TABLE OF CONTENTS. IX 



AET. PAGE 



106 110. The temperatures at points situated at equal distances are 

 represented by the terms of a recurring series. Observation of the 

 temperatures v lt v z , v 3 of three consecutive points gives the measure 



of the ratio*: W e have 



The distance between two consecutive points is X, and log w is the decimal 

 logarithm of one of the two values of w . . . . . . .86 



SECTION II. 

 EQUATION OF THE VARIED MOVEMENT OF HEAT IN A SOLID SPHERE. 



Ill 113. x denoting the radius of any shell, the movement of heat in the 

 sphere is expressed by the equation 



dv K d*v 2dv 



114 117. Conditions relative to the state of the surface and to the initial 



state of the solid 92 



SECTION IH. 

 EQUATION OF THE VARIED MOVEMENT OF HEAT IN A SOLID CYLINDER. ^X 



118 120. The temperatures of the solid are determined by three equations; 

 the first relates to the internal temperatures, the second expresses the 

 continuous state of the surface, the third expresses the initial state of 

 the solid 95 



SECTION IV. 



EQUATIONS OF THE VARIED MOVEMENT OF HEAT IN A SOLID PRISM 

 OF INFINITE LENGTH. 



121 123. The system of fixed temperatures satisfies the equation 



d^v d^v d 2 v 

 dtf + dfi + d^ = ; 



v is the temperature at a point whose coordinates are x, y, z . . . 97 

 124, 125. Equation relative to the state of the surface and to that of the 



first section 99 



SECTION V. 



EQUATIONS OF THE. VARIED MOVEMENT OF HEAT IN A SOLID CUBE. 



126131. The system of variable temperatures is determined by three 

 equations ; one expresses the internal state, the second relates to the 



t state of the surface, and the third expresses the initial state . . . 101 

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