520 
vice, it fhould be—That you would have 
your candidate provided with fome title, 
or employment, before he offers himéelf for 
orders. ' 
Neverthelefs, as I know Dr. Gray to 
be as heartily concerned for the honour 
and fervice of the church as any man, if, 
after what has been faid, you fhall have 
reafons for defiring this young gentleman 
- Proceedings of Learned Societies. 
[ Jan. 1, 
to be ordained, before he can be provided. 
with a better or more beneficial title, E 
will (upon your account, and as knowing 
that you will advife him ufefully to em-, 
ploy his time) take him in ad Titulum 
Epifcopi. Iam, good Dr. Gray, 
Your affectionate Friend 
and Servant, ‘ 
R. Lincoun.” 
PROCEEDINGS OF LEARNED SOCIETIES. 
=e eee 
ROYAL IRISH ACADEMY. 
HIS learned body ulually divide the 
moft valuable papers laid before 
them, and which they regard as fit for the 
public infpection, into three clafles—thofe 
relating to fcience, to polite literature, 
and antiquities. . 
Science.—In the fcientific clafs they 
have lately had prefented to them three 
mathematical papers; one is.a potihu- 
mous work of the late Rev. R. Mur- 
ray, D. D. Provoft cf Trinity Ccllege, 
near Dublin; it relates to Dr. Hailey’s 
feries for the calculation of logarishms, 
and it was drawn up about forty years 
ago, for the inftruétion of his pupils, 
fhortly after his appointment to the pro- 
feflorfhip of mathematics ; it is fhort, and 
the explanations ere fimple, and fuited to 
thofe young men who are fludying the 
elementery parts of pure mathematics. 
The fecond is an examination of vari- 
ous folutions of Kepler’s problem, anda 
fhort, practical folution of it, pointed out 
by the Rev. J. BRINKLEY. The object of 
this effay has been to compare the different 
folutions of Kepler's problem. This com- 
parifon has led the author to point out 
what he confiders as the beft pra€tical fo- 
lution of the problem, particularly 2ppli- 
cable to the planets, and this fclution is 
formed of a combination of the folutions 
of Kepler, Newton, and Caffini, «* The 
very fmall fhare (fays the medeft author) 
I claim in it, is from having recommended 
that combination of folutions. ‘The fo- 
lutions of ‘the two latter have heen fepa- 
rately recommended by writers on aftro- 
nomy. Caflini bas net always been re- 
ferred to as the author of his method, and 
Newton rarely. The merit of Cafiini’s 
method is derived. from its fimplicity, and 
ready application to the planetary orbits. 
Newton’s folution was the firft that was 
ae 
applicable to orbits of every degree of ec= 
centricity.”’ In addition to thefe, Mr. 
Brinkley notices the folutions given -by 
Hermann, in the year 1725, and by Mr. 
Ivory, in the volume of the Ediaburgh 
Tranfaétions. The former is, in fub- 
fiance, the fame as the folution of Dr. 
Matthew Stewart, in which Hermann 
makes ufe of Caflini’s approximation, but 
withouta proper referencetoit. Of Mr. 
Ivory’s method, it is obferved, by Mr. 
Brinkley, that, with regard to the prac 
tical value for the planetary orbits, it 
yields to feveral other methods, and, with 
re{pest to elliptical orbits in general, it 
certainly yields to Newton’s method, and, | 
perhaps, to Machin’s ; and, in the extreme 
cafe, when the ellipfe is evaneicent, the 
folution derived from Newton’s method: 
is much more fimple than that of Mr. 
Ivory. Having made thefe obfervations,. 
Mr. Brinkley adds, “ It is with concern 
T have made thefe remarks on the labours 
of a perfon who has merited fo much by. 
his moft elegant and ufeful folution of 
a problem conne&ied with phyfical 
aftronomy, in the fourth volume of the. 
Edinburgh Tranfaétions :—a problem on. 
which the eminent mathematicians of 
Europe had necefiarily exerted their in- 
genuity for nearly half a century, and. 
whose folutions have all been furpafled by 
that of Mr. Ivory. In his folution of 
Kepler’s problem, he has added the me- 
thod of deriving the place of a comet, 
moving in’an excentric ellipfe, from the. 
place in a parabola having the fame pe-. 
rihelicn diftance. He confiders the pro- 
blem as new, although, befide Simpfon 
and Laplace, referred- to, Lalande men 
tions the problem.” 
The third, and laft, mathematical dif. - 
fertation is by the fame learned profeffor, 
ahd it contains “* A theorem for find-- 
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