SCALE. 
seeds solitaiy. There are two species, vk. 
S. completa, and S. lateriflorh, natives of 
the West Indies. 
SCALE, a mathematical instrument, con- 
sisting of several lines drawn on wood, 
brass, silver, &c. and variously divided, 
according to the purposes it is intended to 
serve ; whence it acquires various denomi- 
nations, as the plain scale, diagonal scale, 
plotting scale, Gunter’s scale, &c. See 
Mathematicai- Instruments. 
Scale, diagonal, is projected thus : first 
draw eleven parallel lines at equal distances, 
the whole length of which being divided 
into a certain number of equal parts, ac- 
cording to the length of the scale, by per- 
pendicular parallels, let the first division be 
again subdivided into ten equal parts, both 
above and below; then drawing the oblique 
lines from the first perpendicular below to 
the first subdivision above, and from the 
first subdivision below to the second subdi- 
vision above, &c. the first space shall there- 
by be exactly divided into one hundred 
equal parts ; for as each of these subdivi- 
sions is one tenth part of the whole first 
space or division, so each parallel above it 
is one tenth of such subdivision, and con- 
sequently one hundredth part of the whole 
first space; and if tliere be ten of the 
larger divisions, one thousandth part of the 
whole scale. If therefore the larger divi- 
sions be accounted units, the first subdivi- 
sions will be tenth parts of an unit ; and the 
second subdivisions, marked by the diago- 
nals on the parallels, hundredth parts of an 
unit. Again, if the larger divisions be 
reckoned tens, the first subdivisions will be 
units, and the second subdivisions tenth 
parts ; and if the larger divisions be ac- 
counted hundredths, the first subdivisions 
will be tens, and the second units; and 
so on. 
Scale, Gunter’s, an instrument, so called 
from Mr. Gunter, its inventor, is gene- 
rally made of box : there are two sorts, the 
long Gunter and the sliding Gunter, having 
both the same lines, but differently used, 
the former with the compasses, the latter 
by sliding. The lines now generally deli- 
neated on those instruments are the fol- 
lowing, viz. a line of numbers, of sines, 
tangents, versed sines, sine of the rhumb, 
tangent of the rhumb, meridional parts, and 
equal parts ; which are constructed after 
the following manner ; 
The line of numbers is no other than the 
logarithmic scale of proportionals, wherein 
the distance bettyeen each division is equal 
to the number of mean proportionals con- 
tained between the two terms, in such 
parts as the distance between 1 and 10 is 
1000, &c. equal the logarithm of that num- 
ber. Hence it follows, that if the number 
of equal parts expressed by the logarithm 
of any number be taken from the same 
scale of equal parts, and set off from 1 on 
the line of numbeis, the division will repre- 
sent the number answering to that loga- 
rithm. Thus, if you take .954, &c. (the 
logarithms of 9) of the same parts, and set 
it off from 1 towards 10, you will have the 
division standing against the number 9. In 
like manner, if you set off .903, &c. .845, 
&c. .778, &c. (ihe logarithms of 8, 7, 6) 
of the same equal parts from 1 towards 10 , 
you will have the divisions answ'ering to the 
numbers 8, 7, 6. After the same manner 
may the whole line be constructed. 
The line of numbers being thus con- 
structed, if the numbers answering to the 
natural sines and tangents of any arch, in 
such parts as the radius is 10,000, &c. be 
found upon the line of numbers, right 
against them will stand the respective divi- 
sions answering to the respective arches, 
or which is the same thing, if the distance 
between the centre and that division of the 
line of numbers, winch expresses the num- 
ber answering to the natuial sine or tan- 
gent of any arch, be set off on its respec- 
tive line from its centre towards the left 
hand, it w’ill give the point answering to 
the sine or tangent of that arch : thus the 
natural sine of 30 degrees being 5,000, &c. 
if tire distance between the centre of the 
line of numbers (which in this case is equal 
to 10,000, &c. equal the radius) and the 
division, on the same line representing 
5000, Sec. be set off from the centre, or 
90 degrees, on the line of sines, towards 
the left hand, it will give the point answer- 
ing to tire sine of 30 degrees. And after 
the same manner may tire whole line of 
sines, tangents, and versed sines be divided. 
The line of sines, tangents, and vej-sed 
sines being thus constructed, the line sine 
of the rhumb, and tangent of the rhumb 
are easily divided ; for if the degrees and 
minutes answering to the angle which every 
rhumb makes with the meridian, be trans- 
ferred from its respective line to that which 
is to be divided, we shall have the several 
points required ; thus if the distance be- 
tween the radius or centre, and sine of 45 
degrees equals the fourth rhumb, be set off 
upon the line sine of the rhumb, we shall 
have the. point answering to the sine of the 
