temperature analysis arbitrary axis b₁ body chaleur co-ordinates coefficients conducibility consider constant temperature convergent series cooling corresponding cosines curve d'v d'v definite integrals denoting determine different points differential equations dimensions distance dv dv dv dx dv dz dx dy dx² dy dz dy² enclosure equa equation dv expressed fixed temperature give given heat equal heat which escapes heat which flows Hence hypothesis infinitely small initial temperatures instant dt integral interior maintained mass mathematical analysis molecule movement of heat multiple arcs multiply ordinates parallel partial differential equations perature permanent temperature perpendicular plane prism problem propagation of heat quantity of heat radius ratio rays represented result satisfies second member sin x sines solution source of heat substitute suppose theorems theory of heat thermometer tion unknowns variable vary versin
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Page 469 - The Pointed Prayer Book, being the Book of Common Prayer with the Psalter or Psalms of David, pointed as they are to be sung or said in Churches.
Page 469 - Greek and English Testament, in parallel columns on the same page. Edited by J. SCHOLEFIELD, MA late Regius Professor of Greek in the University. New Edition, with the marginal references as arranged and revised by DR SCRIvENER, js.