The Analytical Theory of Heat |
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Page vi
... analysis with the study of nature . PAGE 22 26 • 22 27 ib . 22-24 . SECTION II . GENERAL NOTIONS AND PRELIMINARY DEFINITIONS . Permanent temperature , thermometer . The temperature denoted by 0 is that of melting ice . The temperature ...
... analysis with the study of nature . PAGE 22 26 • 22 27 ib . 22-24 . SECTION II . GENERAL NOTIONS AND PRELIMINARY DEFINITIONS . Permanent temperature , thermometer . The temperature denoted by 0 is that of melting ice . The temperature ...
Page xiv
... 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 2x versin 2a + sin 3x versin 3a + & c . , 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 , T is 1 2 1 3 sin x versin a + sin 2x versin 2a + sin 3x versin 3a + & c . , if we attribute to x a quantity greater than 0 and less than a ; and ...
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 1 Sdr cos ( x√g sin r ) ; u = - du dx and the ...
... 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 1 Sdr cos ( x√g sin r ) ; u = - du dx and the ...
Page xx
... analysis , the expo . nents are absolute numbers , and not quantities . We ought not to omit the parts of these exponents which are incomparably smaller than the others , but only those whose absolute values are extremely small . . 376 ...
... analysis , the expo . nents are absolute numbers , and not quantities . We ought not to omit the parts of these exponents which are incomparably smaller than the others , but only those whose absolute values are extremely small . . 376 ...
Page xxi
... analysis which is derived from it dispenses with effecting the develop , ment in series 402. Application to the equations : dev d2v d2v = dt2 dx dy2 • ib . 399 402 and .. ( c ) , dev d1v + = 0 ...... ( d ) . de dx4 404 403. Application ...
... analysis which is derived from it dispenses with effecting the develop , ment in series 402. Application to the equations : dev d2v d2v = dt2 dx dy2 • ib . 399 402 and .. ( c ) , dev d1v + = 0 ...... ( d ) . de dx4 404 403. Application ...
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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 - The Pointed Prayer Book, being the Book of Common Prayer with the Psalter or Psalms of David, pointed as they are to be sung or said in Churches.
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.