The Analytical Theory of Heat |
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Page xiii
... unknowns a , b , c , d , & c . is m only , omitting all the subsequent terms . The unknowns are determined for a certain value of the number m , and the limits to which the values of the coeffi- cients continually approach are sought ...
... unknowns a , b , c , d , & c . is m only , omitting all the subsequent terms . The unknowns are determined for a certain value of the number m , and the limits to which the values of the coeffi- cients continually approach are sought ...
Page xv
... coefficients 267-271 . Elimination of the coefficients in the equations which contain these unknown quantities and the given initial temperatures · 238 247 ART . 272 , 273. Formation of the general solution TABLE OF CONTENTS . XV.
... coefficients 267-271 . Elimination of the coefficients in the equations which contain these unknown quantities and the given initial temperatures · 238 247 ART . 272 , 273. Formation of the general solution TABLE OF CONTENTS . XV.
Page xviii
... unknown coefficients are determined by definite integrals 325. General solution of the problem . PAGE 311 · 313 • 314 • 326 , 327. The problem proposed admits no other solution 328 , 329. Temperatures at points on the axis of the prism ...
... unknown coefficients are determined by definite integrals 325. General solution of the problem . PAGE 311 · 313 • 314 • 326 , 327. The problem proposed admits no other solution 328 , 329. Temperatures at points on the axis of the prism ...
Page xxii
... unknown a , and that the chief variable x is only under the symbol cosine 420. Use of these theorems in the analysis of imaginary quantities 421. Application to the equation + d'v d2v dx dy = 0 422. General expression of the fluxion of ...
... unknown a , and that the chief variable x is only under the symbol cosine 420. Use of these theorems in the analysis of imaginary quantities 421. Application to the equation + d'v d2v dx dy = 0 422. General expression of the fluxion of ...
Page xxiii
... 2 " + & c . L2 Page 300 , line 3 , for A2 , A4 , A6 , read πA ,, π¡ , πÁg . Page 407 , line 12 , for do read dp . Page 432 , line 13 , read ( x - a ) . PRELIMINARY DISCOURSE . PRIMARY causes are unknown to us ; TABLE OF CONTENTS . xxiii.
... 2 " + & c . L2 Page 300 , line 3 , for A2 , A4 , A6 , read πA ,, π¡ , πÁg . Page 407 , line 12 , for do read dp . Page 432 , line 13 , read ( x - a ) . PRELIMINARY DISCOURSE . PRIMARY causes are unknown to us ; TABLE OF CONTENTS . xxiii.
Contents
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Common terms and phrases
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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