403
whatever confidence Mr. Stewart may be hereafter
found to place in those simple methods of investiga-
tion, which he could conduct with so much ingenuity
and success; and will be convinced, that the solution
of a problem, though the most elementary, may be
the least obvious; and though the easiest to be un-
derstood, may be the most difficult to be discovered."
In pursuance of his principle of introducing the
forms of ancient demonstration, as applicable to those
more complicated parts of the science called the
mixed mathematics, for which they had been con-
sidered unqualified, he published, in 1761, his
" Tracts, Physical and Mathematical, containing an
Explanation of several Important Points in Physical
Astronomy; and a New Method of ascertaining the
Sun's Distance from the Earth, by the Theory of
Gravitation." "In the first of these," says his bio-
grapher, "Mr. Stewart lays down the doctrine of
centripetal forces, in a series of propositions, demon-
strated (if we admit the quadrature of curves) with
the utmost rigour, and requiring no previous know-
ledge of the mathematics, except the elements of
plane geometry and conic sections. The good order
of these propositions, added to the clearness and
simplicity of the demonstrations, renders this tract
the best elementary treatise of physical astronomy
that is anywhere to be found." It was the purpose
of the three remaining tracts to determine the effect
of those forces which disturb the motions of a second-
ary planet; and, in particular, to determine the dis-
tance of the sun, from its effect in disturbing the
motions of the moon. Owing to the geometrical
method which he adopted, and likewise to the ex-
treme distance of the sun, which makes all the dis-
turbances he produces on the motion of the moon
very near to that point at which increase of distance
to infinity would not change their force, he could
only proceed on a system of approximation; and in
applying the principles of his plan to a practical
calculation of the sun's distance, which he published
in 1763, entitled " Distance of the Sun from the Earth,
determined by the Theory of Gravitation, together
with several other Things relative to the same Sub-
ject," he was found to have made a very considerable
error. He found the distance of the sun to be equal
to 29,875 semi-diameters of the earth, or about
118,541,428 English miles. About five years after-
wards there appeared a pamphlet from the pen of
Mr. Dawson of Sudbury, called "Four Propositions,
intended to point out certain Errors in Dr. Stewart's
Investigation, which had given a Result much greater
than the Truth." This was followed by a second
attack from Mr. Lauden, who, like Price in arith-
metic, accomplished the difficult task of becoming
an enthusiast in mathematics, and by means of ex-
aggerating errors, and commenting on their atrocity,
astonished the world with a specimen of controversial
mathematics. The biographer thus states the sources
of the mistakes which called forth these animadver-
sions : "As in arithmetic we neglect those small
fractions which, though of inconsiderable amount,
would exceedingly embarrass our computations; so,
in geometry, it is sometimes necessary to reject those
small quantities which would add little to the accu-
racy, and much to the difficulty, of the investigation.
In both cases, however, the same thing may happen;
though each quantity thrown out may be inconsider-
able in itself, yet the amount of them altogether, and
their effect on the last result, may be greater than is
apprehended. This was just what had happened
in the present case. The problem to be resolved is,
in its nature, so complex, and involves the estima-
tion of so many causes, that, to avoid inextricable
difficulties, it is necessary to reject some quantities
as being small in comparison of the rest, and to
reason as if they had no existence." Soon after the
publication of this essay Dr. Stewart's health began
to decline; and in 1772 he retired to the country,
leaving the care of his class to his eminent son, Dugald
Stewart, who was elected joint professor with him
in 1775. He died on the 23d January, 1785, at the
age of sixty-eight. Besides the works above men-
tioned, he published Proposiliones Geometricce More
veterum Demonstrate ad Geometriam Antiquam Illus-
trandam et Promovendam Idonea, 1763.
STEWART, LIEUTENANT-COLONEL PATRICK,
C.B., R.E. This young and distinguished officer,
whose career unexpectedly terminated in the mid-day
of his life, was the second son of James Stewart,
Esq., of Cainsmore. Having adopted the military
service as his profession, he studied at the military
college of Sandhurst, and after distinguishing him-
self by his scientific acquirements connected with the
art of war, he entered the Bengal engineers, where-
he was appointed second-lieutenant on June 14, 1850.
On August I, 1854, he was promoted to a lieuten-
ancy, and on August 27, 1858, to the rank of captain.
During the Sepoy rebellion in India, he served in
the staff of Lord Clyde in the advance to the relief
of Lucknow, the siege of that city, and the battle of
Cawnpore, and in this memorable expedition his
knowledge of science in its application to military
operations was called into full exercise. He was
employed in extending and maintaining telegraphic
communication between the army in its advance and
the head-quarters of government, and this important
office he discharged so ably and energetically as to
obtain honourable mention in the despatches of Vis-
count Canning, the governor-general of India.
Although these were services in which military
enterprise had no field for display, Captain Stewart's
courage and daring as a soldier were so well known
as to call forth the admiration of all ranks in the army,
and these were all the more highly valued as he was
habitually of an amiable and gentle disposition.
During the Indian campaign he lost no opportunity
of signalizing his intrepidity in action; and carrying
the same spirit into his active sports, he on one
occasion nearly lost his life from the attack of a
tiger while hunting. When the rebellion was sup-
pressed he was rewarded with two clasps, and pro-
moted to the rank of brevet-major.
His health having suffered from his Indian services,
Major Stewart returned home, where his health was
restored and his frame invigorated by the bracing
atmosphere of his native Galloway, and the scenes
of his early youth; and he married Miss M'Douall,
daughter of Colonel M'Douall of Logan. Soon
after this he was again called to active service by
being appointed to superintend the extension of tele-
graphic communication with India, an important task
to which his well-known talents recommended him;
and it is enough to add that his services in this de-
partment did not belie the expectations which had
been formed of him. Latterly, in consequence of his
failing health, he had been residing at Constantinople,
where Mrs. Stewart was seized with diphtheria; but
although she recovered, her husband was struck
down with the same disease, which in his case proved
mortal. He died at Constantinople, on the I5th of
January, 1865, at the early age of thirty-two years.
STONE, EDMUND, an ingenious self-taught ma-
thematician, of whom nothing is known except from,
a letter written by the Chevalier Ramsay to Father
Castel, published in the Mémoires de Trlvoux. It
there appears that Stone was the son of a gardener