CHAPTER II. 



Passages. 



3. A passage of two stars and takes place when the distance between 

 them is a minimum. Here, however, we must take this term in a more restricted 

 sense, denoting by passages only sucli approaches as take place at a distance smaller 

 than half the mean distance, B, of the stars. 



J t is further not necessary to refer directly to the true perihel distance of the 

 stars. The relative orbit of two stars being always a hyperbola, we use the distance 

 b from the focus to the asymptote in the relative orbit and define passages as 

 those approaches for which b is smaller than ^B. 



We now take into consideration only stars within the dominion Among 

 these stars different velocities are represented and we take out two groups, As, and 

 zlsg, having the following components of velocity: 



u,±^ Au, i i ^'^2 



Ae,: ± ^ Av, ; As^: v^±^Av^. 

 ■w,± ^ Aw, rv^ ± ^ Aw^ 



Any star whatsoever within As, we denote by m, and any star within At^ 

 by Wg. 



All stars m, move in parallel straight lines in the time At through a distance 

 At and all stars in the same time through the distance <Ji^At, where 



= 4- + + Wi'-* , CO., = + j/wg^ _j_ _|_ ^^^2 _ 



The number of stars of the first kind — i. e. within As., — is 



and the immber of stars is 



/a ^^2 ' 



where 



/, =f[t; X, z; u,, v,, w,) , 



A star m, , that passes a star (at a distance smaller than ^ B), suffers, on 

 account of the attraction oî m^, a sudden change in its velocity, which is no longer 



