SIMPSON. 
ject with success and perspicuity, and his 
conctesions were perfectly conformable to 
Dr. Bradley’s observations, it neverthel^s 
appeared' to Mr. Simpson, that he had 
greatly failed in a very material part, and that 
indeed the only very ditfrcult oue-j that is, 
4n the determination of the momentary alte- 
ration of the position of the Earth’s axis, 
caused by the forces of the Sun and Moon ; 
of which forces, the quantities, but not the 
effects, are truly investigated. The second 
paper contains the Investigation of a very 
exact Method or Rule for finding the Place 
of a Planet in its Orbit, from a Correction 
of Bishop Ward’s circular Hypothesis, by 
Means of certain Equations applied to the 
Motion about the upper Focus of the Ellipse. 
By this method the result, even in the orbit 
of Mercury, may be found within a second 
of the 'truth, and that without repeating the 
operation. The third shows the Manner of 
transferring the Motion of a Comet from a 
parabolic Orbit, to an elliptic One ; being 
of great use, when the observed places of a 
(new) comet are found to differ sensibly 
Jiom those computed on the Hypothesis of 
a parabolic orbit. The fourth is an Attempt 
to show, from Mathematical Piinciples, the 
Advantage arising from taking the Mean of 
a Number of Observations, in practical As- 
tronomy ; wherein the odds, that the result 
in tills way is more exact than from one 
single observation, is evinced, and the uti- 
lity of the method in practice clearly made 
appear. The fifth contains the Determina- 
tion of certain Fluents, and the Resolution 
of some very useful Equations, in the liigher 
Orders Of Flu/ions, by meaiis of the mea- 
sures of angles and ratios, and the right and 
versed sines of circular arcs. The sixth 
treats of the Resolution of algebraical 
Equations, by the Method of Surd-divi- 
sors ; in which the grounds of that method, 
as laid down by Sir Isaac Newton, are in- 
vestigated and explained. The seventh ex- , 
hibits the Investigation of a general Rule 
for the Resolution of Isoperimetrical Pro- 
blems of all Orders, with some examples of 
the use and application of the said rule. The 
eighth, or last part, comprehends the Reso- 
lution of some general and very important 
Problems in Mechanics and Physical Astro- 
nomy ; in which, among other things, tire 
principal parts of the third and ninth sec- 
tions of the first book of Newton’s Prin- 
cipia are demonstrated in a new and con- 
cise hianner. But what may perhaps best 
recommend this excellent tract, is the ap- 
plication of the general equations, thus de- 
VOL. YI. 
rived, to the determination of the lunar 
orbit. 
According to what Mr. Simpson had in- 
timated at the conclusion of his Doctrin 
of Fluxions, the greatest part of this ardu- 
ous undertaking was drawn up in the year 
1750. About that time M. Clairaut, a very- 
eminent mathematician of the French aca- 
demy, had started an objection against New- 
ton’s general law of gravitation. This was 
a motive to induce Mr. Simpson (among 
some others) to endeavour to discover whe- 
ther the motion of the Moon’s apogee, on 
which that objection had its whole weight 
and foundation, could not be truly ac- 
counted for, without supposing a change 
in the received law of gravitation, from the 
inverse ratio of the squares of the distances. 
The success answered his hopes, and induced 
him to look further into other parts of the 
theory of the Moon’s motion than he at first 
intended : but before he had completed his 
design, M. Clairaut arrived in England, and 
made Mr. Simpson a visit ; from whom he 
learned, that he had a little before printed 
a piece on that subject, a copy of which 
Mr. Simpson afterwards received as a pre- 
sent, and found in it the same things de- 
monstrated, to which he himself had di- 
rected his enquiry, besides several others. 
The facility of the raetliod Mr. Simpson- 
fell upon, and the extensiveness of it, will 
in some measure appear from this, that it 
not only determines the motion of the apo- 
gee in the same manner, and with the same 
ease, as the other equations, but utterly 
excludes all those dangerous kind of terms 
that had embarrassed the greatest mathe- 
maticians, and would, after a great number 
of revolutions, entirely change the figure of 
the Moon’s orbit. From whence this im- 
portant consequence is derived, that the 
Moon’s mean motion, and the greatest quan- 
tities of the several equations, will remain 
unchanged, unless disturbed by the inter- 
vention of some foreign or accidental cause. 
These tracts are inscribed to the Earl of 
Macclesfield, President of the Royal So- 
ciety. 
Mr. Simpson’s extreme application in this 
difficult pursuit greatly injured his healtli. 
Exercise and a proper regimen were pre- 
scribed to him, but to little purpose ; for his 
spirits sunk gradually, till he became incapa- 
ble of performing his duty, or even of reading 
the letters of his friends. The effects of this 
decay of nature were greatly increased by 
vexation of mind, owing to the haugh- 
ty and insulting behaviour of his siipe- 
M 
