MEA 
Society of Gottirifren. The first volume of 
his, works was published at that place in 
1775, in folio. 
MAYOR, is the chief magistrate in a city 
or town corporate, who has under him aider- 
men, common-council, and officers of dif- 
ferent kinds. Their authority is different, 
according to different charters ; but they are 
always magistrates witliip the corporation. 
MEAN, a middle state between two ex^ 
tremes : thus we have an arithmetical mean, 
geometrical mean, mean distance, mean 
motion, &c. An arithmetical mean is half 
the sum of the extremes: thus, if 2 and 12 
2 - 4-12 
be the extremes, then 
2 
: 7 is the 
arithmetical mean : likewise between a and 
b it is 
0^6 
Geometrical mean, usually 
called a mean proportional, is the square 
root of the product of the two extremes : 
therefore, to find a mean proportional be- 
tween two given extremes, multiply these 
together, and extract the square root of the 
product. ,Thus, a mean proportional be- 
tween 6 and 24 is 12; for v^6 X 24 = 
\/ 144 = 12 : and between a- and y it is 
-v/ ay. The arithmetical mean is greater 
ffian the geometrical mean between the 
same two extremes: thus, between 6 and 
24 the geometrical mean is 12; but the 
5 -L 24 
arithmetical mean is = 15. Or, ge- 
nerally, let « be the greater and b the less; 
then is greater than \/ a b, or multi- 
a-l-6 : 
2 _ 
plying both by 2 ; a -f- ft is greater 2 ^ab: 
for squaring both we have -f- 2 a 6 -|- 6^ 
greater than 4 ab; for take away 4 a 6 and 
— - 2 a 5 -j- greater than 0 : or a — 
greater than 0 by the supposition. 
To find a mean proportional, geometii- 
cally, between two given right lines, a and 
b, (Plate Miscel. X. fig. 6.) join the two 
given lines together at x in one continued 
line, a b; upon the diameter d b describe a 
semicircle a z b, and erect the perpendicu- 
lar z X, which will be the required mean 
proportional ; for, by a well-known theorem 
in geometry, ax x x b is equal to x z% or 
a X : X z i: X z : X b. 
To find two mean proportionals between 
two given extremes : “ Multiply each ex- 
treme by the square of the other, viz. the 
greater extreme by the square of the less, 
and the less extreme by the square of the 
greater ; then extract the cube root out of 
M EA 
each product, and the two roots will, be the 
two mean proportionals sought.” Thus the 
two mean propj^ionals between a and b are 
^ a‘ b and \/ a b‘-\ or between 2 and 16 
the mean proportionals are S^and 
= 4 and 8. 
Me.in harmonical. See Harmonical 
proportion. 
Mean distance of a planet from the sun, in 
astronomy, is the right line drawn from the 
sun to the extremity of the conjugate axis 
of the ellipsis the planet moves in ; and this 
is equal to the semi-transverse axis, and is so 
called, because it is a mean between the 
planet’s greatest and least distance from 
the sun. See Distance. 
Mean motion, in astronomy, that where- 
by a planet is supposed to move equally in 
its orbit, and is always proportional to the 
time. See Motion. 
MEASLES. See Medicine. 
MEASURE signifies any given quantity, 
estimated as one, to which the proportion 
of other similar quantities may be ex- 
pressed. 
Measure is classed under a variety of 
heads, of which the following are illustra- 
tions. 
Measure of velocity, is the interval of 
space between two points, regularly passed 
through by a substance in constant and uni- 
form motion, within a certain period of time. 
Measure of a solid, is a cubic inch, 
foot, or yard ; in other words, a cube, the 
side of which is an inch, a foot, or a yard. 
Measure of a line, is the extension of a 
right line at pleasure, which is to be consi- 
dered as unity; for instance, an inch, a 
a foot, or a yard. 
Measure of a figure, or a surface per- 
fectly level, thence called a plane surface 
is a square inch, foot, or yard. This square 
is termed the measuring unit, because the 
side is an inch, a foot, a yard, or any other 
determinate extent. 
Measure of a certain portion or quantity 
of matter, is its weight. 
Measure of a number, applies thus : 2 is 
tlie measure bf 4, 3 of 6, &c. ; in fact, it is 
any number which divides without a re- 
mainder. 
It has long been wished by the learned 
that an universal measure, secured by pe- 
nalties in an unalterable state, had hither- 
to been, or may hereafter be adopted, 
which would prove of incalculable advan- 
tage to mankind in their philosophical and 
even less exalted pursuits. Prejudices are 
X 2 
