**MACLAURIN, COLIN** (1698–1746), Scottish mathematician,
was the son of a clergyman, and born at Kilmodan, Argyllshire.
In 1709 he entered the university of Glasgow, where he exhibited
a decided genius for mathematics, more especially for geometry;
it is said that before the end of his sixteenth year he had discovered
many of the theorems afterwards published in his
*Geometria organica*. In 1717 he was elected professor of mathematics
in Marischal College, Aberdeen, as the result of a competitive
examination. Two years later he was admitted F.R.S.
and made the acquaintance of Sir Isaac Newton. In 1719 he
published his *Geometria organica, sive descriptio linearum*
*curvarum universalis*. In it Maclaurin developed several theorems
due to Newton, and introduced the method of generating
conics which bears his name, and showed that many curves
of the third and fourth degrees can be described by the intersection
of two movable angles. In 1721 he wrote a supplement
to the *Geometria organica*, which he afterwards published, with
extensions, in the *Philosophical Transactions* for 1735. This
paper is principally based on the following general theorem,
which is a remarkable extension of Pascal’s hexagram: “If a
polygon move so that each of its sides passes through a fixed
point, and if all its summits except one describe curves of the
degrees *m*, *n*, *p*, &c., respectively, then the free summit moves
on a curve of the degree 2*mnp* . . . . which reduces to *mnp* . . . .
when the fixed points all lie on a right line.” In 1722 Maclaurin
travelled as tutor and companion to the eldest son of Lord
Polwarth, and after a short stay in Paris resided for some time
in Lorraine, where he wrote an essay on the percussion of bodies,
which obtained the prize of the French Academy of Sciences
for the year 1724. The following year he was elected professor
of mathematics in the university of Edinburgh on the urgent
recommendation of Newton. After the death of Newton, in
1728, his nephew, John Conduitt, applied to Maclaurin for his
assistance in publishing an account of Newton’s life and discoveries.
This Maclaurin gladly undertook, but the death of
Conduitt put a stop to the project.

In 1740 Maclaurin divided with Leonhard Euler and Daniel
Bernoulli the prize offered by the French Academy of Sciences
for an essay on tides. His *Treatise on Fluxions* was published
at Edinburgh in 1742, in two volumes. In the preface he states
that the work was undertaken in consequence of the attack on
the method of fluxions made by George Berkeley in 1734.
Maclaurin’s object was to found the doctrine of fluxions on
geometrical demonstration, and thus to answer all objections
to its method as being founded on false reasoning and full
of mystery. The most valuable part of the work is that devoted
to physical applications, in which he embodied his essay
on the tides. In this he showed that a homogeneous fluid
mass revolving uniformly round an axis under the action of
gravity ought to assume the form of an ellipsoid of revolution.
The importance of this investigation in connexion
with the theory of the tides, the figure of the earth, and other
kindred questions, has always caused it to be regarded as
one of the great problems of mathematical physics. Maclaurin
was the first to introduce into mechanics, in this discussion, the
important conception of *surfaces of level*; namely, surfaces at
each of whose points the total force acts in the normal direction.
He also gave in his *Fluxions*, for the first time, the correct theory
for distinguishing between maxima and minima in general, and
pointed out the importance of the distinction in the theory of the
multiple points of curves. In 1745, when the rebels were marching
on Edinburgh, Maclaurin took a most prominent part in
preparing trenches and barricades for its defence. The anxiety,
fatigue and cold to which he was thus exposed, affecting a constitution
naturally weak, laid the foundation of the disease to
which he afterwards succumbed. As soon as the rebel army
got possession of Edinburgh Maclaurin fled to England, to avoid
making submission to the Pretender. He accepted the invitation
of T. Herring, then archbishop of York, with whom he remained
until it was safe to return to Edinburgh. He died of
dropsy on the 14th of June 1746, at Edinburgh. Maclaurin was
married in 1733 to Anne, daughter of Walter Stewart, solicitor-general
for Scotland. His eldest son John, born in 1734, was
distinguished as an advocate, and appointed one of the judges
of the Scottish court of session, with the title of Lord Dreghorn.
He inherited an attachment to scientific discovery, and was
one of the founders of the Royal Society of Edinburgh, in
1782.

After Maclaurin’s death his account of Newton’s philosophical
discoveries was published by Patrick Murdoch, and also his algebra
in 1748. As an appendix to the latter appeared his *De linearum*
*geometricarum proprietatibus generalibus tractatus*, a treatise of remarkable
elegance. Of the more immediate successors of Newton
in Great Britain Maclaurin is probably the only one who can be placed
in competition with the great mathematicians of the continent of
Europe at the time. (B. W.)