354 



KRETZ. 



The coefficients of y, K and P, denoted respectively by U, V, 

 and W, depend only on the time, and may be tabulated. This 

 is here done for' the epochs used by me. Signs at the top are 

 for the dates at the left of the table ; signs at the bottom are for 

 dates at the rieht. 





u 



V 



w 







U 



V 



w 





Epoch. 











Epoch. 











_+ 



- 



+ 





+ 



- 



+ 





1755 



120 



72.000 



1.728 





i860 



15 



1-125 



0.003 



1890 



1800 



75 



28.125 



0.422 





61 



14 



0.980 



0.003 



89 



24 



51 



13-005 



0-133 





62 



13 



0.845 



0.002 



88 



25 



50 



12.500 



0.125 





63 



12 



0.720 



0.002 



87 



30 



45 



10.125 



0.091 





64 



II 



0.605 



cool 



86 



1835 



40 



8.000 



0.064 





1865 



10 



0.500 



O.OOI 



1885 



36 



39 



7.605 



0.059 





66 



9 



0.405 



0.00 1 



84 



40 



35 



6.125 



0.043 





67 



8 



0.320 



O.OOI 



83 



42 



33 



5-445 



0.036 





68 



7 



0.245 



0.000 



82 



43 



32 



5.120 



0.033 





69 



6 



0.180 





81 



1844 



31 



4.805 



0.030 





1870 



5 



0.125 





1880 



45 



30 



4-500 



0.027 





71 



4 



0.080 





79 



47 



28 



3.920 



0.022 





72 



3 



0.045 





78 



50 



25 



3-125 



0.016 



1900 



73 



2 



0.020 





77 



55 



20 



2.000 



0.008 



1895 



74 



I 



0.005 





76 



1856 



19 



1.805 



0.007 



1894 



1875 







0.000 





1875 



58 



17 



1-445 



0.005 



92 













59 



16 



1.280 



0.004 



91 















- 



- 



- 



Epoch. 





- 



' 



- 



Epoch. 



Proper Motion. — Some catalogues take account of the proper 

 motion in reducing from apparent to mean place. As its value, 

 however, in general differs from that assumed in the present 

 paper, a correction to eliminate its effect must be introduced. // 

 being the proper motion as assumed by me, fi' that used in the 

 catalogue under consideration, and T^and t, as usual, the epoch of 

 reduction and the epoch of the catalogue respectively, we have 



Correction for erroneous /w= ( T — ^)(/^ — /^')' 



which becomes, for p.' = o 



It is not always plain whether a certain catalogue uses pro- 

 per motion in the reduction to mean place or not. I subjoin 



(14) 



