The Analytical Theory of Heat |
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Page xiv
... 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 the value of the series is 0 , if x is any quantity included between a and . Application to other ...
... 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 the value of the series is 0 , if x is any quantity included between a and . Application to other ...
Page 194
... versin x , we have 1 2 1 3 ( x ) = versin a sin x + versin 2a sin 2.x + versin 31 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 2a sin 2.x + versin 31 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 mu - sin ( m − 1 ) u ] , sin u we must have , in order to satisfy the condition a , a ,, the equation sin ( n + 1 ) u — sin u = sin ...
... versin u ; it remains only to determine the value of the arc u . The general value of a being a1 [ sin mu - sin ( m − 1 ) u ] , sin u we must have , in order to satisfy the condition a , a ,, the equation sin ( n + 1 ) u — sin u = sin ...
Page 233
... versin ( 1 ( 1 ) , m k h " = − 2 versin ... h (カー 1 ) - m k ( 2 ( 2 ) , A- " - - 2 versin { ( n − 1 ) = } m { (エール) } Suppose then that we have divided the semi - circumference π into n equal parts , and that in order to form u ...
... versin ( 1 ( 1 ) , m k h " = − 2 versin ... h (カー 1 ) - m k ( 2 ( 2 ) , A- " - - 2 versin { ( n − 1 ) = } m { (エール) } Suppose then that we have divided the semi - circumference π into n equal parts , and that in order to form u ...
Page 235
... versin u sin u sin 3u ' - + b1 sin 2u ' sin u e sin 3u " - sin 2u " sin u " - - e M 2kt 772 versin u ' - 2kt versin u " + c + & c .. 1 = - ( a + b + c + & c . ) + a - ( sin nu — sin ( n − 1 ) sin u − 1 ) u ) e 2kt versin u ( sin nu ...
... versin u sin u sin 3u ' - + b1 sin 2u ' sin u e sin 3u " - sin 2u " sin u " - - e M 2kt 772 versin u ' - 2kt versin u " + c + & c .. 1 = - ( a + b + c + & c . ) + a - ( sin nu — sin ( n − 1 ) sin u − 1 ) u ) e 2kt versin u ( sin nu ...
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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
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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.