EQUATIONS OF CONDITION. CCXV 



All these " Additional Equations" are numbered like the rest, the same number being prefixed 

 to those equations which are derived from the same observations. 



It is thus rendered manifest that the term under consideration could not, even for Venus I, 

 amount to so much as 0." 01 for r 33, an interval many times exceeding the largest value of r. 



In the second equation there remain the terms rD,d a and T.D t k.~ir a = rZ> t fca- = rZ> t jo, or 

 the variation of the parallax during the interval. 



Our equations thus assume the form 



= <? jfc. 3+ x + y (t T) + z (t T^ + fi Jm ktw. 



= [ i (if' - d') - rl?A + rD t p | + g + ft + q) + i (ip + f.) 



the upper sign holding when the north limb is first observed. 



Let us now develop the term D t p, the first difference of the parallax in declination for an 

 interval of one day. 



We have for the time t, 



p = & -r- p \ sin if' cos d cos <p' sin d cos (0 a) | 

 and for the time t =h l h , 



p i = ar -r- p \ sin <f' cos d cos if' sin d cos (6 ) cos 15 cos if/ sin 8 sin (0 ) sin 15 ( 



The mean of the deduced variations for the hours immediately preceding and following the 

 middle time t gives us the hourly variation corresponding to that instant, 



Jp = sin 15/> cos if/ ^-r- sin (0 a.) 



The quantity -^L. varies between narrow limits during each series of observations, and p cos <p' 

 is also not very different for the several places of observation. Substituting, then, in the expression 

 for Ap the maximum value of the compound factor p cos <p' - for each series, we readily obtain 



closely approximate values for the maximum hourly variations of the parallax in declination. 

 These are thus seen to be 



for Mars I., + 1".41 sin (6 a) for Venus I., 2".77 sin (0 a) 



Mars II., + 1 .14 sin (6 a) Venus II., + 1 .64 sin (0 a) 



This term will consequently be sensible for Venus, and in some cases also for Mars, although 

 this planet was almost uniformly observed within two hours of the meridian, excepting at 

 Cambridge. 



Inasmuch as r seldom exceeds 3 m , and only once or twice amounts to 5, we shall find it con- 

 venient to introduce the entire interval t" t' =2 IT, and to express it in decades of minutes as 

 units. Then putting /\p = the variation of the parallax in declination during 10 m , we have, 



\ D t p = + i -. sin 2.5 p cos f/Sl sin (0 a) = * SJ sin (0 a), 



and shall find for the several observations which have contributed extra-meridional observations, 

 the following values of the constant *. 



Place. * log. * 



Santiago ..... + 0".156 9.1935 



Washington .... .146 9.1634 



Cape of Good Hope . . 0.155 9.1910 



Greenwich .... .117 9.0669 



Cambridge .... +0 .138 9.1408 



and the following maxima of * ^5J? for the Santiago series. 



