476 
COAST AND GEODETIC SURVEY REPORT, 1904. 
Influence of. Errors of Right Ascension on the Results of the Test. 
The right ascensions of the stars used in the test were all taken from the Berliner 
Jalirbuch, and are therefore all well determined. The total number of different stars 
used was large, about one hundred. 
Moreover, the effect of the errors of right ascension upon the computed relative 
personal equation was eliminated, in part at least, by the practice of having the observer, 
J. F. H,, who observed every night, take, as a rule, stars of even numbers on the list on 
about half of the nights and stars of odd numbers on the remaining nights. The effect 
of errors of right ascension upon the results is therefore almost entirely eliminated from 
the mean values of the relative personal equation for those pairs of observers who 
observed on several nights. In general, the errors of right ascension have increased 
the range of the results, but have had little effect upon the means. 
For every star for which the residual on any night was as great as o s . 15, the resi 
duals for all the nights were tabulated. There were fifty-one such stars. The mean 
residual for each star, which is the best value which can be derived from these observa 
tions for the error of right ascension for that star, was less than o s .io in all but nine 
cases out of fifty-one. There was but one case in which it was greater than o s . 13. In 
this case it was o 8 .16. A careful examination indicates that, except for these nine stars 
out of about one hundred, the errors in right ascension were too small to be detected 
with certainty by the observations. The greatest error in the relative personal equa 
tion derived from a pair of time sets due to errors of right ascension is probably not 
greater than o s .o2, and in most cases is probably much less than this. 
It is a curious fact, of which no explanation is apparent, that eight of the nine 
stars for which a small error in right ascension was detected were stars which culminate 
north of the zenith. 
Number of Nights Necessary to Secure the Required Degree of Accuracy. 
Eet it be assumed that the required degree of accuracy is that which was obtained 
in the primary longitude net of the United States. In other words, let it be assumed 
that the future work is to be done with such accuracy that, if a longitude net were 
developed and adjusted, the corrections to the separate lines found to be necessary would 
be of the same magnitude as those in the present primary longitude net. 
The results of the test indicate that the possible relative personal equation between 
two observers which is liable to be encountered is so small that its possible variation 
may be left out of consideration. The test also indicates that there is no appreciable 
systematic error of any kind involved in transit micrometer observations. The problem 
in hand is, then, to determine how many nights of observation are necessary to reduce 
the effects of accidental errors to the required limit. 
From the fact set forth on pages 469 and 470, that the probable error of obser 
vation of a single star is from 50 per cent to 100 per cent greater with the transit 
micrometer than with the key, it might appear that from twenty to forty nights of 
observation would be necessary with the transit micrometer to secure the same degree 
of accuracy as was obtained from ten nights of observation with a key in the telegraphic 
longitude net.