23

C—la.

Observations for azimuth are required at each base and at a number of intermediate stations. In order to eliminate as much as possible the effects of deflection of the plumb-line the fundamental azimuths on which the triangulation is to rest should be observed at all the trig, stations of a polygon at both bases. Similar remarks apply to the observations for latitude. Former observations at Taranaki, Wellington, Nelson, and Marlborough have disclosed a number of discrepancies which point to large deflections of the plumb-line, and further observations are required to ascertain the extent of the deflections. During the year Mr. H. E. Girdlestone has observed at the following geodetic stations : Ranganui, Pipipi, Maitaimoana, Tauakira, Aramaire, Tuku, Waverley, Kotawhiwhi, Omaranui, Momemome, Ikitara, and Mount Mitchell. Mr. E. J. Williams has assisted at the computations in a satisfactory manner, and now has a good working knowledge of the least-square adjustments of the triangulation. An example is given here showing the adjustment of a polygon by the method of least squares. In the figure the sides PPj., PP 4 , and the included angle at P are to be adopted as correct both in angle and distance. The observed angles are first tabulated in order (for method of observing see " Report on the Survey Operations " for the year 1911-12), with number of complete sets of observations, and observers initial given opposite each angle. The " spherical excess " is then calculated as follows : € 1 = double area in square chains x E: E being a geodetic latitude factor based on Clarke's 1880 Spheroid, and given in Tables of Geodetic Factors, Trans. A.A.A.S., 1904, p. 93. The summation error of each triangle is then found and distributed in the proportion of one-third to each observed angle. N

The next schedule shows the application of the adjustment. Column (1) contains the number of angle, (2) the observed angles corrected for one-third triangle error, (3) the centre spherical angles, (4) the correction to (2) for spherical excess, (5) the angles of the first computation, equal to (2) + (4), (10) and (11) contain the sines and value of 1" of (5), and with these sines the three triangles are solved.