390 REPORT OF THE COMMITTEE ON THE 



Note hy the Committee. — The latitudes and longitudes of the Ame- 

 rican places of observation, reported by the committee, are the result 

 of the most recent determinations, and differ, in some instances, from 

 those furnished at an earlier date to Mr Rumker. 



Letter of Mr Sears C. Walker. 



Philadelphia, July 10, 1839. 

 To the Committee on Astronomical Observations. 

 Gentlemen : 

 Being desirous of deducing the longitudes of the American places 

 of observation from Rumker's expressions for the mean time of con- 

 junction, I have formed thirty-eight equations of condition, from the 

 duration of the eclipse, by subtracting the expression of the conjunc- 

 tion-time derived from the end from that furnished by the begin- 

 ning, and in a similar manner have obtained seven equations from the 

 observed duration of the ring. Of the last I reject that which is derived 

 from No. 44. I thus find by 



^(O— D) ^fi ^-^ 



No. (12) — No. (14) 

 No. (41) — No. (18) 

 No. (33) — No. (35) 



whence, 



= — ■ l"-08 + 0-0504 — 1-3730 — 0-3630 

 = — 3 -65 — 0-5063 — 0-8249 + 0-5336 

 = + 7 -60 + 0-6563 — 1-8772 + 0-3036 



(a) A^ = 0-7044 + 0-0492 X a(o — ])) + 0-1163 X a ^r 



Substituting this value in the seven equations of condition from the 

 duration of the ring, we have from 



No. (12); A (O— 3>)(°) = + 0"-030 + 0-0606 X A^r 



No. (14); A (O— ]))('> = -— -429 — 0-0569 X A !r 



No. (33); A(0 — D)^"^ = —0-501 -f 0-0812 x a ^r 



No. (18); A (o — 3 )("■)= +0-814 + 0-2966 x a ^r 



No. (35); A(Q__5)('v) = + -869 — 0-0718 X A ^ 



No. (41); A (o — !))(''> = +1-626 + 0-2490 X a «• 



No. (44); a(0 — d)(") = —3-161 + 0-0644 X a jt 



