TRIGONOMETRICAL SURVEY OF NEW SOUTH WALES. 215 
little liable to any appreciable change, it is thought the errors 
found in this particular screw might with advantage be brought 
under notice. It is clear that micrometers in frequent use need 
examination at short intervals. 
In the reduction of the value of the revolution of the latitude 
micrometer screw it was recognised at the outset that there were 
certain peculiarities which demanded that it should have more 
detailed examination than is usually needed. The work, though 
apparently most carefully carried out, evidenced the existence of 
systematic error, which depended on the part of the screw used. 
The results show that systematic corrections need to be made 
to the micrometer readings. Each observation of time, after the 
first one of each set, gives an equation of the form aa+by+n=o0 
where « is a correction to the initial observation and y is a small 
correction to an assumed value of the micrometer revolution. 
Substituting the resulting values in the observation equations, the 
residuals in the case of each set of observations exhibit changes 
of which the following, which are the residuals in the case of star 
Cape 1880, No. 6,703, observed 1896, February 19, are an 
example :— 
ee bee PhD iees 
33 —1:29 26) — 0:09 19 +0°83 12 -0°30 
32°5 — 1°40 25°5 — 0°31 18°5 + 0°36 11°5 0:00 
32 -—1°47 25 +0°76 18 +1°57 1] -0-22 
31-5 - 1:28 24°5+ 0°56 17°5+ 1°49 10:5 — 0°94 
31 -—1'52 24 +0°47 Lyf ap llezes 10 -—0-64 
30°5 — 0°67 23°5+1°17 1654117 9:5 —0°23 
30 +0:17 23 +0°06 16 +1-12 9° — 0:93 
29°5 — 1:09 22°5+1°40 15°5+0°52 8'5-—0°75 
29 —0°38 22 +094 15 +0°06 8 -1°86 
28:5+0°18 21°5+ 1°62 14°54 0°74 75 -—1°57 
28 -0°'59 PA SE IL 14 +001 US aleils 
27:5 -—0°76 20°5+0°81 13250219 6°5 — 1:33 
27 -0°45 20 +1-77 13 —0'14 6 —1°16 
26°5 — 0°41 195+ 1°69 12°5+0°80 
The systematic nature of these residuals is plainly visible and 
is Shown throughout the observations, the set given being merely 
typical of what is revealed by all. So definite a curve is shown 
by all that it was clear that a system of corrections of the form 
x (20—R)’ could be determined, which would fairly represent the 
observed facts. Such corrections have been computed, the con- 
stant x being found to be 0’:014. These corrections, required at 
each micrometer reading, are as follows, the first column giving 
the reading of the micrometer, the second the correction in are, 
