54 CATALOGUE OF STARS WITHIN 
LV. 
FINAL STANDARDIZATION. CATALOGUE. 
It now becomes possible to make use of the preceding inter-adjust- 
‘ment to obtain a more complete agreement with the sky by reducing 
the right ascensions and polar distances of the standard stars as ob- 
tained from the several plates to the system of some one particular 
plate and comparing the results thus deduced with the heliometer 
places as in the first determination of the plate constants. (Cf. Col. 
Con. no. 21, p. 74.) The go° plate was selected as the medium of 
comparison and the eight 89° plates were reduced to its standard. 
This was performed by substituting the last eight values from Table 
XII in equations (2) for such of the reference stars as appeared on 
the respective plates. Since the signs of the quantities as they stand 
in this table give the results which must be added to the 90° plate to 
produce agreement with any 89° plate, therefore the corrections 
obtained above must be subtracted from the a’s and z’s of the 89° 
plates to produce agreement with the go° plate. This was accord- 
ingly done and the resulting right ascensions and polar distances 
were compared with the heliometer positions. The differences, 
Photographic minus Heliometer, were inserted in equations (2), and 
a least squares solution gave the corrections to the plate constants 
of the 90° plates upon which the improvement of the entire system is 
based. Equations (2) are then of the form 
w sin ad — w cos ady + pdA’ + da sin zx = 
—w cos ad§ — wu sin ady + pdw + dr =o, 

O, 
in which the photographic place has been reduced to the go° standard 
as just described. The quantities forming the last terms of these 
equations were taken from the values of which Table VI is the mean. 
They are in the sense Photographic minus Heliometer. The dis- 
tribution of the standard stars was such that 124 equations were 
available for the least squares solution, and the following differential 
const ants are the resulting values: 
mm, 
d= = -++ 0.0006 + 0.0005,, 
mm. 
dyn = -+ 0.0033 + 0.0005 , 
" 
dA’ = — 0.0019 + 0. 0004 , 
Ld 
dw = — 0.0013 + 0.0004. 
