1892. ] Repetition of Angles. 67 
adjustment of the instrument will be made up of the sum of the 
errors of each elementary angle divided by the number of repetitions. 
In each angle, it will consist of (a) error of collimation, (6) error due 
to inclination of the horizontal axis. ‘The first, which is expressed 
by + k' (cosec zg — cosec 2), remains constant for each angle, and 
its amount may therefore be simply added to the value obtained by 
repetition. ‘The second may he determined by reading on a striding 
level tle inclination of the horizontal axis in each different position, 
adding the corrections for each angle, and dividing by the number 
of repetitions. Or it may be calculated directly. It consists of the 
sum of the errors due to (1) the inclination of the horizontal axis 
relatively to the vertical axis, (2) the inclination of the vertical axis 
itself. Error (1) is given by 
+ h" (cot z2 — cot 21) 
Fig. 1. Fig. 2. 
To find error (2), let, in fig 1, Z be the point of a sphere where 
it is intersected by the upper vertical axis when levelled truly vertical, 
and JN, the intersection of the lower vertical axis. By rotation about 
the lower axis, Z will describe the small circle ZZ,Z. Call B the 
angle B,ZB, under repetition, A the angle B,ZN, and 2" = ZN, 
- the inclination between the vertical axes. 
In fig. 2, (ut B'|Z,Be be the angle B at the second repetition ; it 
is then equal to. ZNZ,, Z remaining the vertical throughout, draw 
_ the perpendiculars ZP = d, and ZQ = d, equal, respectively, to the 
inclination of the horizontal axis due to that of the vertical axis, for 
~ OB 
