Vlll TABLE OF CONTENTS. 



ABT. PAGE 



several successive envelopes. Remarkable effects of the separation of the 

 surfaces. These results applicable to many different problems . . 67 



SECTION VII. 

 OF THE UNIFOEM MOVEMENT OF HEAT IN THBEE DIMENSIONS. 



92, 93. The permanent temperatures of a solid enclosed between six rec 

 tangular planes are expressed by the equation 



v = A + ax + by + cz. 



x, y, z are the coordinates of any point, whose temperature is v ; A, a, 

 b, c are constant numbers. If the extreme planes are maintained by any 

 causes at fixed temperatures which satisfy the preceding equation, the 

 final system of all the internal temperatures will be expressed by the 



same equation 73 



94, 95. Measure of the flow of heat in this prism 75 



SECTION VHI. 

 MEASUKE OF THE MOVEMENT OF HEAT AT A GIVEN POINT OF A GIVEN SOLID. 



96 99. The variable system of temperatures of a solid is supposed to be 

 expressed by the equation vF (x, y, z, t), where v denotes the variable 

 temperature which would be observed after the time t had elapsed, at the 

 point whose coordinates are x, y, z. Formation of the analytical expres 

 sion of the flow of heat in a given direction within the solid ... 78 



100. Application of the preceding theorem to the case in which the function 



F is e~fft COB x cosy cos z . . . .82 



CHAPTER II. 



Equation of the Movement of Heat. 



SECTION I. 



EQUATION OF THE VARIED MOVEMENT OF HEAT IN A RING. 



101105. The variable movement of heat in a ring is expressed by the 

 equation 



dv_K^ d*v hi 

 di~~CD dy? 



The arc x measures the distance of a section from the origin ; v is 

 the temperature which that section acquires after the lapse of the time t ; 

 K, C, D, 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 



