a0 
id 
4. Systematic errors of the universal instrument. 
a. Division errors. 
I put together below the formulae found in the different series 
of observations for the correction which must be applied to the 
readings « of the vertical circle of my instrument on account of 
the systematic division-errors. I confine myself everywhere to the 
terms in 2a. 
Chiloango 1900 —01 Aa = + 4'74 sin (2a—169°2) 
jn 1903 + 5.15 sin (2a—175.4) 
Matuba 1913 + 3.69 sin (2a—154.5) 
Cabinda 1913 + 2.57 sin (2Qa—171  ) 
Matuba 1914 + 3.98 sin (2a—169.3) 
If we take into consideration the lesser accuracy of the results 
of the 1s* series at Matuba and of the observations at Cabinda, the 
agreement of the 5 formulae may be considered satisfactory. That 
in the division errors a term occurs of the assumed form with a 
coefficient of about +4” may be considered as proved and there is 
no reason to suspect any change with the time. That these errors 
are fairly large, is not surprising either, when we consider that the 
radius of the circle is only 70 mm. . 
Of course the values calculated from this will not represent the 
full amount of the division errors. At the same time the results of 
the most accurate series Matuba II do not point to large residual 
values. Whereas a comparison of the mean results for each posi- 
tion $ (Py + Py) with their mean value here leads to a m.e. of 
+ 0'66, the me. is a 0"82 according to a comparison of the 
Ly ear with the formula including the flexure. 
= \ 
bh. Flexure of the telescope. 
In the table below are given, instead of the previously deduced 
coefficients of siz, the values of the flexure of the straight tele- 
scope (which thus represent the differences of the flexure of the 
objective and ocular halves) directly determined for the mean zenith 
distance of the series. 
Chiloango 1900—01 z= 53° Az= — 0"48 
is 1903 49 — 1.33 
Matuba 1913 52 — 0.04 
Cabinda 1915 44 + 1.24 
Matuba 1914 30 + 2.62 
4 
