DEPARTMENT OF MERIDIAN A8TROMETRY. 195 



The results for Clamp West are just as systematic as those for Clamp 

 East, but are omitted for the sake of brevity. 



FURTHER INVESTIGATIONS DEPENDENT UPON PARALLAX. 



In Astronomical Journal No. 707 Dr. von Flotow^ has shown the 

 existence of two velocity-planes. As systematic errors of observed 

 parallaxes and radial velocities have not yet been carefully discussed, 

 additional material will not lend much strength to the discussion. 

 He therefore considered it best to further develop the parallax problem 

 in its relation to the two velocity-planes, illustrating the methods by 

 means of the 116 stars. 



Not knowing the physical characteristics of the two planes, there 

 is no criterion, in ambiguous cases, to decide in which plane the apex 

 belongs; but studying the computed corrections of parallaxes as they 

 are given by (57r)o and its variation (57r)i, it is possible, in a few cases, 

 to decide whether a given stellar apex belongs to Plane I, to Plane II, 

 or has to be rejected. In this way he obtained a sUght alteration of the 

 two groups. 



Group I. Rejected 1, added 1 

 Group II. Rejected 1, added 3 

 A solution of the corrected groups leads to the following corrected 

 coordinates of the two planes: 



Plane I(32apices) 7i = 192?80=t3?48 ki = +32?55±2?31 



Plane II (31 apices) 72 = 146. 34±5. 84 /C2= -48.89±3.87 

 These values showing little tendency toward better agreement of the 

 mean errors or of the condition of perpendicularity as given by 



tan Ki+cot K2 cos (72 — 71) = +0.0371 

 are taken as a basis for further investigation. 



Newcomb's analytical treatment of three perpendicular principal 

 planes, given in his "Contributions to Stellar Statistics" (Carnegie 

 Inst. Wash. Pub. No. 10), suggests the hypothesis of a third plane per- 

 pendicular to the two given above. Consideration of this hypothesis 

 shows the following distribution of the apices of 89 stars, which may be 

 classified as belonging to one of the three planes: 



Plane 1—46 p. ct. Plane 11—46 p. ct. Plane III— 8 p. ct. 

 The given data show little evidence of the existence of a third perpen- 

 dicular plane. 



Considering all the elements entering in the parallax problem, two 

 are vital and direct further investigation: (1) the influence of the as- 

 sumed solar motion; (2) the influence of the partial differential coejffi- 

 cients of the position angle. 



The derivation of the coordinates of the two planes given above was 

 founded on L. Boss's solar apex A = 270?5, D= +34?3, and on a value 



^ A member of the observatory staff from January 25, 1915, to May 1917. 



