OF ARTS AND SCIENCES. 83 



Argelander's 390 were observed by himself for the modern determi- 

 nation, and with very great accuracy. 



Lundahl's investigation is based upon the 147 stars which Pond had 

 observed, and Argelander not, and whicli exliibited proper motions 

 exceeding 0".09 yearly. 



Galloway used 81 stars from the southern hemisphere ; this investi- 

 gation alone employs an old authority (Lacaille) independent of 

 BesseFs Bradley. 



A later investigation by Miidler takes account of the motions of all 

 the stars (3,222 in number) found in the Fundamenta Astronomiae of 

 Bessel, as observed by Bradley near the epoch 1755. Miidler employs 

 the same method of deducing the apex of solar motion as Argelander 

 and the others ; and his proper motions of the stars were obtained by 

 himself from a discussion of all available observations. The task 

 seems to have been too vast for his strength, as his proper motions 

 are often erroneous ; nor does he appear to have subjected the observa- 

 tions, to the careful criticism which Argelander has always emploved. 

 Hence the errors of observation are often treated as proper motion by 

 him, as happens more unifoi'mly in the thoroughly worthless values 

 contained in the British Association Catalogue ; a work which has 

 served a good purpose as a working-list, but in other respects has re- 

 tarded rather than advanced our knowledge df star-places. 



Miidler's results are: ^ = 261° 38'.5, I> = -{-3d° 53'. 6. 



All these discussions of the solar motion are based upon the appar- 

 ent proper motions of the stars : these are caused by the real motions 

 of both sun and stars ; the latter element is considered to follow the 

 law of casual error, and takes the place of error of observation in the 

 discussion. The special method consists in assuming the pole of solar 

 motion, determining from that in what direction each star should 

 move if its own motion were zero, and comparing this direction with 

 the observed ; then, by the application of conditional equations and 

 the method of least squares, corrections are found to the assumed 

 pole. 



II. To this process Sir George Airy objects : — 



1. That we are not sure of even the rude accuracy of the first 

 assumption. 



2. Therefore our differential equations will not hold good. 



3. And, if they did, the resulting error might change per saltum 

 from -|-179° to — 179° by a small change in the assumption; ren- 

 dering it far from clear whether the method of least squares could 

 properly be thus applied. 



