RECENT ADVANCES IN SCIENCE 529 



in much the same way as in the usual theory, but the great 

 inequalities are not treated as perturbations, since they are of 

 the first order. The intermediary orbit is not periodic, but 

 contains only the principal terms of the periodic solution : to 

 form the complete solution from this orbit are added per- 

 turbations arising from those parts of the perturbative function 

 which were originally neglected and variations due to the fact 

 that the actual constants of integration do not exactly fulfil 

 the conditions of the intermediary orbit. With this method of 

 treatment, the small divisors which arise in the old theory are 

 avoided ; they enter the equations of condition of the inter- 

 mediary orbit, but do not reappear after these have been 

 solved. 



The publications referred to above treat of the theory of the 

 longitudes and radii-vectores ; the theory of the latitudes is to 

 be treated in detail in the second part of the volume. 



In connection with the derivation of the potential function 

 an interesting point is noted. Certain terms were neglected by 

 Laplace which contain a small factor whose value is dependent 

 on the form of Jupiter and the distribution of its mass, but 

 which there was then no means of evaluating. Similar terms 

 were neglected in the complementary part of the perturbative 

 function. The neglect of these terms was justifiable in view of 

 the limit of accuracy which Laplace had set himself. Subse- 

 quent writers, however, have copied Laplace's perturbative 

 function, neglecting the terms in question, although in the 

 development of other terms quantities of the same or higher 

 order of smallness have been included. The supposed degree 

 of accuracy has therefore not been obtained. 



The Motions of the B-Stars. — Reference was made in these 

 notes in the last issue of Science Progress (p. 359) to a new 

 theory advanced by Prof. Perrine to the effect that many of 

 the characteristics of spectral class amongst the stars generally 

 are due to external causes depending upon location in the 

 stellar system and associated with variations in the amount 

 of cosmic matter in different parts. Further evidence bearing 

 on the same theory is advanced in a paper in which the excess 

 of the outward motion of the B-type stars is discussed in 

 Astroph. Journ, 48, 145, 191 8. It is a well-established fact that 

 after the elimination of the solar velocity, there is a strong 



