176 
TT Beebe — The Comet of 1771. 
compute the variation of the geocentric distances from the same 
differentials and residuals as on page 168, omitting June 25 and 
July 11, we obtain a A' = — 7786'', a A — — 5178 ; but omitting also 
April 30 we find A-J r = -f- 15581', A A — — 11159'. 
The only available process, therefore, consists in varying the last 
two normal places as much as it seems reasonable to suppose they 
can be affected by errors of observation and noting the effect upon 
the elements. Also, instead of varying a and d, we may vary 0, since 
errors in both or either of the coordinates a and 6 can affect the 
elements onlv through the change that thev occasion in 6. 
A number of different values were accordingly given to 6 for the 
uncertain places and the results derived so far as to ascertain the 
effect on the equations of condition and on the eccentricity. These 
results show that while it is possible by a change in the value of 6 
for June 25 and July 11, to obtain an orbit of somewhat less eccen- 
tricity, no reasonable change will reduce the excess over unity in the 
eccentricity by more than a small fraction ; and that any thing more 
than a small diminution in the eccentricity occasions an increase of 
the residuals in the equations of condition. 
Repeated attempts to satisfy the normal equations by different 
elements greatly strengthens my belief that the difference between 
the residuals from the hyperbolic and from the parabolic elements 
can be but little reduced by any supposition of error in the Marseilles 
observations. 
In this view of the case we must then conclude that elements (F) 
should be taken as the best definitive elements of this comet, and 
that while the parabolic residuals are not large enough to render the 
supposition of such an orbit untenable, the balance of probability is 
still with the hyperbola. 
New Haven. June 5th, 1879. 
