1892. | _ Repetition of Angles. 
—~I 
er 
ee Error. Square. Lea aorta Error, | Square. 
1323 25 | + 85 | 72:25 | 43 7 30 | 412-7 | 161-29 
2 47°5 — 6°5 41°25 7 20 + 2°7 | Meg 
2 52°5 — 15 2°25 20 + 2°7 7°29 
2 45 — 9:0 81 1 es — 4°8 23°04 
SG) + 6°0 36 ls — 2°3 a2 
3 O + 6°0 36 PAB se (Ar 59°29 
3. 0 + 6:0 36 (fs —12°3 Tale29 
2 40 —140 | 196 1 TS + 02 0-04 
3 10 +16°0 | 256 ie 20 lost 2, 7°29 
2 35 —19°0 | 361 Mls — 23 Ses) 
By 295) + 3:5 12°25 PES + 52 | 27:04 
2 52°5 — 15 2°25 i 50 —12°3 | 151°29 
2 54:0 1192°25 ee Wie | 605°78 
(mean) (mean) 
i 
Taking the two sets together, in order to arrive at an estimate of the 
ordinary probable error of an observed angle, the sum of the squares is 
1797°98, hence the probable error of a single determination (mean of 
direct and reversed) is 
2 eras (UES) ooo 
If a@ the probable error of a bisection be taken at +0":80 for the 
instrument used, 6 the probable error of a reading becomes +6":04 
(a being small in comparison to 6,a small error in the estimation 
of the first scarcely affects the result.) 
The comparison of the corrections applied to the angles of the 
quadrilateral with the probable errors calculated, from the above 
values of aand 6, for angles obtained by direct and reversed series 
and double ead readings is shown below : 
Calculated prob. Mean of 
error. corrections. 
10 repetitions + 0°49 0°49 (mean of 7) 
20 repetitions + 0°28 0°25 (mean of 3) 
The corrections found requisite are thus well within the limits 
indicated by theory, and it is not unlikely that the unsatisfactory 
hiatus which has hitherto prevailed between the theory and the 
practice of repetition may be made to disappear by the adoptior of 
suitable instrume..ts and proper methods of observing. 
