The Analytical Theory of Heat |
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Page ix
... ratio h : we have ' = q , w3 - qw + 1 = 0 , and v 1 + v z V2 h S / log w 2 1 1/2 = 5 ( 1086 ) 2 . K The distance between two consecutive points is λ , and log w is the decimal logarithm of one of the two values of w • PAGE 86 SECTION II ...
... ratio h : we have ' = q , w3 - qw + 1 = 0 , and v 1 + v z V2 h S / log w 2 1 1/2 = 5 ( 1086 ) 2 . K The distance between two consecutive points is λ , and log w is the decimal logarithm of one of the two values of w • PAGE 86 SECTION II ...
Page xi
... ratio of the temperatures of two points whose coordinates are x , y and x , y changes according as the value of y increases ; x1 and x , preserving their respective values . The ratio has a limit to which it approaches more and more ...
... ratio of the temperatures of two points whose coordinates are x , y and x , y changes according as the value of y increases ; x1 and x , preserving their respective values . The ratio has a limit to which it approaches more and more ...
Page xv
... ratios , and decrease with the time , as the ordinates v of a line whose equation is v = A.e - mt . Formation of the general ex- pression . 242-244 . Application to some remarkable examples . Different consequences of the solution ...
... ratios , and decrease with the time , as the ordinates v of a line whose equation is v = A.e - mt . Formation of the general ex- pression . 242-244 . Application to some remarkable examples . Different consequences of the solution ...
Page xvi
... ratio of the variable temperatures of two points in the solid is in the first place considered to approach continually a definite limit . e - Kn't , which expresses sin nx x This remark leads to the equation v = A the simple movement of ...
... ratio of the variable temperatures of two points in the solid is in the first place considered to approach continually a definite limit . e - Kn't , which expresses sin nx x This remark leads to the equation v = A the simple movement of ...
Page xvii
... ratio of the variable tem- peratures of two points of the solid approaches continually a definite limit , and by this we ascertain the expression of the simple movement . The function of x which is one of the factors of this expression ...
... ratio of the variable tem- peratures of two points of the solid approaches continually a definite limit , and by this we ascertain the expression of the simple movement . The function of x which is one of the factors of this expression ...
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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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