Dynamical Theory of Heat and Light. 



n 



through Q on the ellipsoidal surface. It must cut the arc 

 A'C'A at some point between U 3 and U 4 , and, if continued 

 on and on, it must cut the ellipse ACA'C'A successively 

 between TJ 1 and U 2 , or between U 3 and U 4 ; never between 

 U 2 and U 3 , or U 4 and Uj. This, for the extreme case of 

 the smallest axis zero, is illustrated by the path IQQ'Q^Q 7 " 

 Q Ir Q v in fig. 2. 



§ 32. If now, on the other hand, we commence a geodetic 

 through any point J between Ui and U 4 , or between U 2 and 

 U 3 , it will never cut the principal section containing the 

 umbilicus, either between U] and U 2 or between U 3 and U 4 . 

 This, for the extreme case of CC' = 0, is illustrated in fig. 3. 



§ 33. Tt seems not improbable that if the figure deviates by 

 ever so little from being exactly ellipsoidal, Maxwell's condi- 

 tion might be fulfilled. It seems indeed quite probable that 

 Maxwell's condition (see §§ 13, 29, above) is fulfilled by a 

 geodetic on a closed surface of any shape in general, and that 

 exceptional cases, in which the question of § 29 is to be 

 answered in the negative, are merely particular surfaces of 

 definite shapes, infinitesimal deviations from which will allow 

 the question to be answered in the affirmative. 



§ 34. Now with an affirmative answer to the question — is 

 Maxwell's condition fulfilled ? — what does the Boltzmann- 

 Maxwell doctrine assert in respect to a geodetic on a closed 

 surface ? The mere wording of Maxwell's statement, quoted 

 in §13 above, is not applicable to this case, but the meaning 



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