536 
Proceedings of the Royal Society 
west of sontlij the same number of degrees indicating four 
different directions. The awkwardness of ' this is obvious to us ; 
division into two parts of 180° each was substituted, and this again 
is now superseded by the graduation all round to 360°, so that a 
number applies to one direction only ; this gives great clearness to 
the field operations. Having observed, from the station A, the 
bearings of various signals, among others that of the station B, 
and having carried the theodolite thither, we wish so to plant it as 
that it may again indicate the bearings of other signals. For this 
purpose we so place the azimuth circle as that, on looking back to 
A, the reading may be exactly the opposite of the previous reading 
from A to B. As the seamen phrase it, we must box the compass ; 
we have to add or subtract 180“ as the case may be. 
In computing the co-ordinates of the stations, by help of the 
traverse table, or by the logarithmic process, we have to note the 
change from addition to subtraction at 90°, 180°, 270°, 360°, and 
have to pass from the top to the bottom of the page at 45°, 135°, 
225°, and 315°; changing sine into cosine, difference of latitude 
into departure. Whereas, wdth the centesimal division of the 
quadrant, the changes are at the hundreds and fifties, while the 
opposite directions differ by 200°. The improvement both in 
comfort and in freedom from mistakes needs not to be insisted on. 
In astronomical work, the awkwardness of having two numerical 
systems is conspicuous. We observe a planet’s opposition to the 
sun, and again another opposition ; the interval of time is noted in 
days, hours, minutes, seconds ; the change of longitude in signs, 
degrees, minutes, seconds ; and thence, roughly, to compute the 
periodic time we have to make a proportion. If we had been 
habituated to count in sixties, and if the number 24 had not 
occurred, the calculation in sexagesimals would have been the 
natural one ; our logarithms would, according to Nepair’s own 
opinion, have had 60 for their basis, just as now they have 10. 
As things are, no one can make the calculation. We must turn the 
times and the angles into decimals, taking the day or the second as 
the unit of time, the degree perhaps or the second as that of angle ; 
without decimals we are unable to move a single step. 
How these divisions are made for the purposes of calculation; 
intrinsically it is of no moment which way we count, the planetary 
