91 



3606 



92 



5. Formation of Normal Places. 



The horizontal lines ini the list of observations show 

 the grouping for the normal places. As a first approximation 

 all the observations were given unit weight and the simple 

 means were taken. The resulting normal place residuals in 

 the sense observation — ephepieris were found to be 



I 

 Ate 



— of 2 9 



— 0L29 

 0.00 



-I- 0|. I o 



-0105 



— 0.23 



— 0.20 



With these residuals as ordinates and the times as 

 abscissae two curves were plotted which were assumed to 

 represent the deviation of the ephemeris in a and d from 

 the observed positions. Then in order to gain some idea 



of the relative reliability of the different series of obser- 

 vations each observation residual was corrected by the ordi- 

 nate of the curve corresponding to the instant of obser- 

 vation, thus forming a new series of residuals which were 

 assumed to represent very approximately the actual errors 

 of the individual observations, the errors of the star places 

 being in general so small as to be negligible as compared 

 with the errors of observation. The observations were then 

 grouped in series according to the observer and the weight 

 I computed for each series by means of the formula 



/ = 





where // = number of observations in each series, f„ = mean 

 error of an observation of weight unity. 

 For this calculation assume 



£0 = +o?26 for a and rtz"? for 6. 



The following table shows the results of this calculation 

 and also the weights which were finally adopted. 



Observer 



Barnard, i 2 in. Equatorial 



Barnard, 36 in. Equatorial 



Bigourdan 



Brown, Hubb. and And. 



Cerulli 



Howe 



Javelle 



Kobold 



Palisa 



Searle 



Stone 



Wilson 



Comput. Wt. Adopted Wt. 



55 

 5-5 

 3i 

 10.9 



I 2.12 



•313 

 2.2 



3-3 

 2.2 

 I.I 



65 



0.6 



0.8 

 i.o 



0-5 



1.0 



Excepting observations 72 and 



» » 29, 



» » 60, 



» » 61, 



73. 



0-3 

 which give 



38 

 69, 



and 46, 



°-5 

 1 .0 

 0.8 

 0.6 

 0.2 

 0.8 

 1 .0 

 1.0 

 1 .0 

 ° 5 

 0-5 

 0.2 



°-5 

 0-3 . — 

 - , 0-5 

 03 , - 

 0-5 

 05 



0.8 



I.o'-') 

 0.2 



0.8 3) 

 I .0 

 1.0 

 I .0 



°5 

 °5 

 03 



1.0 



0.8 

 0-5 



reii 



101 



U 



ascension of 

 5 made by 



In this connection the residuals in right 

 the five observations Nos. i, 3, 5, 11, and 

 ]^>arnard with the 1 2 in. equatorial at Mt. Hamilton require 

 special attention. It will be noted that in the first normal 

 place these are the only observations giving rise to positive 

 residuals in a. The same is true of the second normal 

 place with the exception of observation No. 20 which gives 

 a small positive residual. After applying to the residuals of 

 the Barnard observations the' ordinates of the normal place 

 curve in the manner above explained the numbers repre- 

 senting the approximate errors of observation were 



-Ho'22 -Ho'77 +o^5S -Ho:53 -t-0^48 



The prevalence of positive errors of roughly the same 



order of tnagnitude would indicate the presence of some 



systematic difference in thesd observations as compared with 



those of the other observers ; but the other observations 



entering into these two normal places were made by several 

 different observers, and that a systematic error should exist 

 in all these observations is out of the question. Upon 

 request Professor Barnard kindly commtmicated the original 

 data for his observations and they were rereduced, but 

 without the discovery of any error in the published values 

 As to the possibility of his having made settings upon a 

 different point from the other observers Prof. Barnard writes: 



»The comet was a faint object, and it is perhaps 

 possible to have observed a different point from what others 

 observed. My recollection is that the comet had a faint 

 tail and a faint nucleus, consequently, unless it was well 

 seen — because of its elongated character — one might not' 

 observe the precise center of the head, but from the fac 

 that it was very small he could not be far out in his] 

 settings.* 



