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POPULAR SCIENCE MONTHLY. 



unity, he computes the superior limit of density for 12 variables, based 

 on their periods and the duration of their partial eclipses. The greatest 

 limit is in the case of Z Herculis and is 0.728. The least is in the 

 ease of S Caneri and is 0.035. The average is about 0.2. As the actual 

 density may be less than the limit by an indefinite amount, the general 

 conclusion from his work may be regarded as the same with that from 

 the work of Boberts. 



The results of the preceding theory are independent of the parallax 

 of the stars. They, therefore, give us no knowledge as to the mass of a 

 binary system. To determine this we must know its parallax, from 

 which we can determine the actual dimensions of the orbit when its 

 apparent dimensions are known. Then the formula already given will 

 give the actual mass of the system in terms of the Sun's mass. 



There are only six binary systems of which both the orbit and the 

 parallax are known. These are shown in the table below. Here the 

 first two columns after the stars named give the semi-major axis of the 

 orbit and the measured parallax. The quotient of the first number by 

 the second gives the actual mean radius of the orbits in terms of the 

 earth's distance from the Sun as unity. This is given in the third 

 column, after which follow the period and the resulting combined 

 mass of the system. The last column shows the actual amount of 

 light emitted by the system, compared with that of the Sim. 



rj Cassiopia? 



Sirius 



Procyon. . . . 

 a Centauri . 

 70 Ophiuchi 

 85 Pegasi . . . 



Light. 



1.0 

 32.0 

 8.5 

 1.7 

 0.7 

 9 9 



Even in these few cases some of the numbers on which the result 

 depends are extremely uncertain. In the case of Procyon, the radius of 

 the orbit, can be only a rough estimate. In the case of 85 Pegasi the 

 parallax is uncertain. In the case of ?/ Cassiopiae the elements are 

 still doubtful. 



So far as we have set forth the principles involved in the question, 

 we do not get separate results for the mass of each body. The latter 

 can be determined only by meridian observations, showing the motion 

 of the brighter star around the common center of gravity of the two. 

 This result has thus far been worked out with an approximation to 

 exactness only in the cases of Sirius and Procyon. For these systems 

 we have the following masses of the companions of these bodies in terms 

 of the Sun's mass: 



