42 Very — On a Possible Limit to Gravitation. 



as far, or 2-7 X(10) 21 cm. Even then, for gravitational 

 wave-impulses which travel along this curve and succeed 

 each other at such a rate that a new one does not start 

 until its predecessor has returned, there will be some- 

 thing like two thousand million million waves per second, 

 or a gravitational frequency equal to the radiant fre- 

 quency in the ultra-violet at A = 0-15 /*. Such impulses, 

 therefore, would not be incompatible with the rapidity of 

 known electronic revolutions, assuming that both have 

 the same periodicity. 



The Bearing of the Spiral Galactic Form upon the Gravitational 



Problem. 



William Sutherland, in an article on "Bode's Law and 

 Spiral Structure in Nebulae, ' ' 7 concludes that the spirals 

 in Messier 51 Canum Venaticorum, M 100 Comcz, and M 

 101 Ursa Majoris, are "approximately logarithmic." 

 The same view is taken by P allien, 8 but has been con- 

 tested by Dr. T. J. J. See in his Researches on the Evolu- 

 tion of the Stellar System (Vol. II) where he says that 



"Thus the similarity of figure always breaks down at 

 some point sufficiently clear and well defined to leave no 

 doubt that the spiral can not be considered, within admis- 

 sible limits of uncertainty, to be truly equiangular in any 

 one case, and still less is this true of all the different 

 cases where the angles vary so greatly. Consequently 

 the law of attraction operating in the observed spirals 

 can not agree with that of the inverse cube of the dis- 

 tance, under which alone a particle may describe the 

 Logarithmic Spiral" (p. 55). 



And on page 59, after noting that "of all the laws of 

 force which give a zero force at an infinite distance, the 

 Newtonian is the only one for which all the orbits are 

 closed curves," Professor See nevertheless ends with the 

 following statement, which seems to me wholly inade- 

 quate and misleading : 



"The spiral paths shown in the nebulae, however, are 

 neither closed curves, nor any kind of algebraic curves ; 

 because the spirals are often broken, so as to become 

 more or less discontinuous, and markedly irregular. 

 Yet it is not to be inferred from this circumstance that 



7 Astrophysical Journal, vol. 34, pp. 251-260, Oct. 1911. 



8 Astronomische Nachrichten, Nr. 4503. 



