The Analytical Theory of Heat |
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Page viii
... origin 0 ; v is the temperature which that section acquires after the lapse of the time t ; K , C , D , h are the specific coefficients ; S is the area of the section , by the revolution of which the ring is generated ; I is the ...
... origin 0 ; v is the temperature which that section acquires after the lapse of the time t ; K , C , D , h are the specific coefficients ; S is the area of the section , by the revolution of which the ring is generated ; I is the ...
Page xvi
... origin of the analysis which we have employed to solve the equation relating to con- tinuous bodies . • 279. Analytical expression of the two preceding results 280-282 . It is proved that the problem of the movement of heat in a ring ...
... origin of the analysis which we have employed to solve the equation relating to con- tinuous bodies . • 279. Analytical expression of the two preceding results 280-282 . It is proved that the problem of the movement of heat in a ring ...
Page xix
... origin , and by v = -ƒ ( x ) at the distance x to the left of the origin . Expression of the variable temperature at any point . The solution derived from the analysis which expresses the movement of heat in an infinite line ...
... origin , and by v = -ƒ ( x ) at the distance x to the left of the origin . Expression of the variable temperature at any point . The solution derived from the analysis which expresses the movement of heat in an infinite line ...
Page 8
... wished to shew the actual origin of the theory and its gradual progress . When this knowledge has been acquired 8 THEORY OF HEAT . General remarks on the method which has served to solve the analytical problems of the theory of heat.
... wished to shew the actual origin of the theory and its gradual progress . When this knowledge has been acquired 8 THEORY OF HEAT . General remarks on the method which has served to solve the analytical problems of the theory of heat.
Page 17
... origin the centre of the cube , and for axes lines perpendicular to the faces , we see that the temperature v of the point m after the time t , is a func- tion of the four variables x , y , z , and t . The quantities of heat F. H. 2 ...
... origin the centre of the cube , and for axes lines perpendicular to the faces , we see that the temperature v of the point m after the time t , is a func- tion of the four variables x , y , z , and t . The quantities of heat F. H. 2 ...
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Common terms and phrases
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
Popular passages
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.