The Analytical Theory of Heat |
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Page vi
... analysis with the study of nature PAGE 22 22-24 . SECTION II . GENERAL NOTIONS AND PRELIMINARY DEFINITIONS . Permanent temperature , thermometer . The temperature denoted by 0 is that of melting ice . The temperature of water boiling in ...
... analysis with the study of nature PAGE 22 22-24 . SECTION II . GENERAL NOTIONS AND PRELIMINARY DEFINITIONS . Permanent temperature , thermometer . The temperature denoted by 0 is that of melting ice . The temperature of water boiling in ...
Page xiv
... analysis of Daniel Bernoulli in the problem of vibrating cords . The value of the series , 1 sin x versin a + 2 1 3 sin 2x versin 2a + sin 3x versin 3a + & c . , is π if we attribute to x a quantity greater than 0 and less than a ; and ...
... analysis of Daniel Bernoulli in the problem of vibrating cords . The value of the series , 1 sin x versin a + 2 1 3 sin 2x versin 2a + sin 3x versin 3a + & c . , is π if we attribute to x a quantity greater than 0 and less than a ; and ...
Page xvi
... 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 admits no other ...
... 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 admits no other ...
Page xvii
... Analysis of this equation . By means of the principal theorems of algebra , it is proved that all the roots of the equation are real . 310. The function u of the variable x is expressed by u = - 1 Sdr cos ( x√g sin r ) ; du dx • • 291 ...
... Analysis of this equation . By means of the principal theorems of algebra , it is proved that all the roots of the equation are real . 310. The function u of the variable x is expressed by u = - 1 Sdr cos ( x√g sin r ) ; du dx • • 291 ...
Page xix
... analysis which expresses the movement of heat in an infinite line • · • · • 354. Expression of the variable temperatures when the initial state of the part heated is expressed by an entirely arbitrary function 355-358 . The developments ...
... analysis which expresses the movement of heat in an infinite line • · • · • 354. Expression of the variable temperatures when the initial state of the part heated is expressed by an entirely arbitrary function 355-358 . The developments ...
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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.