of Edinhurgli, Session 1883-84. 
535 
tens ; and, moreover, the trouble of converting our confused measures 
into decimals exceeds that of the real business in hand. Every 
such conversion is a protest in favour of uniformity. 
Of all the affairs to which calculation is applied, trigonometry 
and astronomy have reaped most copiously the benefits of the 
Indian algorithm. We have only to compare the laborious process 
by which Archimedes determined the ratio of the circumference to 
the diameter of a circle, or the parallax and distance of the moon, 
to perceive how effectively the new numerals smoothed the rough 
road of alpha, beta ; iota, kappa. Yet, great as these benefits were, 
they failed to satisfy the growing needs of science. Each step in 
exactitude added to the toil of the computer, till, discouraged by 
the swelling crowd of multiplications and divisions, of proportions 
among the sines and cosines, the mean distances, excentricities, 
anomalies, and periodic times, Kepler began to despair of the future 
of his science. Can we, then, afford to mar these benefits by a 
slavish adherence to a scheme of subdivision, beautiful in its uni- 
formity, dignified by its age, but inept to the actual requirements 1 
The successive division by sixty, into parts of the first, second, 
and third degree of minuteness, dates back from before the reach of 
authentic history ; it speaks of a great advance and subsequent decay 
of knowledge, for the ancient stadium and the Chinese li agree, 
within an inch or two, with the third subdivision of the earth’s 
circumference in this progression. The convenience of its numer- 
ous divisions has, no doubt, helped to retain it in use. Sixty com- 
bines, in this respect, the advantages of ten and twelve, but is far" 
too large for numeration in the ordinary affairs of life. Its reten- 
tion in the measurement of time and angle is a great hindrance to 
our progress. 
In the exceedingly simple applications of trigonometry to land- 
measuring, we have very little to do even with the addition and 
subtraction of angles, nothing whatever with their ratios ; and thus 
the character of the subdivision has, comparatively, little import- 
ance for the surveyor. Yet even he would be much helped by 
the centesimal division of the quadrant. It is a long time since 
the division of the azimuth circle into four quadrants of ninety 
degrees each was discarded ; the bearings were then read, so many 
degrees to the east or west of north, so many degrees east or 
