SHARP. 
the variations oftlie same while tliey change 
their longitude by one degree. 
But from the fatigue of continually ob- 
serving the stars at night, in a cold thin air, 
joined to a weakly constitution, he was re- 
duced to a bad state of health ; for the re- 
covery of which he desired leave to retire 
to his house at Horton ; where, as soon as 
he found himself on the recovery, he began 
to fit up an observatory of his own, having 
first made an elegant and curious engine for 
turning all kinds of work in wood or brass, 
witha maundril for turning irregular figures, 
as ovals, crosses, wreathed pillars, &c. Be- 
side these, he made himself most of the 
tools use<f by joiners, clock-makers, opti- 
cians, mathematical instrument-makers, &c. 
The limbs, or arcs, of his large equatorial 
instrument, sextant, quadrant, &c. he gra- 
duated with the nicest accuracy, by diago- 
nal divisions into degrees and minutes. 
The telescopes he made use of were all of 
his own making, and tlie lenses ground, 
figured, and adjusted with his own hands. 
It was at this time that he assisted Mr. 
Flamsteed in calculating most of the tables 
in the second volume of his “ Historia Cceles- 
tis,” as appears by their letters, to be seen in 
the hands of Mr. Sharp’s friends at Horton. 
Likewise the curious drawings of the charts 
of all the constellations visible in our he- 
misphere, with the still more excellent 
drawings of the planispheres both of the 
northern and southern constellations. And 
though these drawings of the constellations 
were sent to be engraved at Amsterdam 
by a masterly hand, yet the originals far 
exceeded the engravings in point of beauty 
and elegance ; these were published by 
Mr. Flamsteed, and both copies may be 
seen at Horton. 
The mathematician meets with something 
extraordinary in Sharp’s elaborate “ Treatise 
of Geometry Improved,” (in4to. 1717, sign- 
ed A. S. Philomath), 1st. by a large and accu- 
rate table of segments of circles, its con- 
struction, and various uses in the solution 
of several difficult problems, with compen- 
dious tables for finding a true proportional 
part, and their use in these or any other 
tables exemplified in making logarithms, 
or tlieir natural numbers, to 60 places of 
figures, there being a table of them for all 
primes to 1100, true to 61 figures. 2d. His 
concise “ Treatise ofPolyedra,” or solid bo- 
dies of many bases, both the regular ones and 
others : to which are added twelve new 
ones, with various methods of forming them, 
and their exact dimensiolis in surds or spe-< 
cies, and in numbers ; illustrated with a 
variety of copper-plates, neatly engraved 
by his own hands. Also the models of 
these polyedra he cut out in box-wood with 
amazing neatness and accuracy. Indeed 
few or none of the mathematical instru- 
ment-makers could exceed him in exactly 
graduating or neatly engraving any mathe- 
matical or astronomical instrument, as may 
be seen in the equatorial instrument above 
mentioned, or in his sextant, quadrants, 
and dials of various sorts ; also in a curious 
arihillary sphere, which, beside the com- 
mon properties, has moveable circles, &c. 
for exhibiting and resolving all spherical 
triangles ; also his double sector, with many 
other instruments, all contrived, graduated, 
and finished, by himself. In short, he pos- 
sessed at once a remarkably clear head for 
contriving, and an extraordinary hand for 
executing any thing, not only in mechanics, 
but likewise in drawing, writing, and making 
the most exact and beautiful schemes or 
figures,’ in all his calculations and geometri- 
cal constructions. 
The quadrature of the circle was under- 
taken by him for his own private amuse- 
ment in the year 1699, deduced from two 
different series, by which the truth of it 
was proved to 72 places of figures ; as may 
be seen in the introduction to Sherwin’s 
table of logarithms ; that is, if the diameter 
of the circle be 1, the circumference will 
be found equal to 3.141592653589793238 
462643383279502884197169399375105820 
974944592307816405, &c. In the same 
book of Sherwin’s may also be seen his in- 
genious improvements on the making of 
logarithms, and the constructing of the na- 
tural sines, tangents, and secants. 
He also calculated the natural and loga- 
rithmic sines, tangents, and secants, to 
every second in the first minute of the 
quadrant : the laborious investigation of 
which may probably be seen in the archives 
of the Koyal Society, as they were pre- 
sented to Mr. Patrick Murdock for that 
purpose; exhibiting bis very neat and ac- 
curate manner of writing and arranging his 
figures, not to be equalled perhaps by the 
best peUman now living. 
The late ingenious Mr. Smeaton says, 
(Philosophical Transactions, anno 1786, 
p. 5, &c.): “ In the year 1689, Mr. Flam- 
steed completed his mural arc at Green- 
wich ; and, in .the Prolegomena to his His- 
toiia Cwlestis, he makes an ample acknow- 
