The Analytical Theory of Heat |
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Page i
... PATERNOSTER ROW . CAMBRIDGE : DEIGHTON , BELL , AND CO . LEIPZIG : F. A. BROCKHAUS . 1878 [ All Rights reserved . ] Cambridge : PRINTED BY C. J. CLAY , M.A. , Of the linear and varied Movement of Heat in a ring SECTION.
... PATERNOSTER ROW . CAMBRIDGE : DEIGHTON , BELL , AND CO . LEIPZIG : F. A. BROCKHAUS . 1878 [ All Rights reserved . ] Cambridge : PRINTED BY C. J. CLAY , M.A. , Of the linear and varied Movement of Heat in a ring SECTION.
Page v
... ring , cube , sphere , infinite prism ; the variable temperature at any point whatever is a function of the coordinates and of the time . The quantity of heat , which during unit of time crosses a given surface in the interior of the ...
... ring , cube , sphere , infinite prism ; the variable temperature at any point whatever is a function of the coordinates and of the time . The quantity of heat , which during unit of time crosses a given surface in the interior of the ...
Page viii
... RING . 101-105 . The variable movement of heat in a ring is expressed by the equation dt dv K d2v hl CD dx2 CDS V. The arc a measures the distance of a section from the origin 0 ; v is the temperature which that section acquires after ...
... RING . 101-105 . The variable movement of heat in a ring is expressed by the equation dt dv K d2v hl CD dx2 CDS V. The arc a measures the distance of a section from the origin 0 ; v is the temperature which that section acquires after ...
Page xv
... ring . SECTION I. GENERAL SOLUTION OF THE 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 ...
... ring . SECTION I. GENERAL SOLUTION OF THE 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 ...
Page xvi
... ring , set forth in Article 241 , and the theorem of Article 234. We thus ascertain the origin of the analysis which we have employed to solve the equation relating to con- tinuous bodies . . 279. Analytical expression of the two ...
... ring , set forth in Article 241 , and the theorem of Article 234. We thus ascertain the origin of the analysis which we have employed to solve the equation relating to con- tinuous bodies . . 279. Analytical expression of the two ...
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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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