FEBEUAEY 21, 1902.] 



SCIENCE. 



!7 



a double star orbit consist of a series of 

 observed position angles and distances with 

 the corresponding times of observation. 

 From this data it is customary to derive 

 the apparent orbit of the star by plotting 

 the observed coordinates and drawing 

 through the resulting points thfe best ellipse 

 that can be fitted to them, subject to the 

 condition that in this ellipse the radius 

 vector must sweep over equal areas in equal 

 times. The author knows no published 

 statement showing how this condition is 

 applied in the actual construction of the 

 ellipse and it is not apparent how it can be 

 applied in any satisfactory manner in this 

 purely graphical process. Moreover, the 

 process is open to the additional objection 

 that it takes small account of the cir- 

 cumstance that of the three elements enter- 

 ing into a complete double star observation, 

 position angle, distance and epoch, the time 

 of observation is determined with a pre- 

 cision incomparably superior to that of the 

 measured coordinates, and should therefore 

 play a prominent part in the determina- 

 tion of the orbit instead of the subordinate 

 role commonly assigned it. The method 

 proposed for improving the current prac- 

 tice in these respects reverts to the prac- 

 tice introduced by Sir John Herschel, of 

 plotting the observed position angles with 

 the corresponding times as abscissas, and 

 extends the same practice to the observed 

 distances. From the resulting curves data 

 are derived for assumed epochs, and 

 through a least square adjustment sup- 

 plemented by mechanical qiiadratures are 

 transformed into normal places that satisfy 

 rigorously the condition of constant areal 

 velocity. A partial control upon the 

 character of the data and the treatment to 

 which they have been subjected is furnished 

 by the quasi rigorous condition that the 

 adjusted normal places shall all lie upon 

 some ellipse. In the adjustment of the 

 data there is incidentally determined the 



areal velocity of the radius vector and this 

 in connection with the apparent orbit, 

 plotted from the normal places, leads, 

 immediately to a determination of the 

 periodic time and to the independent de- 

 termination of the dates of periastron and 

 apastron passage. The agreement of the- 

 double interval between these dates with 

 the pei'iodic time first determined furnishes. 

 a partial check upon the work. The transi- 

 tion from the apparent to the real orbit 

 may be made by any of the standard 

 methods, but that of Klinkerf ues when sim- 

 plified by the introduction of the elements 

 above derived is especially convenient. 

 There was presented an application of the 

 method above outlined to the determina- 

 tion of the orbit of Struve 2,107, showing 

 that the labor involved does not greatly 

 exceed that of the ordinary methods and 

 is fully compensated by the checks fur- 

 nished en route as well as by the increased 

 precision of the results. 



A Cosmic Cycle: Frank W. Very. 



An application of a new doctrine of an 

 explosive condition of matter (limited by 

 composition, pressure and temperature) to. 

 various phenomena of the heavenly bodies^ 

 and to stellar evolution. NoviB are re- 

 garded as the culmination of long-enduring 

 antecedent stages of stellar preparation, 

 and as indicating (along with the helium 

 stars) a condition of instability and active 

 modification which is incompatible with 

 planetary growth, but which is followed 

 by other relatively quiescent stages favor- 

 able to the production of planets and to 

 their orderly development. An extension 

 of the doctrine of the conservation of 

 energy is involved, and the problem of the 

 sustentation of solar heat is approached 

 from a new standpoint which admits of a 

 great extension in the duration of the 

 solar system, thus satisfying the demands 

 of the geologist for a prolonged terrestrial 



