216 C. Abbe on the Repsold Portable Circle. 
Assuming the 16 values resulting from the 16 pairs to be free 
from flexure, there results a probable error of latitude from 
one pair = +0'"35. , 
The difference of the latitudes resulting from the two stars of 
each pair depends upon the flexure of the tube and the error in 
the declinations, as well as upon any systematic error in the 
refraction or the graduation, though this is probably insensible, 
Assuming the latitude to be 59° 46’20’-00, we find the differ- 
ences from this to be represented by the formula 
(A.) 3/16 siu (z— 30°'3) ; 
applying this to each of the thirty-two observations, there results 
a probable error of a latitude from two stars +034. From the 
sixteen values of the flexures we derive a probable error result- 
ing from the error in the ephemeris and the error of pointing 
and reading; this is +0'"31. And subtracting the latter source 
of error, there results +0'"25 as the, probable error of the decli- 
nation in the British Nautical Almanac. 
The investigation of flexure might also be made by means of 
observations in the prime vertical, but here we probably have a 
complicated combination of flexure and personal equation. Eight 
determinations of time made by Colonel Smyssloff (each depend- 
ing upon eight pointings on each of a pair of stars observed in 
the 8 oie vertical), compared with simultaneous observations 
by Wagner at the Ertel transit gave 
Wagner—Smyssloff = — 08-02 4-05-03 ; 
the probable error of a single determination resulting ==0°09; 
or, if we allow equal accuracy to each instrument, the probable 
error of a clock correction given by the vertical circle =+0°V0. 
_ A series of comparisons between Messrs. Smyssloff, Bolscheff 
and Demetrieff, in which each observed four of the eight point 
ings gave, 
S.-D.= — 0*-098, S—B.==—05-046, B-D.=+40°132; 
robable error of a determination of time =+0*00, 
which in the latitude 60° corresponds to a vertical angle of 
+0/"45. 
As in the determination of latitude so in that of time, a pair 
_ of stars equally distant from the zenith is always observed, eac 
being pointed upon four times in each position of the circle, the 
eight pointings requiring twenty minutes or less. The stars are 
of course observed near the prime vertical, 
(To be concluded, ] 
