A. MATHEMATICS AND ASTRONOMY. 25 



revolutions about the sun since that time without having 

 been observed. Its short period of revolution gives it an 

 additional interest ; its movement seems to have experienced 

 no disturbance in the course of the two revolutions that it 

 has made during the past fifteen years. 13 II, III., 174. 



OX THE REPULSIVE FORCES OF COMETS. 



Schiaparelli has recently published his views upon the 

 cause of the peculiar phenomena exhibited by comets, views 

 which he has entertained and in part published since 1862, 

 during which time, on the other hand, he has taken so prom- 

 inent a part in the development of our knowledge of shoot- 

 ing-stars. According to Schiaparelli, there actually exists 

 a repulsive force, not only between the sun and the tail, but 

 also between the particles composing the nucleus and the 

 tail of a comet; and the phenomena exhibited by these bod- 

 ies can not be explained without assuming these repulsive 

 forces. In fact, if we consider, first, the formation of the tail 

 itself, we shall find that the solar gravitation and the move- 

 ment of the comet do not suffice to explain it, as has been 

 abundantly testified to by all who have minutely examined 

 the observations that have been made. Again, too, if w r e 

 consider the tail itself, and its path in space, we shall find, as 

 has been shown by Bessel in reference to Halley's comet, and 

 by Pape and Bond in reference to Donati's comet, the exist- 

 ence of a repulsive force repelling the comet from the sun 

 results with as much certainty as the movements of the 

 earth prove the existence of an attracting force toward the 

 sun. The third, comet of 1862, on the other hand, whose tail 

 was not projected in a direction opposite to the sun, but con- 

 tinually approached this direction as the comet moved away 

 from the sun, shows that the repulsive force acts upon the 

 particles of the tail as well as upon the nucleus of the comet ; 

 that, in fact, the tail was first sensibly brought under the in- 

 fluence of the sun after it had been projected from the nucleus 

 of the comet by a force residing therein. Under a minute 

 examination, the head of a comet sometimes shows beams of 

 light projected from the nucleus, but subsequently turning 

 back and forming portions of the tail, so that here, also, the 

 existence of the repulsive force is apparent. Finally, the in- 

 crease in the breadth of the tail as it separates from the 



B 



