166 G. H. KNIBBS. 



the impracticability of Herschel's graphic method when the 

 number of proper motions to be considered was large, and the 

 impropriety of assuming the point to be determined, he proposed 

 a method of rectangular coordinates, with a general weight 

 multiplier to be attached to any class of stars defined by brilliancy 

 or any characteristic, other than the magnitude of the proper 

 motion itself. His system of axes, identical with Biot's, was — x, 

 the sun's centre at a fixed epoch (an equinox); y, the point whose 

 R. A. was 90°, the xy plane being parallel to the earth's equator ; 

 z was parallel to the earth's axis and + to the north. The proper 

 motions reduced on this system were treated as chance quantities 

 by the theory of errors. Airy clearly saw that the probable 

 inequalities of motion, in the stars forming the cluster to which 

 we may be supposed to belong, limited in some measure the strict- 

 ness of this method, and he directed the attention of future 

 investigators to the point. He also considered the influence of 

 the systematic error, which may have crept into the computations 

 by which the proper motions themselves were determined. Those 

 used in his discussion, were taken from Main's papers in the 

 Monthly Notices and the Memoirs of the Royal Astronomical 

 Society, giving altogether the proper motions of about 1,200 stars, 

 from comparisons of Bradley's places computed by Bessel, with 

 the places given in the Greenwich 12-year, and subsequent 6-year 

 catalogues. 1 In the analysis, two extreme suppositions were con- 

 sidered : (a) that the irregularities of proper motion were entirely 

 due to chance errors of observation : (b) that they were due to the 

 motions peculiar to the stars themselves, the latter supposition 

 being regarded as in the main the true one. Airy was guided by 

 F. von Struve as to assumptions respecting the supposed relation 

 between the magnitude and distance of the stars. It is worthy 

 of special remark that he, Airy, seems to have been the first to 

 clearly recognise what may be called the relativity of the problem. 



1 Eev. K. Main — Proper Motions of 875 stars, etc. Monthly Notices, 

 Vol, x„ pp. 118, 122, (1850). Proper motions, Greenwich 12-year cata- 

 logue, etc. Memoirs, Vol. xix., (1851). Proper motions, Greenwich 

 catalogue of 1,576 stars, etc. Memoirs, Vol. xxvin., pp. 127- 142, 1858, 

 published 1860. 



