72 ON THE LONGITUDE OF SEVERAL PLACES IN THE UNITED STATES. 



With the above value of §, the duration of the eclipse furnished for the 

 value of >7, 



At Princeton, . . 

 Germantown, . 

 Williamstown, 

 Washington, . 

 Philadelphia, . 

 Southwick, . 

 Weasel Mountain, 

 Burlington, . . 

 Haverford, . . 

 Dover, . . . 

 New Haven, 

 Alexandria, 



Mean of the tvirelve equations, 

 Mean of first six, " 



Mean of two means, . . . 



»(i) 



n 



(ii) 



^ 



(vi) 



= — 0-261 — 0-056 X n' 

 = — 2-255 — 0-053 X »?' 

 = — 2.875 — 0-022 X »?' 

 = — 2-798 — 0-022 X n' 

 = _ 3-534 _ 0-022 X n' 

 = — 3-941 — 0-017 X n 

 ^(vii) = _ 4-232 + 0-002 X n 

 ^(viii) = _ 4-468 — 0-001 X »?' 

 ^(ix) = — 4-472 + 0-015 X fi' 

 ^W = — 4-675 — 0-074 X n' 

 ^(xi) = _ 5-409 + 0-021 X n' 

 ,(xii) = _ 6-403 + 0-025 X »?' 



n 



n 



V 



= _ 3-760 — 0-017 X r}' 

 = — 2-611 — 0-032 X »?' 

 = — 3-185 — 0-025 X v' 



Whence ^ = — 3-198 



Applying these values of ?, )?, >?' to the equations derived from the Philadel- 

 phia observations, and assuming d equal to — 5h. Om. 39 "00 5., we have 



d — d'~b^ 



c^i 



32- 571 

 2-2035 



= — 14-782 



And making 



d = d' — 14-782 X a — 7-310 Y. b + 



1+ 0-5155 ^ '^ 



we derive the value of d, or the most probable longitude to be deduced from 

 this eclipse, as given in the table above. 



