ANNUAL ADDRESS OF THE PRESIDENT. LXIIl1 . 
passed. Probably the corrections found in the least square adjust- 
ment of extensive systems of longitude determinations afford the 
best criterion for estimating the accuracy of first-class modern time 
observations, and from them it appears that the error of such ob- 
servations may rise as high as + 0°05 of a second. 
During the intervals between successive observations of the 
heavenly bodies we necessarily depend upon clocks and chronom- 
eters for our knowledge of the time, and very erroneous ideas are 
frequently entertained respecting the accuracy of their running. 
The subject is one upon which it is difficult to obtain exact infor- 
mation, but there are few time-pieces which will run for a week 
without varying more than three-quarters of a second from their 
predicted error. As the number of seconds in a week is 604,800, 
this amounts to saying that the best time-pieces can be trusted to 
measure a week within one part in 756,000. Nevertheless, clocks 
and chronometers are but adjuncts to our chief time-piece, which is 
the earth itself, and upon the constancy of its rotation depends the 
preservation of our present unit of time. Early in this century 
Laplace and Poisson were believed to have proved that the length 
of the siderial day had not changed by so much as the one hun- 
dredth part of a second during the last 2,500 years, but later inves- 
tigations show that they were mistaken, and, so far as we can now 
see, the friction produced by the tides in the ocean must be steadily 
reducing the velocity with which the earth rotates about its axis. 
The change is too slow to become sensible within the lifetime of a 
human being, but its ultimate consequences will be most momentous. 
Ages ago it was remarked that all things run in cycles, and there 
is enough truth in the saying to make it as applicable now as on the 
day it was uttered. The Babylonian or Chaldean system of weights 
and measures seems to be the original from which the Egyptian 
system was derived, and is probably the most ancient of which we 
have any knowledge. Its unit of length was the cubit, of which 
there were two varieties, the natural and the royal. The foot was 
two-thirds of the natural cubit. Respecting the earliest Chaldean 
and Egyptian system of weights no very satisfactory information 
exists, but the best authorities agree that the weight of water con- 
tained in the measure of a cubic foot constituted the talent, or larger 
unit of weight, and that the sixtieth or fiftieth parts of the talent 
constituted, respectively, the Chaldean and Egyptian values of the 
mina, or lesser unit of commercial weight. Doubtless these weights 
