290 POOR. 



planet at the point of closest approach. Now the action of 

 Jupiter, even when repeated at several very close appulses, can 

 cause but a slight variation in the value of this function, when 

 taken in respect to that planet : but, on the other hand, the ac- 

 tion of another planet, Saturn for example, may at one approach 

 change considerably the value of this quantity taken with re- 

 spect to Jupiter, although it must leave unchanged the value of 

 the function taken with respect to Saturn itself. 



Hence, in order to establish the identity of Comet Brooks 

 with that of Lexell both of which were disturbed by Jupiter, we 

 must either show that the n's for the two bodies are practically 

 the same or that there was an intermediate disturbance bv an- 

 other planet. 



The values of this function for the two comets under discus- 

 sion and taken with respect to Jupiter are given below. In 

 order to show the possible variations of u due to one approach, 

 I computed its values with those elements of Comet Brooks 

 which correspond to the following three points of its path : (i) 

 February 1883, the action of Jupiter insensible; (2) March 

 24, 1886, entrance into the sphere of activity; (3) September 

 30, 1889, the action of Jupiter again insensible. For Lexell's 

 comet I used the elements as given by Le Verrier 



Comet Brooks (i), w = 0.5308 



(2), « = 0.5253 



" " (3). "=0.5294 



Comet Lexell, « = 0.4852 



The three values derived for the Brooks comet are in strik- 

 ing accord. We thus see that even this remarkably close ap- 

 proach produced only a total change of — 0.0014 in the value 

 of this function and, as the change necessary to bring it into 

 agreement with that for Lexell is — 0.0456, we at once con- 

 clude that no intermediate approach or series of approaches to 

 Jupiter can satisfy the requirements of this criterion. This 

 tends to prove, as was long ago pointed out by Schulhof,' that 

 the two comets, Lexell and Brooks, are not identical, unless it 



' Bulletin Astronomique, December, 1889. 



