COAST AND GEODETIC SURVEY REPORT, 1904. 
468 
or are merely residuals resulting from accidental errors. In Table III there are 5, and 
in Table IV, 9, out of 16 cases in which the value in the third column is less than its 
computed probable error. This corresponds fairly well with the number, 8 in each case, 
which should be expected if these values were entirely due to accidental errors. There 
is but one case in Table III and two in Table IV in which the value in the third column 
exceeds 3)4 times its probable error, as shown in the fourth column. This is a slight 
indication that the values in the third column are relative personal equations rather than 
residuals. 
It is a curious fact, for which no explanation is apparent, that there is no value in 
the third column of Table IV which is larger than the corresponding value in Table III. 
The relative personal equation of J. F. H., as compared with the mean of the 15 
other observers involved in the test, has been computed in three different ways: First, by 
taking the weighted mean of the 15 values involving J. F. H. in Table III, with 
weights depending upon the probable errors there shown; second, by taking the 
weighted mean of the values in Table IV, with weights proportional to the number of 
determinations as shown in column 2; third, by taking the indiscriminate mean of the 
values in Table IV. The three values thus obtained are respectively: 
Mean observer—J. F. H. = — o s .oo4 =fc o s .oo6 
“ “ —J. F. H. = + .009 =fc .009 
“ “ -J. F. H. = + .026 =b .011 
It is therefore uncertain whether there is a relative personal equation between the 
mean observer and J. F. H. 
The conclusion from Tables II, III, and IV must be that the relative personal 
equation between two observers with a transit micrometer is so small as to be masked 
by the accidental errors of observation, and that it is probably less in every case than 
o s .o5o. 
Two interesting contrasts may be shown between the values of the relative personal 
equation here derived from observations with the transit micrometer and those which 
have resulted from longitude observations with a key and chronograph. 
On pages 212-245 of Appendix 2 of the Coast and Geodetic Survey Report for 
1897, “Telegraphic Longitude Net of the United States,” there are shown 59 values 
of the relative personal equation derived from observations in the field, excluding 
European connections and certain cases in which the relative personal equation was 
determined in some unusual way. These 59 values involved 10 different observers. 
Each value is, in general, derived from ten nights of observation, and a total of twenty 
time sets by each observer, and is subject to a probable error of only from ±o s .oo3 to 
±o s .o2o. There are but 16 out of these 59 values less than o s .05o; whereas, Table III 
shows 9 out of 16 values smaller than this limit.* Similarly there are 41 out of these 
59 values greater than o s . 100; whereas Table III shows but 4 values out of 16 greater 
than this limit. Moreover, of these four values, three involved observers having no 
previous experience in this class of observations, and not one of the four is based on as 
much as two complete time sets by each observer. 
* The contrast is still greater if Table IV is used.