Ixxii GENEKAL STATEMENT OP THE PROBLEM. 



The problem before us is then to be distinctly understood as follows : The failure of northern 

 observatories to afford the means necessary for rendering the materials accumulated by Lieu- 

 tenant Gilliss, at Santiago, serviceable for their intended purpose, or, indeed, for testing the 

 method contemplated, renders the desired computations impossible, and their expected results 

 unattainable, so far as these relate to the measurement of the parallax, although, of course, of 

 the highest value for such purposes as demand no corresponding observations elsewhere. 



And what is now proposed is, to combine whatever other contemporaneous observations are 

 at hand with those of Santiago in such manner as to deduce a resulting value for the parallax, 

 without claiming for the results any peculiar pre-eminence, or for the method the advantages 

 which would result from the original plan. Should the value of the solar parallax thus 

 obtained coincide with Professor Encke's value, within the limits indicated by the probable 

 errors, the corroboration thus afforded by a method so widely different will not be without 

 essential importance ; while, in the event of the resulting value differing from that furnished 

 by the transit of 1769, the questions and investigations to which the discordance would give 

 rise could not fail to be of great usefulness. 



3.-METHOD PURSUED. 



Ephemerides of Mars and Venus being computed for the two oppositions with all the precision 

 which Lindenau's tables permit, the several declinations found at the several observatories are 

 to be compared with the ephemeris after the requisite corrections for defective illumination have 

 been applied. Each of the residuals will then afford an equation containing the following 

 unknown quantities : 



1. The semi-diameter at the unit of distance, which we call 



? = ?o + ^ (, 



where ? denotes the assumed value. The quantity f appears only in its function, the apparent 

 semidiameter, or 



A denoting, as usual, the distance of the centre of the planet from the centre of the earth, and i 

 denoting any spurious apparent extension of the semidiameter. 



2. The irradiation, i, assumed to be of the form 



*=A***% 



of which the term t'j is peculiar to the observer and the instrument. 



3. The correction q for the personal equation of the observer, and for the thickness of the 

 threads of the filar micrometer, the influences of these two sources of error becoming inseparable. 



4. The correction p to the adopted value of a revolution of the micrometer-screw. 



5. The correction of the ephemeris in declination 



(A 3J = + p T + r r% 

 T being the time elapsed since the epoch T, assumed near the middle of the series. 



6. The sun's equatorial horizontal parallax, which we will put 



(o- o denoting Encke's value ^'.STUG,) and which appears only in its function 



p = k*i 



where k signifies the ordinary coefficient for the error in parallax dependent upon the declina- 

 tion, the hour-angle, the distance, and the geocentric latitude i. e., if 0be the siderial time. 



p , sin. (3 r) 



-- L sin. <p' r^-y^ ; tan.C = tan. <f/ sec. (0 ) 



