1892. | Repetition of Angles. 65 
small in a good theodolite, and there is no apparent reason why it 
should vary with the nature of the observations. 
The repeating circle being a deservedly obsolete instrument the 
-errors by which it is affected need not be considered here. Besides, 
the classical researches on repetition, namely those of Struve 
(Astron. Nachr., No. 47, 1824), and of Bessel (Astron. Nachr., No. 
256, 1834, and Gradmessung in Ostpreussen, p. 73) had reference 
to observations taken with repeating theodolites, and it was the 
unsatisfactory character of the results obtained with theodolites 
that led ultimately to the abandonment of the method. 
Struve gives the following example of the differences obtained 
by using contrary rotations in the measurement of angles : 
With the graduation. Against the graduation. Diff. Mean angle. 
30°18°35°5 30°48°34°7 —0'8 30°48°35°] 
64°27°25°2 64:27°23°0 —2°2 64°27°24°1 
ole ol 2Oe4 31°51°24°5 —2°2 31°51°25°6 
73°22°38°1 73°22°34°2 —3°9 (a22-36)o 
159°29°58°8 159°29°57°7 —1l'l 159°29°58°25 
360° 0° 4:3 =: 35959541 2°04 = 83.59°59°59-2 
(mean) 
The differences between angles measured with and against tbe 
-graduation may be positive or negative. The table below gives, 
-according to Jordan (Handbuch der Vermessungskunde, p. 270.) the 
differences found in the angles of the triangulation of Baden, carried 
between the years 1823-1852. The number of repetitions was usually 
six ; the number of measures varied from one to four and was not 
_always the same for both series. 
KLOSE’S OBSERVATIONS. 
444 —0'] 43:5 424 
| 41:9 2+ ():9 
0:0 +0°5 +0°5 +1°5. | —2'0 —1lo 
0:0 3°] +04 050) | = (0F —4-0 
—4°8 , +01 JG StS 9-0 ee 
Sere eee Sh Asa): ey) H5A-0 18 
2D 0:0 +20 | 0-0 —16 
Pee | 4-22 eed. | + 0:8 —2°5 
41:9 44°] —2°3 | +0! 4 0°2 
{ 
