296 



SCIENCE. 



LN. S. Vol. XV. No. 3T 



On the Discovery of 300 Double Stars: R. 



G. AlTKEN. 



The writer's experience in observing 

 double stars led him to conclude that it 

 was desirable to make a systematic search 

 for new pairs. As a contribution toward 

 such a piece of work, 10,917 stars brighter 

 than 9.1 magnitude have been examined by 

 him since April, 1899, with the result that 

 301 new double stars have been found. 

 These all have distances between their com- 

 ponents of less than 5". 00, 217 or 72 per 

 cent, being closer than 2".00, and 19 closer 

 than 0".25. The search has been made 

 mainly with the 12-inch, telescope. The 

 zones examined also contain 530 stars 

 previously catalogued as double, but only 

 308 of these pairs are comparable with the 

 new pairs with respect to the angular sepa- 

 ration of their components. A new double 

 star has been found for every 36 stars ex- 

 amined and one star in every 18 examined 

 is double within the adopted limit. On 

 this basis it is estimated that more than 

 3,000 close double stars, within the reach of 

 the telescopes of the Lick Observatory, still 

 await discovery. 



A Kinematic Study of Hansen's Ideal Co- 

 ordinates: Kurt Laves. 

 In the ' Auseinandersetzung ' of Hansen 



the ideal coordinates are defined by the 



equations 





+ Y 



rf/3 



,dy 



„da' 



dt 

 dP" 



dt 

 ^dY' 



") /^! ?') '■■ t" ^^^ functions of the time, the 

 fixed coordinates xyz are connected with 

 the movable coordinates X, Y, Z by means 

 of the equations 



x = aX-\-(iY+yZ 



y = a'X+li'y-^yZ (2) 



z=a"X-\-P"Y-Yy'Z. 



Hansen joins to the conditions (1) the con- 

 dition : 



Z=0 (3) 



and obtains a well-defined system of ideal 

 coordinates. Hansen has shown that the 

 three homogeneous equations (1) lead to 

 the following theorem : "In every ideal 

 system of coordinates, referred to m.ovable 

 axes, the instantaneous axis of rotation 

 coincides with the radius vector, drawn to 

 the point." It is the intention of this 

 paper to show that the last condition (3) 

 will give rise to a kinematic theorem of 

 similar import. Indeed, when we consider 

 the three vectors, (1) the vector A of abso- 

 lute acceleration of the point, (2) the vector 

 of A''' of relative acceleration of the point 

 and (3) the vector A"' of the acceleration 

 of the movable system, we obtain for their 

 components along the fixed axis three equa- 

 tions, of which only one is written do^vn: 



■dX 

 dt 



da dY dji 



(4) 



' ^ \ dt dt ' dt dt 



^ dt dt )^^ 

 Calling the middle terms on the right sides 



Rx^ Jty, Mz 



respectively, and projecting them upon the 

 movable axis, we obtain 



Rx 



Rz = - 



dY 

 dt 



dZ 

 ' dt ' 



dX 

 " dt 



,dZ 

 , dX 



'i + HfP 



(5) 



p, q, r having their usual meaning, 

 will therefore be the moment of 



U = ■/ p2 + 52 + ,-2 



with respect to the point, which has for 

 coordinates the quantities 



dX 

 dt ' 



dY dZ 

 dt ' dt ' 



