OP ARTS AND SCIENCES. 349 



Applying, then, the correction -|-0^24 to the Jahrbuch position for 

 1883.0, but adopting the first hypothesis, that the personal equation is 

 directly proportional to sec. 8 and overlooking the difference of equi- 

 nox with G. altogether, we find 



B. — G. Aa cos 8 (in mean) = +0^024 ; 

 probable error of one star = ±0*.010. 



On the second hypothesis, that the constant error is due to clock 

 correction, but omitting its uncertainty in calculating the probable 

 error, that is, multiplying the individual residuals by cos 6 before cal- 

 culating their sum of squares, we find 



B.— G. (Aa) = +0^36 ; p. e. of one star € cos 8 = ± 0\007. 



For both B. — G. and S. — G. this hypothesis is rather more favor- 

 able than the other, but the evidence is yet far too scanty. 



In fact, one object of tiie present publication is to induce the collec- 

 tion of more observations of these stars, and others at a somewhat 

 greater distance from the pole. I find incidentally that a considerable 

 portion of the stars of the present catalogue are now elsewhere in 

 process of observation. 



A form of personal equation has lately been noticed by Mr. Gill, 

 which has some bearing hei-e, — the difference in clock correction as the 

 star seems to move eastward or westward. Of this I have as yet but 

 trifling indications in my own case. As its cause is probably identical 

 with that which makes it difficult to bisect au interval by the eye 

 when the objects are at rest, it will have no more effect on the time 

 of transit of a polar star than on that of an equatorial one, but will 

 tend to produce difference (as Mr. Gill has found it to do) between 

 the clock corrections from stars north and stars south of the zenith ; 

 it will also tend to produce difference between the resulting right 

 ascensions of stars from observations above and below pole. This 

 last difference I have found for these declinations to be imperceptible; 

 but the half-difference of clock corrections is yet to be applied, as all 

 my clock stars have been south of the zenith. So that the personal 

 equations derived from this cause are probably either too small to be 

 sensible in these declinations, or are merged in the form of personal 

 equation discussed above. 



