474 
COAST AND GEODETIC SURVEY REPORT, 1904. 
The mean values for N may be converted into probable errors by the use of the 
table on page 435 of Wright’s Adjustment of Observations. The fourth column of 
Table IX has been so converted and is shown in Table X below. There is placed 
beside it in the fourth column of Table X the probable error reduced to angular 
15 
measure by multiplying it by the factor 
The fourth column indicates that for all 
sec S' 
stars of declination less than 58° the bisections were about equally accurate, expressed 
in angular measure, but that for the extremely slow stars of greater declination included 
in the last two groups the bisections are considerably more accurate. By inspection of 
Table IX, it may be seen that this statement also holds good for J. F. H. with the 
rapid speed of the driving heads. 
Table X. 
For J. 
F. H. with slow speed of driving heads 
The same ex 
pressed as an 
angular error 
Declination for group 
Mean colli 
mation fac 
tor for 
group 
Probable error 
of the sum of 
two records 
O 
O 
S 
ff 
2 to - 
-22 
I. 0 
±. 06 
±0. 9 
3 to 
l6 
I. 0 
. 06 
0.9 
17 to 
29 
I. I 
. 06 
0. 8 
30 to 
38 
I. 2 
.07 
0.9 
39 to 
46 
1-3 
.07 
0.8 
47 to 
52 
i-5 
.07 
0. 7 
53 to 
57 
i-7 
. II 
i. 0 
58 to 
64 
2. 1 
. 08 
0. 6 
65 or more 
3-4 
±. 14 
±0.6 
The mean value of Wfor J. F. H. with the slow speed of the driving heads is 11.7. 
This corresponds to the probable error of d=o s .07i for the sum of two records. For 
comparison with key observations the computation was made in precisely the same 
manner for the forty time sets involved in the determination of the difference of longi 
tude of Charleston and Key West in 1896 by Assistants Sinclair and Putnam, two 
observers of long experience. The probable error of the sum of two records was for 
that work found to be ±o s .077. This is in substantial agreement with the value shown 
above, ±o s .o7i for the transit micrometer. 
Most Favorable Speed of Driving Heads. 
If the speed of the driving heads is made very great, the observer will have diffi 
culty in making the moving line keep up with the moving star image, and this difficulty 
will be greater for the fast-moving equatorial stars than for others. The errors of 
bisection expressed in angular measure should be considerably greater for equatorial 
stars than for slow-moving stars under these conditions. 
If the speed of the driving heads is made very small, there will be no difficulty in 
keeping up with any star. A given error in the position of the driving heads at any 
instant will produce, however, a much larger displacement of the movable line in the 
field of view than when the driving heads are geared to move mudi more rapidly. 
The consequent difficulty in placing the movable line in a desired position will tend to