1919 .] 
Astronomical Notes 
195 
into the blank space in fig. 1 ; the star-chart A is then hidden except for 
the oval portion, which appears through the celluloid window, and which 
represents the portion of sky which is above the horizon at the time 
indicated. 
To set the Planisphere . — Set the longitude of the place on B 2 to the 
standard meridian on C 2 and clamp B. Then set the date on A 1 to the 
time on B r The visible celestial hemisphere is then shown on A through 
the aperture in C. The local time is shown on C x opposite the time on B 1 . 
Thus by setting the longitude of Wellington, 174f° E., to Greenwich as 
standard meridian we can read both Greenwich mean time and local time. 
By setting 174J ° E. to the meridian for New Zealand standard time, 172J° E., 
we get the proper setting for New Zealand time at Wellington. This setting 
will show, for example, that 10 o’clock by New Zealand standard time is 
9 minutes past 10 by Wellington local time. 
In the particular planisphere which is here described the star-chart is 
constructed as a true perspective projection, so that the horizon, the 
ecliptic, and all the curves traced on the celluloid window are true ellipses. 
The centre of projection 0 is taken on the polar axis at a distance sec </> 
—i.e.j sec. 40°—from the centre of the sphere (the radius of the sphere being 
unity), so that the extreme parallel of declination, 50° N., is the line of contact 
of the tangent cone from 0. The object of this is to make the zenith 
lie as nearly as possible at the centre of the ellipse which represents the 
horizon. It can be shown that in order that the zenith may be exactly 
at the centre of this ellipse the distance /x of the centre of projection from 
the centre of the sphere is determined by the equation /x 2 — /*, sin </> — 1=0. 
Eor cjy = 40° this gives /x — 1-372, while sec 6 = 1-305. If this distance 
had been taken for the centre of projection the margin of the chart would 
have overlapped, the declination circle 50° N. being turned in and coin¬ 
ciding with that of 43° 36' N. Unless the latitude is greater than 45° it is 
impossible, with a true perspective projection, to have the zenith at the 
centre of the aperture. Even with this compromise there is the objection 
of considerable distortion at the margin of the star-chart. The following 
table shows the amount of distortion, and gives the ratio of the scales in 
B.A. and declination for various declinations :— 
Declination 
90° S. 
60° S. 
30° S. 
0° 
30° N. 
35° N. 
o 
O 
45° N. 
50° N. 
Ratio of scales 
1-00 
1-01 
1-09 
1-31 
2-32 
2-91 
4-12 
7-75 
CO 
It would probably be better, as is done in most planispheres, to sub¬ 
stitute for a true perspective projection an equidistant projection in which 
the meridian is divided uniformly in degrees of declination. In this case 
the distortion is shown by the following table :— 
Declination 
90° S. 
60° S. 
30° S. 
0° 
30° N. 
35° N. 
o 
o 
£ 
45° N. 
50° N. 
Ratio of scales 
1-00 
1-05 
1-21 
1-57 
2-42 
2-66 
2-96 
3-33 
3-80 
Up to about 32° N. the perspective projection is actually the better 
representation, but the equidistant representation has always the advantage 
that the zenith is at the centre of the meridian. 
D. M. Y. SOMMERVILLE. 
Victoria University College, Wellington. 
