320 THE BINARY STARS. 



of his immense orbit in one hundred and sixty-five of our years, 

 and by bringing Kepler's third law to bear upon the problem, we 

 can easily discover what the period of revolution of this imaginary 

 planet would be, situated at a distance from the sun represented 

 by the number 36, as compared with Neptune, whose dis- 

 tance we represent by 30. Kepler's third law says that the square 

 of the periodic time of a planet in the solar system always 

 bears the same relation to the cube of its distance as in the case 

 of any other planet, so that the square of the periodic time of our 

 imaginary planet must bear the same relation to the cube of its 

 distance (36) as the square of 165 (Neptune's periodic time) bears 

 to the cube of Neptune's distance (30). 



Now, if we work this out, we shall find that if such a planet 

 existed in the solar system at the distance we have assigned to it, 

 it would take about two hundred and seventeen years to revolve 

 round the sun. But the companion to Sirius completes its revo- 

 lution in forty-nine years ; we therefore see that it revolves very 

 much quicker in comparison to its distance from its primary than 

 do the planets of the solar system ; and we know that the greater 

 the attraction of a central sun the quicker all its planets must 

 revolve in order that they may not fall into it. It is evident, 

 therefore, that the mass of Sirius must be much greater than that 

 of the sun. 



The law of gravitation, as discovered and explained by Sir 

 Isaac Newton, tells us that the square of the time of revolution 

 of any planet varies inversely as the gravitational pull existing 

 between itself and its central sun, and the gravitational force 

 exerted by two bodies upon each other at a given distance is 

 directly proportional to their joint masses. Therefore, the mass of 

 Sirius together with his companion, is to the mass of the sun and 

 his imaginary planet as the square of 217 is to the square of 49 ; 

 that is to say, about nineteen times as great. 



Now, the masses of the planets of the solar system are almost 

 inappreciable when compared with the mass of the sun. The 

 mass of our imaginary planet may therefore be left out of our 

 calculation, and we therefore find that the joint mass of Sirius and 

 his companion is nineteen times as great as the mass of the sun. 

 The correctness of this result depends mainly upon the accuracy 



