The Analytical Theory of Heat |
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Page xii
... plane 200-204 . It is proved that the problem proposed admits of no other solu- tion different from that which we have just stated . • • 159 • 161 ART . SECTION V. FINITE EXPRESSION OF THE RESULT OF xii TABLE OF CONTENTS .
... plane 200-204 . It is proved that the problem proposed admits of no other solu- tion different from that which we have just stated . • • 159 • 161 ART . SECTION V. FINITE EXPRESSION OF THE RESULT OF xii TABLE OF CONTENTS .
Page xiv
... problems which are based upon the analysis of Daniel Bernoulli in the problem of vibrating cords . The value of the series , T is 1 2 1 3 sin x versin a + sin 2x versin 2a + sin 3x versin 3a + & c . , if we attribute to x a quantity ...
... problems which are based upon the analysis of Daniel Bernoulli in the problem of vibrating cords . The value of the series , T is 1 2 1 3 sin x versin a + sin 2x versin 2a + sin 3x versin 3a + & c . , if we attribute to x a quantity ...
Page xv
... PROBLEM . 238-241 . The variable movement which we are considering is composed of simple movements . In each of these movements , the temperatures pre- serve their primitive ratios , and decrease with the time , as the ordinates v of a ...
... PROBLEM . 238-241 . The variable movement which we are considering is composed of simple movements . In each of these movements , the temperatures pre- serve their primitive ratios , and decrease with the time , as the ordinates v of a ...
Page xviii
... 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 . 315 317 330. Application to the case in which the thickness of the prism is very ...
... 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 . 315 317 330. Application to the case in which the thickness of the prism is very ...
Page xix
... problem may also be solved by means of another form of the integral . Formation of this integral • • 365 , 366. Application of the solution to an infinite prism , whose initial temperatures are nul . Remarkable consequences 367-369 ...
... problem may also be solved by means of another form of the integral . Formation of this integral • • 365 , 366. Application of the solution to an infinite prism , whose initial temperatures are nul . Remarkable consequences 367-369 ...
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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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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.