The Analytical Theory of Heat |
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Page xiv
... 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 the value of the series is 0 , if x is any quantity included between a and 1⁄4 ” . Application to other ...
... 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 the value of the series is 0 , if x is any quantity included between a and 1⁄4 ” . Application to other ...
Page 194
... versin x , we have 1 2 1 3 ( x ) = versin a sin x + versin 2x sin 2x + versin 31⁄2 sin 3x + & c.1 This series , always convergent , is such that if we give to x any value whatever included between 0 and a , the sum of its terms will be ...
... versin x , we have 1 2 1 3 ( x ) = versin a sin x + versin 2x sin 2x + versin 31⁄2 sin 3x + & c.1 This series , always convergent , is such that if we give to x any value whatever included between 0 and a , the sum of its terms will be ...
Page 232
... versin u ; it remains only to determine the value of the arc u . The general value of a being a1 sin u - [ sin mu — sin ( m − 1 ) u ] , - we must have , in order to satisfy the condition a , a , the equation sin ( n + 1 ) u - sin u ...
... versin u ; it remains only to determine the value of the arc u . The general value of a being a1 sin u - [ sin mu — sin ( m − 1 ) u ] , - we must have , in order to satisfy the condition a , a , the equation sin ( n + 1 ) u - sin u ...
Page 233
... versin ( 1 ) , h " == m k - 2 versin ( 2 m ( 2 ) , ... k h ( n - 1 ) ; == 2 versin m Suppose then that we have divided the semi - circumference π into n equal parts , and that in order to form u , we take i of those parts , i being less ...
... versin ( 1 ) , h " == m k - 2 versin ( 2 m ( 2 ) , ... k h ( n - 1 ) ; == 2 versin m Suppose then that we have divided the semi - circumference π into n equal parts , and that in order to form u , we take i of those parts , i being less ...
Page 234
... versin u an equation whose second member is reduced to 0 provided the arc u does not vanish ; but in that case we ... versin + b1 sin u ' - sin Ou ' sin u ' ext - versin u m e sin u " - sin Ou " 2kt versin u " + G12 + & c . , 772 sin u ...
... versin u an equation whose second member is reduced to 0 provided the arc u does not vanish ; but in that case we ... versin + b1 sin u ' - sin Ou ' sin u ' ext - versin u m e sin u " - sin Ou " 2kt versin u " + G12 + & c . , 772 sin u ...
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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.