The Analytical Theory of Heat |
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... passes . The value of this common flow is that which would exist , if the coefficients a and b were nul • · dz PAGE • 104 140 , 141. Analytical expression of the flow in the interior of any solid . The dv equation of the temperatures ...
... passes . The value of this common flow is that which would exist , if the coefficients a and b were nul • · dz PAGE • 104 140 , 141. Analytical expression of the flow in the interior of any solid . The dv equation of the temperatures ...
Page 6
... passing from a common . expression to a particular solution subject to all the given con- ditions . This difficult investigation requires a special analysis founded on new theorems , whose object we could not 6 THEORY OF HEAT .
... passing from a common . expression to a particular solution subject to all the given con- ditions . This difficult investigation requires a special analysis founded on new theorems , whose object we could not 6 THEORY OF HEAT .
Page 8
... passes on . The progress of the phenomenon becomes more regular and simpler , remains finally subject to a definite law which is the same in all cases , and which bears no sensible impress of the initial arrangement . All observation ...
... passes on . The progress of the phenomenon becomes more regular and simpler , remains finally subject to a definite law which is the same in all cases , and which bears no sensible impress of the initial arrangement . All observation ...
Page 14
... passes slowly from the parts which are more heated to those which are less ; and at the same time it is dissipated at the surface , and lost in the medium or in the void . The tendency to uniform dis- tribution and the spontaneous ...
... passes slowly from the parts which are more heated to those which are less ; and at the same time it is dissipated at the surface , and lost in the medium or in the void . The tendency to uniform dis- tribution and the spontaneous ...
Page 15
... passes through the ends of these ordinates will represent the permanent state of the temperatures , and it is very easy to determine by analysis the nature of this line . It is to be remarked that the thickness of the ring is supposed ...
... passes through the ends of these ordinates will represent the permanent state of the temperatures , and it is very easy to determine by analysis the nature of this line . It is to be remarked that the thickness of the ring is supposed ...
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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.