VER 
VER 
will the excess of one division of A be com- 
pounded of the ratios of one of A to A, and 
of one of B to B. For, let A contain 11 
parts, tiien ope of A to A is as 1 to 11, or 
Let B contain 10 parts, then one of 
B to B is as 1 to 10, or—. Now ^ — i 
’ 10 10 11 
_ n — to _ 1 _ 1 j_ 
~10 X it “10 X 11 “ 10 ^ 11‘ 
Or it B contains n parts, and A contains 
n -1- 1 parts ; then i is one part of B, and 
— j — is one part of A. And ^ — =: 
+ 1 n n-^ 1 
n 1 — n 1 1 
n X 1 “ “+ 
Tiie most commodious divisions, and 
their aliquot parts, into which the degrees 
on the circular limb of an instrument may 
be supposed to be divided, depend on the 
radius of that instrument. 
Let R be the radius of a circle in inches ; 
and a degree to be divided into n parts, each 
being ^ th part of an inch. 
Now the circumference of a circle, in 
partsofits diameter 2 R inches, is 3.1415926 
X 2 R inchc.s. 
Then 360“ : 3.1415926 X 2 R : : 1“ : 
3.1415926 
360 ^ 
2 R inches. 
Or, 0.0174.5329 X R is the length of one 
degree in inches. 
Or, 0.01745329 X R X p is the length of 
1“, in pth parts of an inch. 
But as every degree contains n times such 
parts, therefore = 0.01745329 X R X p. 
The most commodious perceptible divii- 
sion is - or — of an inch. 
8 . 10 
Example. Suppose an instrument of 30 
inches radius, into how many convenient 
parts may each degree be divided ? bow 
many of these parts are to go to the breadth 
of the vernier, and to what parts of a de- 
gree may an observation be made by that 
instrument ? 
Now, 0.01745 X R = 0.5236 inches, the 
length of each degree : and if p is supposed 
about - of an inch for one division ; then 
0.5236 Xp= 4.188 shows the number of 
.such parts in a degree. But as this number 
must be an integer, let it be 4, each being 
1.5"; and let the breadth of the vernier con- 
tain 31 of those parts, or 7|’, and be di- 
vided into 30 parts. 
Here n = i ; ot = — ; then ~ x — = 
— of a degree, or 30', which is the least 
part of a degree that instrument can show. 
1 111 
If M = “, and »i = — : then - x — = 
o 36 ’ 5 36 
60 ~ „ 
r of a minute, or 20 . 
o X o6 
VERONICA, in botany, speedwell, a ge- 
nus of the Diandiia Monogynia class and 
order. Natural order of Persouatae. Pe- 
diciilares, Jussieu. Essential character: co- 
rolla four-cleft, wheel-shaped, with the low- 
est segment narrower ; capsule superior, 
two-celled. There are fifty seven, species. 
VERSED sine of an arch, a segment of 
the diameter of a circle, lying between the 
foot of a right sine, and the lower extremity 
of the arch. 
VERT, in heraldry, the term fora green 
colour. It is called vert in the blazon of 
the coats of all under the degree of nobles ; 
but in coats of nobility, it is called eme- 
rald ; and in tliose of kings, Venus. In en- 
graving, it is expressed by diagonals, or 
lines drawn athwart from right to left, from 
the dexter chief corner to the sinister 
base. 
Vert, or Green hue, in forest law, any 
tiling that grows and bears a green leaf 
within the forest, that may cover a deer. 
This is divided into over-vert and nether- 
vert ; over vert is the great woods which, 
in law-books, are nsiially called haiilt-bois ; 
nether-vert is the under woods, otherwise 
called snb-bois. We sometimes also meet 
widi special vert, which denotes all trees 
growing in the King’s woods within the fo- 
re.st ; and those which grow in other men’s 
woods, if they be such trees as bear fruit to 
feed the deer. 
VERTEBRAE, in anatomy, the twenty- 
four bones of which the spine consists, and 
on which the several motions of the trunk - 
of our bodies are performed. 
VERTEX is used, in astronomy, for the 
point of heaven perpendicularly over our 
heads, properly called the zenith. 
VERTICAL circle, in astronomy, a great 
circle of the sphere, passing through the 
zenith and nadir, and cutting the horizon at 
right angles: it is otherwise called azi- 
muth. 
Vertical prime, is that vertical circle or 
azimuth which passes through the poles of 
the meridian ; or which is perpendicular to 
the meridian, and passes through the eqiii- 
noctial points. 
