198 THE POPULAR SCIENCE MONTHLY. 



clination may be produced. I made a similar research a few 

 years ago concerning eccentricities, and found a region of in- 

 stability corresponding with a still smaller distance from the sun, 

 1*83. The perturbations caused by Jupiter and Saturn must there- 

 fore be regarded as insufficient to explain the considerable values 

 of the eccentricities and inclinations of so many asteroids. These 

 values were never small, and consequently the conditions in which 

 Laplace's nebula existed were not the same at the times of the 

 formation of the asteroids as they were when the old planets were 

 fixed. An interesting cosmological question is presented here, 

 and the accumulation of new discoveries of asteroids can only 

 facilitate its solution. 



The distribution of the asteroids, according to their mean dis- 

 tances from the sun, or (which amounts to the same thing) accord- 

 ing to their mean diurnal motions,* offers some curious facts. A 

 table showing this factor for all the asteroids but three presents 

 the striking feature of accumulations of minor planets about the 

 mean motions 640", 780*, and 815", with which correspond the mean 

 distances 3'13, 275, and 2*67. Two principal voids may also be 

 recognized, about 600" and 900", or the mean distances 3*27 and 

 2*50 from the sun. The mean diurnal motion of Jupiter is 299*42" 

 or very nearly 300". The voids that have been pointed out thus 

 correspond with regions where the mean motion of the planet 

 would be exactly double or triple that of Jupiter. There are other 

 less well-defined voids, in which the relation of the mean motions 

 to that of Jupiter, instead of being 2 or 3, would be represented by 

 one of the fractions f , f , f , and . Prof. Kirkwood first brought 

 out this fact in 1866, and generalized it by saying that the parts 

 of the zone of the asteroids in which exists a simple relation of 

 commensurability between the period of revolution of a minor 

 planet and that of Jupiter are represented by gaps like the inter- 

 vals between the rings of Saturn. "We remark in addition that 

 the gaps are less sharply marked than in the case of the rings 

 of Saturn, in that after a void the number of asteroids does not 

 increase suddenly, but gradually, till it regains its normal value. 



Can the voids be accounted for by the theory of perturbations ? 

 We should have a very simple explanation if we could show that 

 two planets, the durations of whose revolutions are in a simple 

 commensurable relation, exist for that reason in an eminently un- 

 stable condition which they are liable to abandon at any moment. 

 If these conditions are realized, the usual theory of perturbations 

 defaults ; but we can not conclude that instability would result 

 from it. Recent calculations seem rather to lead to opposite con- 



* The mean diurnal motion is the quotient of the division of the number of seconds 

 (1,290,000) in the circumference by the number of days of the planet's revolution. 



