472 MASSES OF VISUAL lUNAKV STARS. 



P = The period of a binary system in years : 



M nz a \'P- = R^a-/P' 

 (} =: Annual anjs^ular motion in degrees or 



3607F. 

 Then we have 



360- M :r= R^a'0\ 

 or, by using logarithms. 



log = 2.5563 + jA (log M - log Rci 



If we can suppose that in stars of the same spectrum or 

 constitution, the density and surface brilliancy are constants for 

 every mass or volume, then for n times the diameter we have 

 n- the surface and ;;' the volume, and therefore )i' times the 

 mass. If under these sui)positions m is the magnitude for mass 

 M, the magnitude for mass )iM will be 



5 

 ;// log ;/. 



3 



If, again, a star of magnitude m is divided into /; stars. 

 each of the same emissive power as the original star, the mag- 

 nitude of each would be 



.S 



111 -\ log II, 



and the magnitude of the resulting cluster, omitting chance 

 eclipses, would be 



5 



w/ :rr ;// log H 



6 



Thus, \{ 11 := 2, we have log 2 = 0.301 and /;;' = /;; — 0-25. 



We learn, incidentally, that the mass of a cluster remaining 

 unaltered, the smaller the stars of which it is composed the 

 brighter the cluster. 



The cluster w Centaurus, which shines as a hazy star of 

 the 4th magnitude, is comjjosed of 6,400 stars. If these could 

 be combined into one star of the same emissive power, its mag- 

 nitude would be 



5 

 4 H log 6400 = 7.2, 



6 

 so that it would be invisible to the naked eye. 



So that the implication may not be missed, another example 

 may be given. The Sun, if removed^ to a radial distance of 100 

 (parallax = o".oi). would shine as a star of the loth magni- 

 tude. A cluster of t.ooo solar-type stars at that distance, each 



