ON MEAN RELATIVE AND ABSOLUTE PARALLAXES. 

 By KEIVIN burns. 

 {Read April 22, 192 1.) 



In computing the mean parallax of a group of stars by compar- 

 ing the radial velocities with the proper motions, it has been the 

 custom to proceed in one of two ways. Knowing the apices of 

 the sun's way, a great circle is passed through these points and the 

 star. The total proper motion is then divided into two parts, one 

 at right angles to the plane of this great circle, and the other in the 

 direction of the circle. The former is called the tau component 

 and the latter the upsilon component. The tau component is 

 evidently free from any motion due to the motion of the sun, 

 while the upsilon component contains all of the efifect of the solar 

 motion. Knowing the sun's velocity, the mean parallax of a group 

 of stars distributed at random over the whole sky can be derived 

 from a study of the mean algebraic upsilon component taken for 

 each part of the sky. The formulae used in this and the following 

 method are found in " Stellar Motions," by W. W. Campbell, page 

 214 and following. It is seen that for the average of a group of 

 stars Fr = 4.74(T/7r), where Vr denotes the radial velocity freed 

 from the motion of the sun. For each star Fw =^4.74(/A/7r), Vm 

 being the total velocity across the line of sight. Let Vr be the total 

 radial velocity, then for the mean of a group Vm='i-S7Vr. For, 

 denoting the cross velocity freed from the motion of the sun by Vm, 

 Campbell shows that in the mean, F,« = 1.57^0 and Sm=i-S7Sr, 

 S being the velocity of the sun with respect to any star, the sub- 

 scripts denoting cross and radial motion as above. The individual 

 values of Sr and Vr unite by addition and subtraction to form the 

 values of Vr, and the quantities Sm and Vm unite in the same 

 manner to form Vm- Hence we have Vm^F(Sm, F^) = 1.57F 

 X (Sr, Vr) = i-SyVr. The relationship deduced by Campbell, Vm = 

 i.SyVr, holds equally well if we choose a coordinate system fixed 



496 



