The Analytical Theory of Heat |
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Page vii
... coefficients , by comparing the results of calculation with very exact experiments PAGE 43 . ib . SECTION IV . OF THE UNIFORM AND LINEAR MOVEMENT OF HEAT . 65. The permanent temperatures of an infinite solid included between two ...
... coefficients , by comparing the results of calculation with very exact experiments PAGE 43 . ib . SECTION IV . OF THE UNIFORM AND LINEAR MOVEMENT OF HEAT . 65. The permanent temperatures of an infinite solid included between two ...
Page viii
... , h are the specific coefficients ; S is the area of the section , by the revolution of which the ring is generated ; I is the perimeter of the section 85 ART . equal distances are Observation of the 106-110 . viii TABLE OF CONTENTS .
... , h are the specific coefficients ; S is the area of the section , by the revolution of which the ring is generated ; I is the perimeter of the section 85 ART . equal distances are Observation of the 106-110 . viii TABLE OF CONTENTS .
Page x
... coefficients a and b were nul · 140 , 141. Analytical expression of the flow in the interior of any solid . The dv equation of the temperatures being r = f ( x , y , z , t ) the function - Kw dz expresses the quantity of heat which ...
... coefficients a and b were nul · 140 , 141. Analytical expression of the flow in the interior of any solid . The dv equation of the temperatures being r = f ( x , y , z , t ) the function - Kw dz expresses the quantity of heat which ...
Page xii
... coefficients in the equation 1 = a cosx + b cos 3x + e cos 5x + d cos 7x + etc. or 30 PAGE From which we conclude 1 4 - 2i -1 ( − 1 ) i + 1 , 1 = C0S - 4 3 1 cos 3x + 008 5x- 1 cos 7x + etc. 137 SECTION III . REMARKS ON THESE SERIES ...
... coefficients in the equation 1 = a cosx + b cos 3x + e cos 5x + d cos 7x + etc. or 30 PAGE From which we conclude 1 4 - 2i -1 ( − 1 ) i + 1 , 1 = C0S - 4 3 1 cos 3x + 008 5x- 1 cos 7x + etc. 137 SECTION III . REMARKS ON THESE SERIES ...
Page xiii
... coefficients in the following equations infinite in number : A = a + 2b + 3c + 4d + & c . , B = a + 236 + 33c + 43d ... coefficient a , isda ( x ) sin ix . Whence we derive the very simple theorem ( x ) = sinx da ( a ) sina + sin 2x ...
... coefficients in the following equations infinite in number : A = a + 2b + 3c + 4d + & c . , B = a + 236 + 33c + 43d ... coefficient a , isda ( x ) sin ix . Whence we derive the very simple theorem ( x ) = sinx da ( a ) sina + sin 2x ...
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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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