The geographical coordinates thus found were plotted directly on to the plane-table sheets, on which the graticule at 10′ intervals was the first thing drawn. The odd minutes and seconds were first converted into minutes and decimals, and then into kilometres by multiplying by the factors appropriate to the latitude, so that the plotting could be done by the ordinary scale of kilometres. To avoid difficulties of paper-shrinkage, as many points as possible were plotted at the time of drawing the graticule, and in general the points had to be plotted as far ahead as possible for controlling the traversing and sketching. =Astronomical Observations.=—Astronomical checks on the triangulation were obtained by observations of latitude at certain selected main stations 60-120 kilometres apart, and by azimuth observations for certain main lines. The method used for =latitude= was that of observing the times of equal altitudes of three or more stars, selected as near to the meridian[64] as possible. This method presents great advantages over the usual _Polaris_ and circummeridian altitudes, in that the observations are more easily made, and yield much more accurate results, because uncertainties in refraction are largely eliminated and the errors of circle graduation are not involved, the altitudes not being read at all.[65] The theodolite used was the same as was employed in triangulation, and the times were taken by a half chronometer watch, preferably one marking sidereal time with a rate which could be considered negligible during the hour or so occupied by the observation. The first star taken was usually _Polaris_, and the vertical circle was left clamped at its altitude. For the other stars, any dislevelment was corrected by touching up the levelling screws just before the instant of observation; this was found better, than taking bubble readings and correcting for slight difference of altitude. The method which I found best in the field for reducing the observations differs somewhat from that described by Chauvenet. Assuming approximate values for the latitude and watch error, I first calculated the altitude of each star from the formula sin _h_ = sin φ sin ε + cos φ cos δ cos _t_ If the assumed latitude and watch error were correct, all the stars would give the same value for _h_. If not, each star would give an equation of the form _h_ + cos _A_ _d_φ + cos φ sin _A_ _dT_ − _h_0 = 0 where _A_ is the star’s azimuth, _d_φ the required correction to the assumed latitude, _dT_ the required correction to the assumed watch times, and _h_0 the true altitude common to the three stars. The values of cos _A_ and cos φ sin _A_ were calculated from the ordinary formula sin _A_ = (cos δ sin _t_)/cos _h_