392 ANNALS NEW YORK ACADEMY OF SCIENCES 



tions, Auwers assumes arbitrary and variable personal equations for the 

 different observers. Some of the more important of the fifty-seven personal 

 equations of the Greenwich observers as used by Auwers are given in the 

 following table. Under the head "First System" will be found the values 

 of personal equations as determined by Auwers in his first reduction; under 

 the head "Second System" will be found the variable equations used in the 

 second reduction: 



Table I. 



First System. Second System. 



^ ,. +0*084) ^^^ +0«.058—0s.006(t— 1860.5) 



Dunkin +0*02.5 (^^ 



Downing — 0«.023 —0«.010 + 0s.010(t— 1878.5) 



Thackeray H-0».03S — 0«.014 ; 



+ 0*.063r^^^ 

 Stone — 0».057 — 0*.135 > 



+ 0«.041 } 1863 

 Pead — 0».034 — 0«.035 ■> 



+ 0«.013i^^^^ 

 + 0«.221i +0S.2301 



H. Breen — 0».021 1 ^^^^ — 0«.02S i ^^^^ 



Criswick +0«.062 +0».061 



J. Carpenter — 0».095 — 0».099 



The dates following a bracket indicate the year in which an abrupt 

 change in personal equations was adopted. The system of equations 

 adopted for the vertical diameters was still more complicated; those of 

 Dunkin, Ellis, Criswick, J. Carpenter and H. Carpenter varying with the 

 time. The personal equation of Criswick contained a term involving the 

 square of the time, and that of Ellis showed an abrupt change in 1871. 

 Besides these, the equations of Lynn, Downing and Thackeray, show abrupt 

 changes. 



By using this new set of personal equations, Auwers was enabled to 

 reduce the apparent variations in the observations, so that all semblance 

 of periodicity disappeared; and, because the outstanding residuals are so 

 reduced, he concludes that this system best represents the observations, 

 and that the diameter of the sun is constant while the personal equations 

 of the different observers are variable. This may be the true explanation 

 of the observed discordances; but it is evident that, with a different sys- 

 tem of variable personal equations, an entirely different result could be 

 obtained. 



By similar discussions of all the various series of observations made 

 between 1851 and 1883, Auwers reached the conclusion that the meridian 



