The Analytical Theory of Heat |
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Page x
... differential equation of the surface which bounds the solid , and q being equal to ( m2 + n + p2 ) . To discover this equation we consider a molecule of the envelop which bounds the solid , and we express the fact that the temperature ...
... differential equation of the surface which bounds the solid , and q being equal to ( m2 + n + p2 ) . To discover this equation we consider a molecule of the envelop which bounds the solid , and we express the fact that the temperature ...
Page xv
... Differential equations suitable to the problem ; integration of these equations . The variable temperature of each of the masses is ex- pressed as a function of the coefficient which measures the conducibility , of the time which has ...
... Differential equations suitable to the problem ; integration of these equations . The variable temperature of each of the masses is ex- pressed as a function of the coefficient which measures the conducibility , of the time which has ...
Page xvii
... differential equation of the second order . A number enters into this function , and must satisfy a definite equation 308 , 309. Analysis of this equation . By means of the principal theorems of algebra , it is proved that all the roots ...
... differential equation of the second order . A number enters into this function , and must satisfy a definite equation 308 , 309. Analysis of this equation . By means of the principal theorems of algebra , it is proved that all the roots ...
Page xx
... differential equation dv dt = d2v d2v + + dav dx dy dz2 ' and if at the same time they have the same value for a certain value of t . • • • 368 377-382 . The heat contained in a part of an infinite prism , all the other points of which ...
... differential equation dv dt = d2v d2v + + dav dx dy dz2 ' and if at the same time they have the same value for a certain value of t . • • • 368 377-382 . The heat contained in a part of an infinite prism , all the other points of which ...
Page xxiii
... differential equations of the movement of heat • • 464 430. Terminology relative to the general properties of heat 431. Notations proposed ERRATA . Page 9 , line 28 , for III . read IV . Pages 54 , 55 , for k read K. Page 189 , line 2 ...
... differential equations of the movement of heat • • 464 430. Terminology relative to the general properties of heat 431. Notations proposed ERRATA . Page 9 , line 28 , for III . read IV . Pages 54 , 55 , for k read K. Page 189 , line 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.