354 G. H. KNIBBS. 
this case therefore must be taken into account the values of X 
and Y in (46)§16. The appropriate observing programme is as 
follows :— 
Type 2. 
Morning Observations. 
Instrument N: read direction RO: put on dark glass : 
N Alt. 2’: leading limb, read direction and time: reverse instr. 
R ,, A’: following ,, remove dark glass 
- 
ae 
instr. being N, re-read direction R O: take means. 
Afternoon Observations. 
Instrument R: read direction RO: put on dark glass: 
R Alt. 4”: leading limb, read direction and time: reverse instr. 
N ,, A’: following,, ,, yy yy Femove dark glass 
instr. being N, re-read direction R O: take means. 
The azimuths are subject to no correction, for even though the 
contractions differ in the afternoon, the differences cannot sensibly 
affect the azimuths.! If the vertical wire be supposed to be inclined 
the amount x, similarly to FQ in Fig. 3, so that the upper part 
of the wire is to the right of the vertical, and the lower to the 
left, the correction to the mean of the zenith distances in the 
morning by (46) will be -sin x (c’—c”) 8,9,; and in the after- 
noon the same with the opposite sign, and with 8,0, in place of 
the last factor. Hence the total error d(’ of the afternoon 
observation, in zenith distance, may be regarded, similarly to (52) 
in the preceding case, as 
df =(c’ —e”) sin x (8,6, +8,9,)..» (56) 
The whole term is so small that we may generally omit the 8 8 
terms and write sin 2 as the factor instead of 2 sin x. 
The ¢ term must be taken into account as in the preceding case, 
since we employ the mean of the zenith distances. The total error, 
for which an azimuthal correction is required, i is consequently 
d(=d{'+ (r+e) (8,64 —Bi9, Dcvisepert (57) 
1 That the contraction terms in (46) for Y cannot have any appreciable 
ee eee ares. The terms § cos X sec h' ete. 
cancel one another. 
