JANUABY 20, 1911] 



SCIENCE 



93 



librations more extended than those of the 

 four at present known. As such bodies are 

 moving most slowly when farthest from 

 the triangular points the search would have 

 greater chances of success within twenty- 

 three degrees to thirty-five degrees of Jupi- 

 ter on either side, or nearly in opposition to 

 Jupiter. These three areas are nearest to 

 the earth at different times of the year. 



Another practical problem is presented 

 by the computation of the orbits. This is 

 mainly a matter of expense so far as the 

 ordinary asteroid is concerned, and one 

 way of meeting the difficulty was shown by 

 "Watson, who endowed those discovered by 

 himself. We need not, however, demand 

 that explorers should be responsible for 

 looking after their own discoveries. The 

 asteroids of each type of motion form a 

 group which it would be most economical 

 to treat together if at any time a fund were 

 obtained for the development of the prob- 

 lem. For the present, ephemerides suffi- 

 cient to identify each body will serve. 

 When a reasonable number of accurate 

 observations, extending over a considerable 

 period of time, has been obtained, the com- 

 parison of the observations with theory 

 will be of interest to students of celestial 

 mechanics, and the rest of the work will 

 take care of itself. 



In particular, the Trojan group revolv- 

 ing at the same mean distance as Jupiter 

 and at present consisting of the four bodies. 

 Hector, Achilles, Patroclus and one as yet 

 unnamed, will not suffer from neglect. 

 They appear to show one, perhaps the 

 main, stage of transition from bodies 

 superior to the orbit of Jupiter to those 

 inferior to that planet and possibly to those 

 which have become his satellites. Their 

 separate paths of motion are interesting to 

 the mathematician, but even more so to the 

 astronomer, since they appear to indicate 

 a new set of periodic orbits in the problem 



of three bodies. The remarkable series of 

 families of such orbits obtained by Sir 

 George Darwin has shown how far such 

 an investigation may lead. A single 

 family may have several types. Those 

 which I have described appear to belong to 

 perhaps two families at the most, but 

 nevertheless the extent of the work neces- 

 sary to discuss them is very considerable, 

 and the mathematical portion of it is by no 

 means simple. They may be peculiar to 

 systems like our own. The work of Sir 

 George Darwin will doubtless have appli- 

 cations to multiple systems of stars, the ob- 

 servational material of which is being 

 rapidly gathered by means of the spectro- 

 scope, the heliometer and photographic 

 plate. 



Theories as to the mode of formation and 

 development of our solar system will, I be- 

 lieve, receive some assistance from these 

 orbits of transition. If I have not touched 

 on such questions it is not because the 

 temptation to do so was not present. Such 

 matters, however, require an extended dis- 

 cussion under various hypotheses. As 

 Brodetski has shown, different hypotheses 

 concerning the nature of possible resisting 

 media lead to quite different results. My 

 main object has been to attempt to set 

 forth certain actual and possible types of 

 motion within our solar system at the pres- 

 ent time in such a manner as to indicate in 

 what direction the theorist and the ob- 

 server can best act in cooperation. The ob- 

 server, now that the mass of accumulating 

 material threatens to become too great for 

 permanent record, needs assistance from 

 the theorist so that he may direct his 

 energies into the most useful channels, and 

 not less does the theorist need the help of 

 the observer so that his results may receive 

 confirmation and that he may obtain sug- 

 gestions for future investigations. 



Ernest W. Brown 



