MACLAURIN. 
dents attending his lectures every year ; 
who being of different standings and profi- 
ciency, he W’as obliged to divide them into 
four or five classes, in each of which he em- 
ployed a full hour every day, from the first 
of November to the first of June. In the 
junior class he taught the first six books ot 
“ Euclid’s Elements,” plane trigonometry, 
practical geometry, the elements of fortifi- 
cation, and an introduction to algebra. The 
second class studied algebra, with the ele- 
•venthand twelfth books of Euclid, spherical 
trigonometry, conic sections, and the gene- 
ral principles of astronomy. The third 
went on in astronomy and perspective, read 
a part of “ Newton’s Principia,” and had 
performed a course of experiments for il- 
lustrating them ; he afterwards read and de- 
monstrated the elements of fluxions. Those 
in the fourth class read a system of fluxions, 
the doctrine of chances, and the remainder 
of ‘‘ Newton’s Principia.” 
In 1734, Dr. Berkley, Bishop of Cdoyne, 
published a piece called the “ Analyst in 
which he took occasion, from some disputes 
that had arisen concerning the grounds of 
the fluxionary method, to explode the me- 
thod itself ; and also to charge mathemati- 
cians in general with infidelity in religion. 
Maclaurin tliought himself included in this 
charge, and began an answer to Berkley’s 
book ; but other answers coming out, and 
as he proceeded, so many discoveries, so 
many new theories and problems occurred 
to him, that instead of a vindicatory 
pamphlet, he produced a complete system 
of fluxions, with their application to the 
most considerable problems in geometry 
and natural' philosophy. This work was 
published at Edinburgh in 1742, 2 vols. 
4to. ; and as it cost him infinite pains, so it 
is the most considerable of all his works, 
and will do him immortal honour, being in- 
deed the most complete treatise on that 
science that has yet appeared. 
In the mean time, he was continually ob- 
liging the public with some observation or 
performance of his own, several of which 
were published in the fifth and sixth vo- 
lumes of the Medical Essays at Edinburgh. 
Many of them were likewise published in 
the Philos. Trans, as the following : 1. On 
the construction and measure of curves, 
vol. 30. — 2. A new method of describing alt 
kinds of curves, vol. 30. — 3. On equations 
with impossible roots, vol. 34. — 4. On the 
roots of equations, &c. vol. 34. — On the 
description of curve lines, vol. 39. — 6. Con- 
tinuation of the same, vol. 39. — 7. Observa- 
tions on a solar eclipse, vol. 40. — 8. A 
rule for finding the meridional parts of a 
spheroid, with the same exactness as in a 
sphere, vol. 41. — 9. An account of the 
treatise of fluxions, vol. 42. — 10. On the 
basis of the cells, wdiere the bees deposit 
their honey, vol. 42. 
In the midst of these studies, he was al- 
ways ready to lend his assistance in con- 
triving and promoting any scheme which 
might contribute to the public service. 
When the Earl of Morton went, in 1739, to 
visit his estates in Orkney and .Shetland, he 
requested Mr. Maclaurin to assist him in 
settling the geography of those countries, 
which is very erroneous in all our maps ; to 
examine their natural history, to survey the 
coasts, and to take the measure of a degree 
of the meridian. Maclaurin’s family af- 
fairs would not permit him to comply with 
this request ; he drew up however a memo- 
rial of what he thought necessary to be ob- 
served, and furnished proper instruments 
for the work, recommending Mr. Short, the 
noted optician, as a fit operator for the 
management of them. 
Mr. Maclaurin had still another scheme 
for tlie improvement of geography and na- 
vigation, of a more extensive nature ; which 
was the opening a passage from Greenland 
to the South Sea by the north pole. That 
such a passage might be found, he was so 
fully persuaded, that he used to say, if his 
situation could admit of such adventures, 
he would undertake the voyage, even at 
his own charge. But when schemes for 
finding it were laid before the parliament 
in 1741, and he was consulted by several 
persons of high rank concerning them, and 
before he could finish the memorial he pro- 
posed to send, the premium was limited to 
the discovery of a north-west passage ; and 
he used to regret that the word west was in- 
serted, because he thought that passage, if at 
all to be found, must lie not fer from the pole. 
In 1745, having been very active in forti- 
fying the city of Edinburgh against the re- 
bel army, he was obliged to fly from thence 
into England, where he was invited by Dr. 
Herring, Archbishop of York, to reside with 
him during his stay in this country. In 
this expedition, however, being exposed to 
cold and hardships, and naturally of a weak 
and tender constitution, which had been 
much more enfeebl,ed by close application 
to study, he laid the foundation of an illness 
which put an end to his life, in June 1746, 
at 48 years of age, leaving his widow with 
two sons and three daughters. 
