193 
1907-8.] Dr Edward Sang’s Tables. 
part of the degree. These sines were computed directly from degree to 
degree, then for each quarter of a degree, using the multiples of 2 ver. 25', 
then to each 20th of a degree, and lastly to each minute. The work thus 
represents three independent computations. 
No. 45. Circular Segments. 
These circular segments are measured in parts of the surface of the 
circle as divided into 400 degrees of surface, and these subdivided into 
1 0000 0000 parts. They have been computed by the integration of the 
second differences of the sines measured in degrees, and are carried round 
the entire 400 degrees of the circumference. 
This table is intended to facilitate calculations concerning the elliptic 
motions of the planets ; it gives us the mean anomaly when the planet’s 
position is given, from the formula — 
Mean anomaly = J { segm (p + e) + segrn (p — e) } , 
in which p is the angle of position and e the angle of eccentricity of the 
orbit. (Also in transfer duplicate.) 
No. 46. Mean Anomalies (. A ). 
These are the mean anomalies in orbits of each degree of eccentricity 
from e = 0 c to e = 100°, given for each arc of position f rom p = 0° to p — 200 c , 
and carried to the eighth decimal place of the degree. 
No. 47. Mean Anomalies ( B ). 
In this volume the anomalies are given only to the nearest second, but 
the differences for a change of l c of position, and the variations for a 
change of l c in ellipticity, are filled in ; and thus, of the three — the 
eccentricity, the position, the anomaly — any one may be determined from 
the others. (Also in transfer duplicate.) 
31 Mayfield Road, Edinburgh, 
July 1890. 
Explanatory Statement from Miss Flora Chalmers Sang. 
“ 12 Marchmont Street, 
“Edinburgh, 20 th December 1907. 
“I desire to supplement the above documents with the following 
personal explanation. 
“ On the evening on which my father first brought his MS. Calculations 
VOL. XXVIII. 13 
