450 TRANSACTIONS OF SECTION E. 
lowed and the order of precision attained, more detailed treatment being confined 
to three matters which are engaging attention at the present moment, viz., the 
general question of periodic errors of instrument graduation; the relation 
between the height of an observed ray above ground surface and the coefficient 
of refraction; the third matter being a preliminary comparison of the geodetic 
with the astronomical latitudes, longitudes, and azimuth, for the purpose of 
estimating the relative forms of the surface covered by the survey and that of 
the assumed spheroid of revolution. 
The survey extends between latitudes 30° and 37° south and longitudes 
145° and 153° east, roughly including an area of 100,000 square miles. The 
fundamental object of the survey as a whole is to provide the positions of 
a series of points of sufficient accuracy to control the detail surveys made for 
the purposes of land alienation and administrative surveys generally and at the 
same time to facilitate map construction. Throughout the work, however, the 
necessity has been kept in view of observing certain chains of the triangulation 
with the greatest precision attainable not only so as to strengthen the remainder 
but to afford data for incorporation with other similar surveys in determining 
earth dimensions. It is this primary triangulation which the paper deals with. 
Base lines have been measured at Lake George and at Richmond, and the 
Paper refers to the need for further bases of verification owing to the exten- 
sion of the survey. In preparation for measurement of these, invar tapes have 
been lately obtained and standardised and the site of one further base (nineteen 
miles in length) determined on. The angle work has till recently been observed 
with theodolites (Troughton & Simms) of eighteen inches diameter read by 
four micrometers, but a 270-millimetre Repsold of the type used in the Geodetic 
Survey of South Africa has now been installed. For minor details of the 
methods of observing and reduction the Paper refers to one read by the writer 
in 1898 to the Australasian Association for the Advancement of Science, the 
methods there described having been continued. It will suffice here to state 
that the mean closing errors of the 171 primary triangles is + 0//-70 and that 
applying Ferrero’s criterion [m= (=5)'] the value of m is ascertained 
to be --0/-54, which indicates that the work is of a high order of precision. 
The purchase of the Repsold theodolite necessitated an examination of its 
circle errors which has resulted in a general discussion of such errors. This it 
is thought may be of interest and has already caused consideration to be given 
to the possible need for a change of observing routine. As already mentioned 
instruments read by four microscopes have hitherto been used. The Repsold is 
read by two microscopes. The mean reading of two opposite microscopes is 
affected by periodic errors, p, sin (2@+e€,) . . . .p,sin (27@+er), @ being the circle 
reading. If after an arc ‘ Circle Left’ the telescope is turned over and swung 
through 180 degrees horizontally to prepare ‘Circle Right’ the mean bearing 
of a signal derived from the combined observations will remain affected with 
these periodic errors. It is the practice on the survey to use five settings of the 
horizontal circle, each differmg from the preceding by 36°. The new 
instrument has furnished results showing the large range of 4/ amongst 
its bearings derived from the different settings. Although the means of bear- 
ings derived from the five settings are free from periodic error (other than those 
involving 100, 200, ... ., it has nevertheless been desired to determine 
accurate expressions for these errors for various reasons, and particularly with 
a view to estimating the accuracy of the graduation of the horizontal circle. 
An analysis shows how expressions for these errors may be determined from 
the observations of horizontal angles. From observations made at trigono- 
metrical station Rocks to 23 beacons the value —2/-19xsin (20-55°) has been 
derived for the first term, while from others at station Ovens to 17 beacons 
the value found is—2/”-11 sin(2@—53°). The terms containing 4@ and 6@ seem 
to have an amplitude of 0/-3 or 0/-2. Combining all the results yet available 
the correction to a microscope reading of the horizontal circle is, as far as 
has been determined, — 17-4 sin (8@+101°)—2’’-2 sin (28—54°)—1”-0 sin (38+228°). 
... There is no suggestion in this series that the amplitude of the term 
containing 10@ is of any importance, and it is highly probable that the five 
