The Analytical Theory of Heat |
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Page x
... perpendicular to the axis of 2 , at the point whose coordinates are x , y , z , and whose temperature is v after the time t has elapsed • · PAGE 104 • 109 142-145 . It is easy to derive from the foregoing theorem the general equation of ...
... perpendicular to the axis of 2 , at the point whose coordinates are x , y , z , and whose temperature is v after the time t has elapsed • · PAGE 104 • 109 142-145 . It is easy to derive from the foregoing theorem the general equation of ...
Page xii
... perpendicular to the base . This expression of the flow suffices to verify the solution 196-199 . Consequences of this solution . The rectangular slab must be considered as forming part of an infinite plane ; the solution expresses the ...
... perpendicular to the base . This expression of the flow suffices to verify the solution 196-199 . Consequences of this solution . The rectangular slab must be considered as forming part of an infinite plane ; the solution expresses the ...
Page 15
... perpendicular to the plane of the ring , whose length is proportional to the fixed temperature at that point , the curved line which passes through the ends of these ordinates will represent the permanent state of the temperatures , and ...
... perpendicular to the plane of the ring , whose length is proportional to the fixed temperature at that point , the curved line which passes through the ends of these ordinates will represent the permanent state of the temperatures , and ...
Page 17
... 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 whole ...
... 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 whole ...
Page 18
... the permanent state of the rectangular prism , flows , during a unit of time , across a certain section perpendicular to the axis , has a determinate ratio to the quantity of heat taken as unit . This 18 [ CHAP . I. THEORY OF HEAT .
... the permanent state of the rectangular prism , flows , during a unit of time , across a certain section perpendicular to the axis , has a determinate ratio to the quantity of heat taken as unit . This 18 [ CHAP . I. THEORY OF HEAT .
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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.