i 
ae en 2a 
et a a — a a 
ee es 
§; 
366 
whom the fons volunteered into the fervice 
of their country ; two were killed in the laft 
war;and two were ftillemployed in the fame 
fervice, whep this account was received.”” 
The Society of Arts awarded him their 
filver medal and fifteen guiaeas, as an en- 
couragement of virtuous and diftinguifhed 
induitry. 
—=_ae— 
ROYAL SOCIETY OF LONDON. 
MATHEMATICS, &c. 
R. WoopHousE’s paper * On the 
WM. Integration of certain differential 
Expreffions, with which Problems in Piy- 
fical Aftronomy . are connected,” ad- 
mits of noabridgement. Its main objeé& 
is to thew the correfpondence that there is 
between the artifices of calculation and 
the properties of geometrical figures, and 
to reduce the feveral methods into one, 
which will be allowed to be ufeful in the 
inveftigation of {cience. 
‘* On fimilar reduétions,” fays Mr. 
Wocdhoufe ‘ the perfection of anaiyfis 
toa great degree, depends: for, a frequent 
refult of a careful inveftigation is, the dil. 
covery that methods apparently different, 
becaule differently exprefled, are founded 
on the fame principle and fundamental no- 
tion; but if examination and ftudy thus 
diminifh the feeming bulk of our know- 
ledge, they, at the fame time, increafe its 
precifion and purity.” ‘ 
Dr. HERsCHEL’s ‘* Continuation cf an 
Account of the Changes that have happen- 
ed in the relative Si:uation of double 
Stars,”” will merit the attention of prac- 
tical aftronomers; from which it appears, 
that, of fiity changeable double ftars, 
which are given, twenty-eight have under- 
gone alterations that do not amount to an 
angle of ten degrees: thirteen have altered 
their fituation above 10°, and lefs than 
29°: three have undergone a change in 
the angle of pofition of more than 20 and 
net fo faras 30°: the fix remaining flars 
afford initances of a ftill greater change, 
which, in the angle of peition of {ome of 
them, amounts to more than 30° 3 in 
others to near 40, 50, 60, and upwards 
to 130°. 
We thall give the fubftanceof what Dr. 
Her{chel fays of @ Herculis, which, in his 
Catalogue is the fecond ftar in the fecond 
clais. Tie two ftars of this double ftar 
have undergone confiderable alterations : 
by a meafare taken, May 20, 1781, it 
was 21° 28’ fouth-following. April 3, 
1803, it was 25° 29’. In 1802, it was 
31° 38’. Inthe beginaing of 1804, it was 
31° sa’ and on the 3d-of June laf it was 
32° 50', which gives a change of 11° 22! 
Proceedings of Learned Societies. 
| [May fy 
in twenty-three years and fourteen days ; 
but the diftance has not undergone any 
perceptible alteration. If this ftar has 
three motions, a real, a parallactic, and an 
apparent one; the latter being a compofi- 
tion of the former two; the parallactic 
motion will carry it, in an angle of 583° 
towards the fouth- preceding part of the 
heavens ; but the motion affigned to it in 
the new tables, has a direction towards 
the north: Hence Herculis has alfo a 
real motion, which, by its compofition 
with the parallaétic one, produces the ta- 
bular apparent one. 
Wearetoexamine the effect of thefe three 
motions, on the pofition of the two ftars 
of the double fiar, to account for the ob- 
ferved change. The two fiars are fufi-_ 
ciently different in magnitude, to lead us_ 
to expect a difference of parallax, on the: 
fuppofition that their changes from us are 
inverfely as their apparent magnitudes. 
The change of the angle of pofition, ari- 
fing from a fuperior parallaétic motion of 
the large ftar, would have occafioned a re- 
trogade motion of the {mall one; but this 
by obfervation has moved according to the 
order of the figns ; its change, therefore, 
will admit of no explanation from the ef-. 
feét' of parallax. 
The real motion of « Herculis, being 
fuch as, with the union of the parallagtic. 
one, will produce an apparent motion to- 
wards the north is determined by the velo- 
Cities and dircétions of the other two mo- 
tions ; but fince it is known to be com- 
pounded with the parallactic one, we muft 
confult the dire&tion and. velocity of that 
compofition, which is fuch that the large 
far, in twenty-three years and fourteen 
days, muft have been carried 5'’.299 to- 
wards the north. If the ftars are not con- 
ne€ted, and fuppofe the {mall one at reft, 
and at fuch a diftance from us as to been- 
tirely free from fenfible paraliax, then the 
large ftar, by its motion fhould have left 
the {mali one fo far behind, that the cen- — 
tres of the two ftars, which was, in Sep-_ 
tember, 1781, 4.34" fhould now be 
7".92'", while the angle of pofition 
ought to have increafed to 524°. Dr. . 
Herichel’s obfervations give (e different a 
refult, that this hypothefis muft be aban- 
doned: and if the fmall ftar partake of a 
paralla&tic motion, the objection will be 
ftill greater. jn: 
“© Hence,” he fays, ‘* it follows, that, 
unlefs we fhould admit the fuppofition of 
three independent motions, the highimpro- 
bability of which has been fufficiently 
fhewn, we have reafcn to believe, that the 
large ftar has, during the twenty-three laft 
years, 
