where _M_ and _m_ represent the masses of the two stars. We have already seen that _k_, the gravitation constant, is equal to 1 when the masses are measured in terms of the sun's mass taken as unity, and when _T_ and _a_ are expressed in years and radii of the earth's orbit respectively, and with this value of _k_ we may readily find from the above equation, _M_ + _m_ = 2.5--i. e., the combined mass of the two components of α Centauri is equal to rather more than twice the mass of the sun. It is not every double star to which this process of weighing can be applied. The major axis of the orbit, _a_, is found from the observations in angular measure, 35" in this case, and it is only when the parallax of the star is known that this can be converted into the required linear units, radii of the earth's orbit, by dividing the angular major axis by the parallax; 47 = 35" ÷ 0.75". Our list of distances (§ 189) contains four double stars whose periodic times and major axes have been fairly well determined, and we find in the accompanying table the information which they give about the masses of double stars and the size of the orbits in which they move: ---------------------+-------+-------+----------+------- STAR. | Major | Minor | Periodic | Mass. | axis. | axis. | time. | ---------------------+-------+-------+----------+------- α Centauri | 47 | 40 | 81 y. | 2 70 Ophiuchi | 56 | 48 | 88 | 3 Procyon | 34 | 31 | 40 | 3 Sirius | 43 | 34 | 52 | 4 ---------------------+-------+-------+----------+------- The orbit of Uranus, diameter = 38, and Neptune, diameter = 60, are of much the same size as these double-star orbits; but the planetary orbits are nearly circular, while in every case the double stars show a substantial difference between the long and short diameters of their orbits. This is a characteristic feature of most double-star orbits, and seems to stand in some relation to their periodic times, for, on the average, the longer the time required by a star to make its orbital revolution the more eccentric is its orbit likely to prove. Another element of the orbits of double stars, which stands in even closer relation to the periodic time, is the major axis; the smaller the long diameter of the orbit the more rapid is the motion and the shorter the periodic time, so that astronomers in search of interesting double-star orbits devote themselves by preference to those stars whose distance apart is so small that they can barely be distinguished one from the other in the telescope.