334 Prof. G. H. Darwin. On JacoMs Figure of [Nov. 25, 



It will be noticed that the longer the ellipsoid the slower it rotates. 

 It is interesting to observe that while the angnlar velocity continually 

 diminishes, the moment of momentum continually increases. The 

 long ellipsoids are very nearly ellipsoids of revolution about an axis 

 perpendicular to that of rotation. Thus in fig. 2 the section through 

 h and c is not much flattened. 



The most remarkable point is that there is a maximum of kinetic 

 energy when a/a is about 3, or when the length of the ellipsoid is 

 about five times its diameter. However, notwithstanding this maxi- 

 mum of kinetic energy, the total energy always increases with the 

 length of the ellipsoid. 



The kinetic energy is the product of two factors, one of which 

 always increases, and the other of which always diminishes; thus it is 

 obvious that it must have a maximum. The result was, however, 

 quite unforeseen, and it seems worth while to obtain simpler formulae 

 for the case of the long ellipsoids. This may be done by taking as the 

 parameter a/a, or the length of the ellipsoid, instead of 7. 



From the table we see that in the later entries y3 is very nearly 



