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 • 67 73 3123 75 SECTION VIII . MEASURE OF THE MOVEMENT OF HEAT AT A ...
... 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 • 67 73 3123 75 SECTION VIII . MEASURE OF THE MOVEMENT OF HEAT AT A ...
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 , T is 1 2 1 3 sin x versin a + sin ...
... 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 , T is 1 2 1 3 sin x versin a + sin ...
Page xxi
... preceding form , from the integral ( a ) 399 , 400. First development of the value of v according to increasing powers of the time t . Second development according to the powers of v . The first must contain a single arbitrary function ...
... preceding form , from the integral ( a ) 399 , 400. First development of the value of v according to increasing powers of the time t . Second development according to the powers of v . The first must contain a single arbitrary function ...
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Common terms and phrases
a₁ abscissa action actual temperature analysis arbitrary axis b₁ body chaleur co-ordinates coefficients conducibility consider constant temperature convergent series cooling corresponding cosines curve d'v d'v definite integrals denoting determine different points differential equations dimensions distance dv dv dv dx dv dz dx dy dx² dy dz dy² enclosure equa equation dv expressed fixed temperature give given heat equal heat which escapes heat which flows Hence hypothesis infinitely small initial temperatures instant dt integral interior maintained mass mathematical analysis molecule movement of heat multiple arcs 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 solution source of heat substitute suppose theorems theory of heat thermometer tion unknowns variable vary versin
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Page 469 - Greek and English Testament, in parallel columns on the same page. Edited by J. SCHOLEFIELD, MA late Regius Professor of Greek in the University. New Edition, with the marginal references as arranged and revised by DR SCRIvENER, js.