222 CARNEGIE INSTITUTION OF WASHINGTON. 



between the line and its companion, by utilizing the hypothesis, 

 elaborated by St. John, "that the lines of any one element originate at 

 depths increasing with decrease of solar intensity." The moderate 

 preponderance of evidence in favor of a relation between displacement 

 and ratio of intensities of the two components is not sufficient to be 

 regarded as more than possibly a crude indication of such an effect. 



The observed facts of these two investigations seem sufficiently 

 definite to be considered established. In regard to their interpretation 

 it may be said that the theory of anomalous dispersion in the sun as 

 developed by Julius and modified by Larmor does account for them. 

 However, as it is quite clear that this subject is in the early stages of 

 development, final judgment may well be suspended for the present. 



VELOCITY PLANES INDICATED BY APICES OF STELLAR MOTIONS. 



The parallax problem in its application to the real motions of the 

 fixed stars, in the investigations of Dr. von Flotow, is based upon two 

 fundamental equations which are the keys to all further considerations. 

 The investigation of the motions of the stars, based on the measured 

 parallaxes and radial velocities, becomes more important with the 

 increasing amount of data derivable from photographic methods. 



A canvass of 654 large proper-motion stars of the PreHminary 

 General Catalogue for stars with a positive measured parallax and 

 with measured radial velocity netted 116. Computing the individual 

 apices of these stars, and charting them, two planes of preference were 

 clearly indicated, one along the galaxy, the other at right angles to it. 

 The second plane very nearly passes through the generally accepted 

 apices of preferential motion. While the available data are admittedly 

 meager, it seemed desirable to establish a criterion whereby any par- 

 ticular apex might be assigned a position in or outside the two planes 

 of velocity. For this purpose the equatorial coordinates A' and D' of 

 the star's apex were transfonned to coordinates G and H of the assumed 

 plane, whose pole has the equatorial coordinates y, k. Then we have 

 the condition 



Sin H = cos K cos D' cos (A ' — 7) + sin /c sin D' = 



If this condition is not realized, we may attribute it to three causes: 



(1) In consequence of errors in t and p the coordinates A', D' are in 

 error. 



(2) The assumed pole of the velocity plane may be in error. 



(3) The star's apex does not belong to the assumed plane. 



The first cause, assuming d-w and dp to be observational errors, leads 

 to the condition 



tani/+//d7r+Pc?p = 



where the coefficients II and P are known functions of the star's 

 motion and of the position of the assumed plane. Through this 



