189 
1907-8.] Dr Edward Sang’s Tables. 
change, at the same time that each augmentation of our stock of 
data arranged in the ancient way adds to the difficulties. How much 
the change is needed may be estimated by an inspection of the Nautical 
Almanac. Every page in it cries out aloud in distress, ‘ Give us decimals.’ 
For the Sun’s meridian passage, the usual difference columns are suppressed, 
and those titled var. in 1 hour are substituted ; and similarly for the Moon’s 
hourly place a column titled var. in 10 m is given; while for the interpolation 
of lunar distances, proportional logarithms of the difference are given. 
While artisans and physicists are using the ten-millionth part of the Earth’s 
quadrant as their unit of linear measure, astronomers are still subdividing 
the quadrant into 90, 60, 60, and 100 parts. The labour of interpolation is 
unnecessarily doubled at the very least, and that heavy burden is laid on 
the shoulders of all the daily users of the ephemeris. The trouble attend- 
ing the reduction of observations tends to lead the navigator to shun the 
making of observations. The matter is not merely of national, it is of 
cosmopolitan interest — and this continuous waste of labour has much need 
to be ended. 
“The collection of computations above described contains all that is 
essentially needed for the change of system, as far as the trigonometrical 
department is concerned ; the great desideratum being the Canon of 
Logarithmic Sines and Tangents. In addition to the results being accurate 
to a degree far beyond what can ever be needed in practical matters, it 
contains what no work of the kind has contained before, a complete and 
clear record of all the steps by which those results were reached. Thus we 
are enabled at once to verify, or if necessary, to correct the record, so 
making it a standard for all time. 
“For these reasons it is proposed that the entire collection be acquired 
by, and preserved in, some official library, so as to be accessible to all 
interested in such matters ; so that future computers may be enabled to extend 
the work without the need of recomputing what has been already done ; 
and also so that those extracts which are judged to be expedient may be 
published. 
“ Seeing that the Logarithmic Canon is useful in all manner of calcula- 
tions, the printing of the table of nine -place logarithms might be 
advantageously proceeded with at once. The publication of the correspond- 
ing Canon of Logarithmic Sines and Tangents would only be advisable in 
the expectation of its early adoption by astronomers. 
“ But land-surveyors, when transporting the theodolite from one station 
to another, have to compute the new azimuth from the previously observed 
one. This is easily done by adding or subtracting 180° ; yet in the hurry 
