The Analytical Theory of Heat |
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Page x
... axis of z is the same , through whatever point of that axis the plane passes . The value of this common flow is that which would exist , if the coefficients a and b were nul · 140 , 141. Analytical expression of the flow in the interior ...
... axis of z is the same , through whatever point of that axis the plane passes . The value of this common flow is that which would exist , if the coefficients a and b were nul · 140 , 141. Analytical expression of the flow in the interior ...
Page xviii
... axis of the prism . 315 317 330. Application to the case in which the thickness of the prism is very small 318 . • 331. The solution shews how the uniform movement of heat is established in the interior of the solid • · 332. Application ...
... axis of the prism . 315 317 330. Application to the case in which the thickness of the prism is very small 318 . • 331. The solution shews how the uniform movement of heat is established in the interior of the solid • · 332. Application ...
Page 17
... axes lines perpendicular to the faces , we see that the temperature v of the point m after the time t , is a func- tion of the four variables x , y , z , and t . The quantities of heat F. H. 2 which flow out at each instant through the ...
... axes lines perpendicular to the faces , we see that the temperature v of the point m after the time t , is a func- tion of the four variables x , y , z , and t . The quantities of heat F. H. 2 which flow out at each instant through the ...
Page 18
... axes , the axis of the prism . itself , and the two perpendiculars on the sides : the permanent temperature of the point m , whose co - ordinates are x , y , z , is a function of three variables F ( x , y , z ) : it has by hypothesis a ...
... axes , the axis of the prism . itself , and the two perpendiculars on the sides : the permanent temperature of the point m , whose co - ordinates are x , y , z , is a function of three variables F ( x , y , z ) : it has by hypothesis a ...
Page 50
... axes in the second body , will fix also the position of the points p and p ' . Now , the distance from the point n to the point n ' is equal to the distance from the point p to the point p ' , and since the two bodies are formed of the ...
... axes in the second body , will fix also the position of the points p and p ' . Now , the distance from the point n to the point n ' is equal to the distance from the point p to the point p ' , and since the two bodies are formed of the ...
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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.