The Analytical Theory of Heat |
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Page vii
... preceding articles are founded on divers observations . The primary object of the theory is to discover all the exact consequences of these propositions . We can then measure the variations of the coefficients , by comparing the results ...
... preceding articles are founded on divers observations . The primary object of the theory is to discover all the exact consequences of these propositions . We can then measure the variations of the coefficients , by comparing the results ...
Page viii
... preceding equation , the final system of all the internal temperatures will be expressed by the same equation . . 94 , 95. Measure of the flow of heat in this prism SECTION VIII . . 67 MEASURE OF THE MOVEMENT OF HEAT AT A GIVEN POINT OF ...
... preceding equation , the final system of all the internal temperatures will be expressed by the same equation . . 94 , 95. Measure of the flow of heat in this prism SECTION VIII . . 67 MEASURE OF THE MOVEMENT OF HEAT AT A GIVEN POINT OF ...
Page xii
... preceding development , which gives the value of the function of x and m , we determine rigorously the limits within which the sum of all the terms is included , starting from a given term 189. Very simple process for forming the series ...
... preceding development , which gives the value of the function of x and m , we determine rigorously the limits within which the sum of all the terms is included , starting from a given term 189. Very simple process for forming the series ...
Page xiv
... preceding theorems are applicable to discontinuous functions , and solve the problems which are based upon the 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 ...
... preceding theorems are applicable to discontinuous functions , and solve the problems which are based upon the 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 ...
Page xvi
... preceding results 280-282 . It is proved that the problem of the movement of heat in a ring admits no other solution . The integral of the equation evidently the most general which can be formed = dv d2v k dt dx2 is PAGE 253 255 • 259 ...
... preceding results 280-282 . It is proved that the problem of the movement of heat in a ring admits no other solution . The integral of the equation evidently the most general which can be formed = dv d2v k dt dx2 is PAGE 253 255 • 259 ...
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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.