DIAMETERS. 



The equations deduced from measurement with the Santiago instruments may be slightly 

 improved by introducing the new-found values of v. The original equations of condition 

 derived from direct measurements were of the form 



when n represents the excess of the computed above the measured semi-diameters, 



The numerical value of the quantity \ ( d 2 # r ) is to be increased (since the value of v is in 

 both cases positive) by the amount 



f v = ft Am =. fi r = fj. -5J2- 



inasmuch as we may, without perceptible error, substitute for Am the computed semi-diameter. 

 The numerical correction having the same sign as the measured semi-diameter, it is clear that 

 the correction to be applied to n is negative, so that the corrected value will be 



, J_ 



A 

 and we find 



[ n'n' ] = [nn] 2[ew] ./*? + [ ee ] (/^f) 2 



For those equations which are derived from direct measurements, the case is not quite so 

 simple. We have in these instances 



n= it 5 (5 2 dj T D t d + r D t f 



and as before Am =r ^ (d t 5j). We cannot now so boldly substitute the computed semi-diameter 

 in the place of this quantity ; but a glance at the actual value of the new terms 



=F (r V t d -- D t p) 



will assure us that their small average value and constant change of sign render more precise 

 computation altogether needless. 



The normal equations for semidiameter derived from Santiago observations are therefore to 

 be modified by the introduction of n' instead of n; so that 



[dn ! ] =n' = [dn] [de] ^ 



[en 1 ] =. [en] [ee] /zj 



[n'n'] = [nn\ 2 [en] ^ + [ee] (//j) a 



The values of v, already obtained, were for the Santiago equatorial, +0".57, and for the 

 Santiago meridian-circle, + 0".39 ; whence, 



Equatorial. Meridian-circle. 



