The Analytical Theory of Heat |
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Page ix
... satisfies the equation d2v d'v d2v + + = 0 ; dx3 dy3 dz2 v is the temperature at a point whose coordinates are x , y , z • 124 , 125. Equation relative to the state of the surface and to that of the first section 97 66 99 SECTION V ...
... satisfies the equation d2v d'v d2v + + = 0 ; dx3 dy3 dz2 v is the temperature at a point whose coordinates are x , y , z • 124 , 125. Equation relative to the state of the surface and to that of the first section 97 66 99 SECTION V ...
Page xviii
... satisfies a transcendental equation , all of whose roots are real .. 324. All the unknown coefficients are determined by definite integrals 325. General solution of the problem . PAGE 311 · 313 • 314 • 326 , 327. The problem proposed ...
... satisfies a transcendental equation , all of whose roots are real .. 324. All the unknown coefficients are determined by definite integrals 325. General solution of the problem . PAGE 311 · 313 • 314 • 326 , 327. The problem proposed ...
Page xix
... satisfies the condition F ( x ) = F ( -x ) . Expression of the variable temperatures . • • . 348. Application to the case in which all the points of the part heated have received the same initial temperature . The integral 8 PAGE • 333 ...
... satisfies the condition F ( x ) = F ( -x ) . Expression of the variable temperatures . • • . 348. Application to the case in which all the points of the part heated have received the same initial temperature . The integral 8 PAGE • 333 ...
Page 100
... satisfies the general equation d'v d'v d'v dx dy dz2 + dy2 + h K 2nd , it satisfies the equation + = = 0 ; dv = 0 , when y is equal to dy l or , whatever x and z may be , 100 [ CHAP . II . THEORY OF HEAT .
... satisfies the general equation d'v d'v d'v dx dy dz2 + dy2 + h K 2nd , it satisfies the equation + = = 0 ; dv = 0 , when y is equal to dy l or , whatever x and z may be , 100 [ CHAP . II . THEORY OF HEAT .
Page 101
... satisfies the equation h dv ― v + = 0 , when z is equal to 7 or 1 , whatever x and y may K dz be ; 3rd , it satisfies the equation v = A , when x = 0 , whatever y and z may be . SECTION V. Equations of the varied movement of heat in a ...
... satisfies the equation h dv ― v + = 0 , when z is equal to 7 or 1 , whatever x and y may K dz be ; 3rd , it satisfies the equation v = A , when x = 0 , whatever y and z may be . SECTION V. Equations of the varied movement of heat in a ...
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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.