474 
as many observations were made as in the 1st, but this can only 
partially explain the great difference. Our results give as the mean 
error for the mean of 2 pointings L,R, after correction for division 
errors and flexure, for the two series + 2"09 and + 1"32 respectively 
and it is not probable that the uetual accidental errors would differ 
so much. Presumably, therefore, the somewhat great differences 
zg have cansed an insufficient elimination of the systematic 
errors in the mean results for the single positions. 
In the same way as previously (these Proceedings 4, p. 274, 
1901) I deduced the correction-formulae for systematic division errors 
and flexure for both series from the values for gy— gs. For the 
former I found 
1s' series + 3"69 sin (2u—154°5) 
2nd gg + 3"98 sin (2a—169°3) 
The two formulae agree sufficiently, but, as I mentioned before, 
the first formula does not agree well with the results of observation, 
which suggested to me a possible deformation of the circle; for a 
proper agreement another term dependent upon 4@ with a coefficient 
3/13 was necessary. but such a term can have little real significance. 
As, however, the formula for the 2"d series undertaken a year 
later agrees very well with the observations, and at the same time 
differs very little from those deduced from previous observations, 
my fear of a deformation of the circle must be regarded as un- 
founded. Probably the inequality of the zenith distances is the 
principal cause of the anomaly. 
For the flexure assumed to be proportional to sin z 
Ist series © z=—=— 0"04 sin 
2d series + 5.20 sin 2 
© 
was found. 
The two values are very discordant, and the result from the 
more accurate second series seems also to deviate very greatly from 
the earlier results; the divergence becomes less striking, if we do 
not assume that the influence of flexure must be proportional to 
sin z. I shall return to this and in general to the systematic errors 
of my instrument in section 4. 
In conclusion the most probable final result for the latitude of 
Matuba may be established. The 2rd series of observations [ also 
calculated in a different manner, correcting the single results according 
to my formulae and then taking the mean value from them. My 
final result now became —5°16' 59"13, exactly the same as that deduced 
above, a new proof that this time T had succeeded in arranging 
