The Analytical Theory of Heat |
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Page xii
... of this plane 200-204 . It is proved that the problem proposed admits of no other solu- tion different from that which we have just stated . • • 159 • 161 ART . SECTION V. FINITE EXPRESSION OF THE RESULT OF xii TABLE OF CONTENTS .
... of this plane 200-204 . It is proved that the problem proposed admits of no other solu- tion different from that which we have just stated . • • 159 • 161 ART . SECTION V. FINITE EXPRESSION OF THE RESULT OF xii TABLE OF CONTENTS .
Page xiii
... RESULT OF THE SOLUTION . 205 , 206. The temperature at a point of the rectangular slab whose co- ordinates are x and y , is expressed thus π 2 cos y 2 v = arc . tang · · ex -x -e PAGE · 166 SECTION VI . DEVELOPMENT OF AN ARBITRARY ...
... RESULT OF THE SOLUTION . 205 , 206. The temperature at a point of the rectangular slab whose co- ordinates are x and y , is expressed thus π 2 cos y 2 v = arc . tang · · ex -x -e PAGE · 166 SECTION VI . DEVELOPMENT OF AN ARBITRARY ...
Page xvi
... result 274-276 . Application and consequences of this solution 277 , 278. Examination of the case in which the ... results 280-282 . It is proved that the problem of the movement of heat in a ring admits no other solution . The integral ...
... result 274-276 . Application and consequences of this solution 277 , 278. Examination of the case in which the ... results 280-282 . It is proved that the problem of the movement of heat in a ring admits no other solution . The integral ...
Page xx
... result is not due to the increase of the distance included between any point of the mass and the part which has been heated ; it is entirely due to the increase of the time elapsed . In all problems submitted to analysis , the expo ...
... result is not due to the increase of the distance included between any point of the mass and the part which has been heated ; it is entirely due to the increase of the time elapsed . In all problems submitted to analysis , the expo ...
Page xxii
... result for f ( x ) • 418. The same remark applies to the general equation f ( x ) ==== *** daf ( a ) cos 1 8 = + 00 + ∞ Σ 2π 8118 2in ( x - a ) , X the second member of which represents a periodic function 419. The chief character of ...
... result for f ( x ) • 418. The same remark applies to the general equation f ( x ) ==== *** daf ( a ) cos 1 8 = + 00 + ∞ Σ 2π 8118 2in ( x - a ) , X the second member of which represents a periodic function 419. The chief character of ...
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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.