XVI 11 TABLE OF CONTENTS. 



CHAPTER VII. 



Propagation of Heat in a rectangular prism. 



ART. PAGE 



321 323. Expression of the simple movement determined by the general 

 properties o he^t, ar^d by the form of the solid. Into this expression 

 enters an arc e which satisfies a transcendental equation, all of whose 

 roots are real 311 



324. All the unknown coefficients are determined by definite integrals . 313 



325. General solution of the problem ........ 314 



326. 327. The problem proposed admits no other solution .... 315 

 328, 329. Temperatures at points on the axis of the prism .... 317 



330. Application to the case in which the thickness of the prism is very 

 small 318 



331. The solution shews how the uniform movement of heat is established 



in the interior of the solid 319 



332. Application to prisms, the dimensions of whose bases are large . . 322 



CHAPTER VIII. 



Of the Movement of Heat in a solid cube. 



333, 334. Expression of the simple movement. Into it enters an arc e 



which must satisfy a trigonometric equation all of whose roots are real . 323 



335, 336. Formation of the general solution . 324 



337. The problem can admit no other solution . . . . . . 327 



338. Consequence of the solution ib. 



339. Expression of the mean temperature 328 



340. Comparison of the final movement of heat in the cube, with the 

 movement which takes place in the sphere 329 



341. Application to the simple case considered in Art. 100 .... 331 



CHAPTER IX. 



Of the Diffusion of Heat. 

 SECTION I. 



OF THE FHEE MOVEMENT OF HEAT IN AN INFINITE LlNE. 



342 347. We consider the linear movement of heat in an infinite line, a 

 part of which has been heated; the initial state is represented by 

 v F(x). The following theorem is proved : 



fl 

 dq cos qx I da F(a) cos ga. 

 o 



