The Analytical Theory of Heat |
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Page x
... derive from the foregoing theorem the general equation of the movement of heat , namely dv K ( dv d2v dr \ = dt CD dx dy3 TM dz2 • • · 112 SECTION VII . GENERAL EQUATION RELATIVE TO THE SURFACE . 146-154 . It is proved that the variable ...
... derive from the foregoing theorem the general equation of the movement of heat , namely dv K ( dv d2v dr \ = dt CD dx dy3 TM dz2 • • · 112 SECTION VII . GENERAL EQUATION RELATIVE TO THE SURFACE . 146-154 . It is proved that the variable ...
Page xiii
... derive the very simple theorem ( x ) = sinx da ( a ) sina + sin 2x whence i = ∞ • 179 181 ƒ ” " da p ( a ) sin 2a + ... derived the remarkable 184 series , π COS x = 2 1.3 sin x + 4 sin 4.x + 3.5 6 8 sin 7x + 5.7 sin 9x + & c . . 7.9 ...
... derive the very simple theorem ( x ) = sinx da ( a ) sina + sin 2x whence i = ∞ • 179 181 ƒ ” " da p ( a ) sin 2a + ... derived the remarkable 184 series , π COS x = 2 1.3 sin x + 4 sin 4.x + 3.5 6 8 sin 7x + 5.7 sin 9x + & c . . 7.9 ...
Page xiv
... derive the remarkable series 1 sin'x = 1 cos 2x 1.3 cos 4x 3.5 cos 6x 5.7 - & c . PAGE 190 226-230 . The preceding theorems are applicable to discontinuous functions , and solve the problems which are based upon the analysis of Daniel ...
... derive the remarkable series 1 sin'x = 1 cos 2x 1.3 cos 4x 3.5 cos 6x 5.7 - & c . PAGE 190 226-230 . The preceding theorems are applicable to discontinuous functions , and solve the problems which are based upon the analysis of Daniel ...
Page xix
... derived from the analysis which expresses the movement of heat in an infinite line • • • · • · 354. Expression of ... derive from it agrees with that which has been stated in Articles 347 , 348 • 354 356 362 ART . 370 , 371. Remarks on ...
... derived from the analysis which expresses the movement of heat in an infinite line • • • · • · 354. Expression of ... derive from it agrees with that which has been stated in Articles 347 , 348 • 354 356 362 ART . 370 , 371. Remarks on ...
Page xx
... derived immediately from that of the linear movement . The integral of the equation dv d2v d2v d2v = + + dt dx dys dz2 solves the proposed problem . It cannot have a more extended integral ; it is derived also from the particular value ...
... derived immediately from that of the linear movement . The integral of the equation dv d2v d2v d2v = + + dt dx dys dz2 solves the proposed problem . It cannot have a more extended integral ; it is derived also from the particular value ...
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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.