The Analytical Theory of Heat |
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Page xiv
... definite integral . We have in general and 2πA = √ ** dx F ( x ) , -π + παρ = Sax dxF ( x ) cos ix , + π тb1 = √ _ = " dx F ( x ) sin ix . · We thus form the general theorem , which is one of the chief elements of our analysis : PAGE ...
... definite integral . We have in general and 2πA = √ ** dx F ( x ) , -π + παρ = Sax dxF ( x ) cos ix , + π тb1 = √ _ = " dx F ( x ) sin ix . · We thus form the general theorem , which is one of the chief elements of our analysis : PAGE ...
Page xvi
... definite limit . e - Kn't , which expresses sin nx x This remark leads to the equation v = A the simple movement of heat in the sphere . infinity of values given by the definite equation The number n has an nx tan nX = 1 - hX . The ...
... definite limit . e - Kn't , which expresses sin nx x This remark leads to the equation v = A the simple movement of heat in the sphere . infinity of values given by the definite equation The number n has an nx tan nX = 1 - hX . The ...
Page xvii
... definite equation which gives all the values of n • • CHAPTER VI . Of the Movement of Heat in a solid cylinder . 306 , 307. We remark in the first place that the ratio of the variable tem- peratures of two points of the solid approaches ...
... definite equation which gives all the values of n • • CHAPTER VI . Of the Movement of Heat in a solid cylinder . 306 , 307. We remark in the first place that the ratio of the variable tem- peratures of two points of the solid approaches ...
Page xviii
... definite integrals 325. General solution of the problem . • 313 • • · 314 326 , 327. The problem proposed admits no other solution 328 , 329. Temperatures at points on the axis of the prism 330. Application to the case in which the ...
... definite integrals 325. General solution of the problem . • 313 • • · 314 326 , 327. The problem proposed admits no other solution 328 , 329. Temperatures at points on the axis of the prism 330. Application to the case in which the ...
Page xix
... definite integral has a nul value , if x is not included between 1 and -1 . · 349. Application to the case in which the heating given results from the final state which the action of a source of heat determines 350. Discontinuous values ...
... definite integral has a nul value , if x is not included between 1 and -1 . · 349. Application to the case in which the heating given results from the final state which the action of a source of heat determines 350. Discontinuous values ...
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2kt versin a₁ abscissa action actual temperature analysis arbitrary function axis b₁ b₂ body chaleur co-ordinates coefficient conducibility consider constant temperature convergent series cooling corresponding cosines curve d'v d'v d²v definite integrals denoting determine different points differential equations distance dv dv dv dx dx² enclosure equation dv expressed fixed temperature function f(x give given heat equal heat which escapes heat which flows Hence hypothesis infinitely small initial temperatures instant dt integral interior layers maintained mass mathematical analysis molecules movement of heat 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 source of heat sphere substitute suppose theorems theory of heat thermometer unit of surface unknown variable vary
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Page 470 - Bible, an edition such as, to use the words of the Editor, 'would have been executed long ago had this version been nothing more than the greatest and best known of English classics.' Falling at a time when the formal revision of this version, has been undertaken by a distinguished company of scholars and divines, the publication of this edition must be considered most opportune.