( 42<S ) 



tr;msil (»\'er llic middle tliivad should lake place nxm'v near ihc middle, 

 tlie transits over the otliei' threads were ohserxed on either side of' 

 it. it niav he easily slio\\ n. however, that in the present ease no 

 appreciable errors can arise from this. 



in th(^ lii'st place we sludl show that e\'eii the (M-rors in tjie ahso- 

 Inte zcjiith distances g-enerally will he small. l»y the symmeti-ical 

 arranti'einenl of the ol)ser\ati()ns, the inHnence of" an inclination of the 

 I'eticnle as a \\ hole will he eliminated from the mean resnlt and 

 the intlnence of the cnr\atni-e of the parallel of altitude ^vill always 

 he small for my observations. A\ a horizontal distance c from the 

 middle of the tield the influence of the cnr\atui'e of the parallel on 

 the zenith distance is : 



1 . 



A r = — <•'■' c<>f(i. : xiii 1" 

 2 



Now the pro[»ortio]i of the hoi'izontal to the vertical motion, putting 

 for the parallactic angle ^>, is cotj/. [j, and for a transit over a thread 

 at a distance / fVom the middle thread the cori-ection of the zenith 

 distance will be 



A^ = — /'" rof(r p cotq z sin 1" 

 2 ■ 



while the extreme threads ai-e at distances of alx>nt IT"* or 250" from 

 the middle thread. In one observation, tiiat of 1901 Febi-. 25, \vhich 

 owing to the inifavonrable i-elative ])ositions of the moon and the 

 star ])erhaps had best l)e excluded, the value of <"('///. /> was 0.(58, 

 while for the rest its greatest value amoiiuted to 0.34 and it was 

 generally nuich smaller. In the uiost nnfavourable case, therefore, we 

 have for the extreme threads <■ = 170" and A: = 0".08. Tn all the 

 other observati<nis we have always A: <^ 0".02. 



The inlluence on the dillereuce between the zenith distances of 

 the moon and the stai', however, is nnich smaller still, as the moon 

 and the stai' always differed little in declination and hence at the 

 nn)meins of the ol)servalions wci-e at about the same ]»arallactic 

 angle. The dilference between the juirallactic angles was, excluding 

 the obsei'xatiou of 1901 Fein-. 25. foi' which p — y/=:7^ in maxinio 

 l)°. So the inlluence of the cur\ature of the pai'allel is almost entirely 

 eliminated iji the results of the observations. The same is the case 

 with the inlbuMice of the inclination of the indixidual threads. 



That 1 did uoi follow the star in azimuth has therefore had no 

 injurious consecpiences and uo coi-rec(ions are reipiired. ()n the other 

 hand the consequence may ha^•e been that the stability of the instrument 

 during each transit was greater. 



