of Edinburgh, Session 1879-80. 727 
observing that the area AOM is equivalent to ASQ, we have, 
denoting the segment AOM by m, — 
2 m — segm. (p + e) + segm. (p-e), 
and thus the determination of m from p, or of p from m, is to be 
accomplished by help of a table of circular segments, which must be 
measured, not in parts of the square of the radius, but in degrees of 
the surface of the circle. 
For the purpose of rendering this exceedingly simple formula 
available for actual calculation, a table was constructed of the sines 
for each minute of the quadrant, measured in degrees of arc ; by its 
help the values of the circular segments for each minute of the 
whole circumference were written out, true to within one ten- 
thousandth part of a second of the modern division. 
When we have got a tolerable first approximation, this table 
enables us to compute the position corresponding to a given mean 
anomaly by a simple proportion. 
In order to guide us to a first assumption, tables were con- 
structed of the mean anomalies corresponding to each degree of 
position from 0° C. to 200° C., and for every value of e from 0° C. to 
100° C., with their differences and variations, true to the nearest 
second ; and thus, in every possible case, the solution of Kepler’s 
problem is obtained in a few minutes, true to far within the 
hundredth part of a second of the new division. 
For the construction of these tables, one million six hundred 
thousand figures were written, and of these the three volumes placed 
on the table contain about twelve hundred thousand. If the 
ancient division of the quadrant had been used, the labour would 
have been more than doubled. 
8. The Discharge of Electricity through Olive Oil. By A. 
Macfarlane, D.Sc., and P. M. Playfair, M.A. 
9. Note on the Colouring of Maps. By Frederick Guthrie. 
From the Proceedings of the Eoyal Society of Edinburgh, 
No. 106, p. 501, it appears the colouring of maps is receiving atten- 
tion. This note bears chiefly upon the history of the matter. 
4 s 
VOL. x. 
