METHOD PURSUED. Ixxiii 



Putting the observed declination of the lirah = o, the computed declination of the centre = 

 <J , and the distance traversed by the micrometer thread =i Jm, wejiave the equation 



S d == J3 = - (f, + <J ff + O + + ,3 r + ;- r s + k ( + 5 -) + /; Jm (t + g) 

 or, written in another form, 



= w + ax + Z>y + cz + dt-r-c 



where ra = (J ?. + * ""o 3 



a= +1 x = a. 



b = ^(t-T) y = 20 ,9 



c = T ^(t Ty z =iooo r 



Of the eight terms composing the second member of this equation, the first consists of known 

 quantities, the next three, together with the last, are independent both of the instrument and 

 the observer, while t, u, and v are entirely local in their character. For errors in the adopted 

 star-places, of course no provision can be made, such errors combining with the errors of obser- 

 vation. 



In the equations for those observations in which (as should, of course, be the case, at least with 

 Mars,) the comparisons of the two limbs are nearly equal in number, and their means nearly 

 contemporaneous ; the terms containing t and u are eliminated from the resultant comparison 

 of the centre, and may be applied exclusively to the determination of the diameter, and of the 

 law and magnitude of the constants of irradiation. So, too, will the term /v be necessarily 

 omitted from the equations derived from observations not given with sufficient detail. And, 

 finally, the three terms dependent upon the error of the ephemeris would also have been elimi- 

 nated from those pairs of " correspondent" observations, for which it was the aim of the expe- 

 dition to provide materials, and by which each couple of comparisons with the same star, at 

 nearly the same time, in both a northern and a southern latitude, would furnish an independent 

 value for the solar parallax. 



The simple course thus indicated has been pursued in the present discussion, and appears to 

 be the only method practicable. Some of the more delicate refinements of reduction and com- 

 putation are necessarily excluded ; but the question may well be raised whether, under the 

 peculiar circumstances of the case, these would have added to the precision of the result had 

 their application been possible. 



To insure as great accuracy as possible for the data, the published observations, wherever, 

 and by whomsoever made, have been reduced anew ; beginning with the crudest form in which 

 they are accessible, and although the Santiago observations were furnished by Lieutenant Gilliss 

 in the printed sheets, as already prepared for the present volume, he has also courteously given 

 full access to the original manuscript note-books for all observations directly or indirectly 

 employed in these computations. 



Those observations which have been found available, and are employed in the discussion, are 

 shown in the annexed table, which gives the places of observation and the number of observations 

 of each planet diiring each series at the respective places. 



