of Halley's Comet at its last Appearance. S9 



atlons of the elements themselves were not considered as un- 

 known magnitudes, but the quantities w, x^y, z, 7c, v, where 

 {Aa)=Aw, {Ae) = Ez, (AT) = T(;, (A«) = Oj/, 

 ( A n) = N a-, (A = I M. 

 log A = 5-684! 

 log E = 2-943 

 log T = 6-425 

 log O = 9-761 

 log N = 9-754 log I = 0-064. 

 I denoted the coefficients of these magnitudes immediately 

 sought, with the same letters as the elements of the comet's 

 path, with which they correspond. If, therefore, the deviation 

 of the ephemeris from the observations is called v, the form 

 of every equation of conditions is : 



0=zv + a'w-i-ez + To + cuy + 7i x + i u 

 Every equation of condition was multiplied by the square 

 rootof then imiber belonging to the corresponding observation 

 (in coUimn W of the above table*) ; and besides, the equations 

 belonging to the right ascensions (as observed before) were 

 multiplied by the cosine of the declination of the comet. 



If m be the mean error of Messier's right ascensions ob- 

 served in the equator (which error is found by deducino- an 

 orbit from Messier's observations in right ascension only by 

 varying the elements e, T and /) and m^ the mean error of a 

 declination found by treating his observations in declination 

 in the same manner; I found 



log w?- = 2-94737, log w'- = 3-39142. 



I employed the quotient — ^= 0*3597 (for which, for bre- 

 vity, I put 036) as mentioned before, only for the purpose 

 of uniting all the observations of Messier, through which 

 I obtained the square of the mean error of a right ascension 

 log m"* = 2-95993. In the same manner I found for the 

 observations of tlie other astronomers ; viz. 



Maraldi, — —■ = 0-170 log ?«"^ = 3*34606 



IT? 



Cassini, —rr = 0*25625 = yVrr log w"^ = 3*37313 



m 



Bradley, — yj- = 0*745 log m"* = 3*56636 



?«'■ 



Hell, —^ = 0*298 log m"^ = 3*62092 



m" 



* In the tables of observattonB, for which the reader is referred to the 

 Aitr. Nach. 



The 



