578 



SCIENCE 



[N. S. Vol. XLV. No. 1171 



diiBcult to say until a thorougli examina- 

 tion shall have been made of the range of 

 practical solution for each case. When a 

 planet or comet has been observed for a con- 

 siderable length of time, or on several re- 

 turns, the elements require no further ex- 

 amination if they have been properly cor- 

 rected on the basis of the observational 

 material. But the comet and planet lists 

 are full of orbits based upon comparatively 

 short arcs and the lists contain little indi- 

 cation of the degree of accuracy in each 

 ease. 



Sometimes when physical and mathemat- 

 ical indeterminateness does not prevail the 

 range of solution with precise observations 

 is quite limited even for a very short are, 

 and the resulting orbit is fairly accurate. 

 In other eases conditions may be such 

 that even for a comparatively long arc the 

 orbit is inadequate to secure rediscovery 

 at a later return. Comet e 1913 Neujmin 

 was of a star-like appearance and admitted 

 of a high degree of accuracy in the ob- 

 served positions. The first three observa- 

 tions at one-day intervals admitted of the 

 determination of a periodic orbit agreeing 

 closely with a more accurate orbit deter- 

 mined from a 38-day arc. On the other 

 hand, orbits of planet (702) discovered in 

 1910 based on arcs of several months show 

 a wide range of practical solution amount- 

 ing to about four degrees in the eccen- 

 tricity. 



An accurate knowledge of the eccentric- 

 ities of comet orbits is of importance in 

 determining the origin of comets. On theo- 

 retical grounds it has long been recognized 

 that parabolic orbits are practically impos- 

 sible if comets came from without the solar 

 system, formerly a favorite theory of 

 astronomers. The majority of orbits should 

 be elliptic if comets have their origin within 

 the solar system. A rare parabola and some 

 hyperbolas might, of course, be accounted 



for through the perturbations of the major 

 planets on an original ellipse. But if 

 comets came from without they should be 

 predominatingly hyperbolic. Now the pub- 

 lished comet lists show that about three 

 fourths of all comet orbits have been found 

 to be parabolic. A study of the published 

 eccentricities of comet orbits on the basis of 

 the accuracy with which, and the length of 

 time during which they were observed has 

 shown conclusively that all comet orbits are 

 elliptic if observed with sufficient accuracy 

 and for a sufficient length of time. This 

 conclusion was received with doubt when I 

 first announced it in 1907 on the basis of a 

 study of the eccentricities of comet orbits. 

 That three fourths of the comet orbits are 

 parabolic is due to the fact that comet 

 orbits in general have a high eccentricity 

 and that the parabola lies within the range 

 of possible solutions. Since the lower limit 

 of the eccentricity has never been sought 

 the orbits have simply been set down as 

 parabolic and much confusion has been 

 created with reference to the determination 

 of the origin of comets. A few well-deter- 

 mined hyperbolas do exist, but Stroemgren 

 has shown that these are accounted for by 

 perturbations of the original ellipses on 

 the part of the major planets. The high 

 eccentricity found for comet orbits lies in 

 the nature of things. Long-period comets 

 can not come within the range of visibility 

 from the earth unless their orbits are highly 

 eccentric. The othei's must remain invis- 

 ible. It is only within recent years that 

 the old idea that comets are visitors from 

 without the solar system has been aban- 

 doned. Keference to the existing confusion 

 in regard to the origin of comets is made 

 here only because it is clear that if in the 

 past astronomers had worked by methods 

 which readily enable the computer to ascer- 

 tain the range of possible solutions, partic- 

 ularly the lower limit, three fourths of all 



