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VII. Direct and expeditious methods of calculating the excentric 
from the mean anomaly of a planet. By the Reverend Abram 
Robertson, D.D. F.R. S. Savilidn Professor of Astronomy in 
the University of Oxford , and Radcliffian Observer. Commu- 
nicated by the Right Hon. Sir Joseph Banks, Bart. G. C. B. 
P. R. S. 
Read February 15, 181b. 
Since the publication of Kepler's discoveries in astronomy, 
the attention of men of science has frequently been directed 
to the problem distinguished by his name, and their exertions 
have frequently been employed to overcome the acknowledged 
difficulty of its solution. A statement of the various degrees 
of success, with which these endeavours have been made, is 
foreign to the present design. An account of this kind is now 
also needless, as Dr. Brinkley's examination of such attempts, 
published in the ninth volume of the Transactions of the Royal 
Irish Academy, affords a satisfactory review of most of the 
proceedings on this subject, previous to the year 1802. 
After the following methods had occurred to my consider- 
ation, and I had fully proved their utility by actual application 
to examples, I was anxious to ascertain whether any author 
had anticipated me in the manner in which the investigations 
are conducted. With this view I examined such solutions as 
are referred to in Dr. Brinkley's very able Memoir, all those 
mentioned by Montucla,* of which I could procure a sight, 
* Histoire des Mathematiques, Tom. II. p. 343, &c. I have searched, without 
success, for Lorgna’s and Trembley’s publications. 
