OF ARTS AND SCIENCES. 9 



, . J , 2 IT a sin i mt • i /« 



traversed in one year, dz' =: - p — cos u. Ihe maximuna value of 



this expression occurs when m ^ 0° or tt, and is . If the 



orbit is elliptical, p and u may be deduced from the elements, and dz 

 may be expressed as a function of the eccentricity, node, and time, 



a sin I 



multiplied by the factor, which is constant for each orbit. 



Let V denote the velocity of light, v the velocity of approach of a 

 star, X the wave-length of a given ray of light, and I the corresponding 

 change it undergoes, due to the velocity. Then V-\- v:V=X-\-l: X 



or V = V-r; v and Fare commonly expressed in kilometers per 



second, I and X in ten-millionths of a millimeter; F= 300000. The 

 line F is frequently used in these measures, and for it X = 4865, Sub- 

 stituting these values, v = 62 ?. For the D line, X = 5900, and 

 since the interval between the two components equals 6, a velocity of 

 305 kilometers per second will be required to produce a deviation equal 

 to the interval between these lines. It will be more convenient to 

 measure the velocity of a star in terms of m, the annual motion, tak- 

 ing the distance from the Earth to the Sun as a unit. This may then 

 be reduced to seconds of arc, if tlie distance of the star is known, by 

 multiplying by the parallax p- Light traverses the distance from the 

 Earth to the Sun in about 498 seconds, or would traverse 63300 times 



this distance in a year. Accordingly, v =. 63300 — ; for the F line 

 V = 13 /, for the interval of the D lines, r = 64 Z. If / is positive or 

 the line moves toward the red end, it denotes that the star is receding 

 from the observer. We have thus two values of the relative motion of 

 the stars in the line of sight ; one, d z, deduced by computation from 

 the micrometer measurements ; the other, v p, or 13 I p, if the F line is 

 observed, found by the spectroscope. Equating these values, since p 



is the only unknown quantity, jo = \^- '^^® dimensions of the orbit 



a , .... 



are now found directly, since - will equal the semi-axis major in terms 



of the distance of the Sun from the Earth. 



It not uufrequently happens that we have an estimate of the differ- 

 ence in magnitude of the two components of a double star by one 

 observer using a telescope, and also an estimate of their combined 

 light by another observer viewing them with the unassisted eye. From 

 these data we wish to determine the brightness of either component 

 alone. Sometimes we have the opposite problem, given the magnitude 

 of tlie separate stars to find that of both, as seen by the eye or in a 



