(V XVI 



EQUATIONS OF CONDITION 



The last column, H, shows the hour-angle at which the maximum value of r Dja attains the 

 limit O."03. 



Denoting similarly by D t S the variation of the planet's declination in 10 m , we may prepare 

 an ephemeris for D t 8, and our formulas assume the shape, 



0= 8. k*. 3 + 



y (t T) + *(< T)* + 

 sin - 



JOT 



in which the upper sign is to be used when the observation of the north limb precedes. 



The first term of the second equation will ordinarily be negative, since r is usually so small 

 that 2 T D, 8, the planet's motion during the interval, is much less than ^ (3" ff.) A convenient 

 form of the equation will therefore be 



in which we may avoid all need of attention to the signs offf'-ff and ^ ; and use, as before, the 



upper sign when the north limb has been first observed. 



The correction for defective illumination has, for simplicity's sake, not been introduced into 

 these formulas. When appreciable, it is to be applied with reversed sign to the value of the 



computed apparent sernidiaineter c, with which our formula assumes it to be merged. 



We have now the equations of condition, represented like those of 3. 

 = n + a.x + b.y -f c.Jt +/.v + gr.w. 



n representing in each equation the numerical value (c o.) 



The equations derived from direct measurements of diameters are obtained in the same form, 

 simply by making t = o; so that for these cases, 



1 



The " Additional Equations" of condition, derived from the differences of limb-measurements, 

 are given for each series and each observatory, and immediately follow the regular equations, 

 from which the quantities depending upon the apparent diameter have been entirely or chiefly 

 eliminated. They are arranged in the form of tables, which likewise contain the principal 

 auxiliary quantities employed in the formation of the coefficients. It will be borne in mind 

 that the declinations ff and 9' are supposed to be already corrected for refraction, and the tabular 

 apparent semidiameter to be corrected for defect of illumination. The quantity D^p is taken 

 into account in the computation of n. Those equations deduced from direct measurement of 

 diameter are given by themselves. 



