36 ANNUAL RECORD OF SCIENCE AND INDUSTRY. 



contiguous edges multiplied by the sine of the triedral an- 

 gles formed by these edges. Its volume in:iy also be ex- 

 pressed as equivalent to multiplying one half of the product 

 of two opposed edges by the sine of the angle comprised 

 between them, and by one third of the shortest distance be- 

 tween these faces. In the regular tetnedron, the radius of 

 the circumscribed sphere is triple the radius of the inscribed 

 sphere. Grunerfs Archiv, LVII., 113. 



OEB1T OF THE DOUBLE STAE 42, COM.E BEEEXICES. 



The star 42, Comce Berenices, was discovered to be double 

 in 1826 by the elder Struve, but it appeared single in 1833, 

 since which time it has been observed regularly either by 

 the discoverer or by his son, Otto Struve, as well as by other 

 astronomers. Since 1826 it has four times presented the 

 appearance of a single star, one of the bodies being actually 

 occulted by the other. The very accurate observations of 

 Otto Struve made since 1840, after having been corrected 

 for the personal errors peculiar to his observations, and 

 which have been most carefully investigated by himself, 

 have sufficed to enable him to determine with very con- 

 siderable accuracy the position and apparent dimensions of 

 the relative orbits of these stars. The plane of their orbits 

 coincides so nearly with the line joining them to the sun, 

 that we can not certainly state that there is any appreciable 

 inclination between the two. We have therefore to adopt 

 as the inclination between the line of sight and the orbit 

 of the stars, and there results 11, or the mean of all observed 

 directions, as the anode between the ascending node and the; 

 declination circle. The remaining elements of the orbit of 

 the stars, viz., the mean annual motion, the eccentricity, the 

 major axis, the time of passage through the periaster and 

 the angle in' the orbit between the periaster and the as- 

 cending node, must all be deduced from micrometric meas- 

 ures of the relative distances of two stars. Observations of 

 this nature are proverbially so difficult that up to this time 

 astronomers have avoided employing them when position an- 

 gles could be used instead. The great accuracy of Struve's 

 micrometric observations, however, is fully illustrated by the 

 remarkable agreement between the observed distance and 

 those computed in accordance with the numerical values 



