366 SCIENTIFIC RECORD FOR 1883. 



ence of the visible Milky Way itself. It would necessarily disintegrate 

 more and more with the lapse of time, and it would really be purely by 

 accident that we live at a time when this disintegration has not yet 

 been accomplished — an hypothesis which at least calls for many-sided 

 proofs before it can be accepted as plausible. 



'• If we take now the galactic co-ordinates of a star, namely, radius- 

 vector, galactic longitude, and latitude (r. I. &.), the simplest form we can 

 give to the above assumption is contained in the equations dr = 0, db = 

 0, dl = constant, which really are expressive of the conditions that all 

 stars are firmly united or interdependent and rotate together, like the 

 atoms of a planet, about an axis perpendicular to the Milky Way through 

 its center of gravity. This to be sure is noticeably untrue for individ- 

 ual stars (for example, our sun), but for an average of many stars the 

 variations of b and r will vanish, which is the case also for small groups 

 of stars, perhaps even if we take our normal numbers from spaces of 

 100 to 200 square degrees. 



"If we take therefore the foregoing equations as expressing approx- 

 imately the conditions of the problem, and use them as a basis for our 

 investigations, it is easy to determine the relations which precession, 

 proper motion, and the universal rotation of the fixed stars bear to each 

 other. 



" Let all the co-ordinates be referred in the usual way to the equator 

 and the vernal equinox, and let 



a, d, p represent the heliocentric (and geocentric), R. A., Decli- 

 natiou, and distance of a fixed star; 



A. D. R. represent the corresponding galactic co-ordinates of the 



s»u; 

 (T, r, c represent the co-ordinates of its apex and its angular 

 velocity, the latter seen at a distance, one perpendicular to 

 the line of sight ; 

 da, dS represent the excess of the star's apparent changes of 

 position over the precessions computed with an assumed 

 constant of luni-solar precession ; 

 dtp represent the required correction of the assumed precession, 



referred to the same unit of time as dl, c, da, dti ; 

 go represent the corresponding inclination of the (fixed) ecliptic; 

 Q, i represent the R. A. of the ascending node of the Milky Way 

 on the equator, and the mutual inclination of the two 

 planes. Neglecting the correction for the planetary con- 

 stant of precession, which it may be necessary to make, we 

 have 

 d a = cos go d cp + cos i dl + other terms, 

 d d = (sin go d if> -f cos Q> sin i, dl) cos a + other terms, 

 and in the treatment of the equations only such stars will be used as 

 have on an average the same distance p, that is, for instance, stars of 

 the same magnitude ; similar to the attempt made at a previous time 



