54 ANNUAL RECORD OF SCIENCE AND INDUSTRY. 



surface. They are apparently the result of cooling, depend- 

 ino' on the radiation from the surface of the sun ; and this 

 explanation by ZoUner is the only one that seems to him not 

 to contradict both ordinary laws of physics and well-known 

 facts. 



VARIABLE STARS U, W, AND X SAGITTARII. 



Dr. Julius Schmidt, Director of the Athens Observatory, 

 has lately published the results of his investigations on the 

 variable stars U, W, and X Sagittarii. The variations ob- 

 served in their brightness are of a similar character, as they 

 all have periods in the neighborhood of seven days. These 

 periods, however, are complicated by longer subsidiary cycles 

 of three and a half, eight, and two years respectively. In 

 each case the increase in light is more rapid than the de- 

 crease, the progress from a minimum to the next maximum 

 requiring about three days, and from this maximum to the 

 next minimum about four days. In W Sagittarii there is a 

 well-marked secondary maximum and minimum. 



No adequate physical causes for these changes have yet 

 been assigned. A still more remarkable and inexplicable 

 case of variation has been investigated by Dr. Schmidt in 

 U Herculis. The period of this star is between thirty-eight 

 and forty days, but secondary changes having a period of 

 about twelve hours occur throughout a large portion of the 

 main cycle certainly, and possibly throughout the whole du- 

 ration. These secondary changes are large in amount for 

 the eight or ten days near each minimum, but quite small 

 near the maxima. 38 (7, Nos. 2071 and 2075. 



somoff's barycentric theorem. 



SomofF has presented a note to the Academy of Sciences 

 at St. Petersburg on a barycentric theorem discovered by 

 him, and which offers an elegant method of expressing the 

 duration of any movement whatever of a point with refer- 

 ence to two right lines. The theorem may be enunciated 

 as follows : 



Let T be the duration of any movement whatever of a 

 point, M; and let the curved line AMB be that described 

 during the tmie T ; AB will be the chord that limits the 

 space AMB, Put v for the velocity acquired by the body, 



