The Analytical Theory of Heat |
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Page 111
... 141. COROLLARY . If we represent by e the abscissa of this curve or the distance of a point p of the straight line from a fixed point o , and by v the ordinate which SECT . VI . ] 111 GENERAL EQUATIONS OF PROPAGATION .
... 141. COROLLARY . If we represent by e the abscissa of this curve or the distance of a point p of the straight line from a fixed point o , and by v the ordinate which SECT . VI . ] 111 GENERAL EQUATIONS OF PROPAGATION .
Page 144
... abscissa and y for ordinate , is composed of separated straight lines , each of which is parallel to the axis , and equal to the circumference . These parallels are situated alternately above and below the axis , at the distance , and ...
... abscissa and y for ordinate , is composed of separated straight lines , each of which is parallel to the axis , and equal to the circumference . These parallels are situated alternately above and below the axis , at the distance , and ...
Page 186
... abscissa extends from x = 0 to x = π , and if on the same part of the axis the known trigonometric curve , whose ordinate is y = sin x , be constructed , it is easy to represent the value of any integral term . We must suppose that for ...
... abscissa extends from x = 0 to x = π , and if on the same part of the axis the known trigonometric curve , whose ordinate is y = sin x , be constructed , it is easy to represent the value of any integral term . We must suppose that for ...
Page 217
... abscissa denoted by X in this equation be 2πr , let x be the variable abscissa , and let f ( x ) represent the initial state of the ring , the integrals must be taken from x = 0 to x = 2πr ; we have then πrf ( x ) = 1 } [ ƒ ( x ) [ f ...
... abscissa denoted by X in this equation be 2πr , let x be the variable abscissa , and let f ( x ) represent the initial state of the ring , the integrals must be taken from x = 0 to x = 2πr ; we have then πrf ( x ) = 1 } [ ƒ ( x ) [ f ...
Page 220
... abscissa being equal to the time which has elapsed . This law has been known for a long time , but it must be remarked that it does not generally hold unless the bodies are of small dimensions . The previous analysis tells us that if ...
... abscissa being equal to the time which has elapsed . This law has been known for a long time , but it must be remarked that it does not generally hold unless the bodies are of small dimensions . The previous analysis tells us that if ...
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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.