MEA 



MEA 



MEAN, a middle state between two 

 extremes ; 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 



2 I 12 

 and 12 be the extremes, then ^ - 



7 is the arithmetical mean : likewise be 

 Geometrical 



tween a and b it is 



mean, usually called a mean proportional, 

 is the square root of the product of the 

 two extremes : therefore, to find a mean 

 proportional between two given ex- 

 tremes, multiply these together, and ex- 

 tract the square root of the product. 

 Thus, a mean proportional between 6 and 

 24 is 12 ; for ^/ 6 x 24 = ^/ 144 = 12 : 

 and between x and y it is ^/ x y. The 

 arithmetical mean is greater than the geo- 

 metrical mean between tlie same two ex- 

 tremes : thus, between 6 and 24 the geo- 

 metrical mean is 12 ; but the arithmetical 



64-24 

 mean is '- = 15. Or, generally, let 



a be the greater and 6 the less; then 



a -f- b 



~ is greater than v/a,or multiply- 



ingjboth by 2 ; a -f A is greater 2 

 v/ b : for squaring both we have * -+- 

 '2 a b - \- b^ greater than 4 a b ; for take 

 away 4 a b and o a 2 a b -f- b'- greater 

 than 0: or a 6\- greater than by the 

 supposition. 



To find a mean proportional, geometri- 

 cally, between two given right lines, a 

 and 0, (Plate Miscel. X. fig. 6.) join the 

 two given lines together atx in one con- 

 tinued line, b ; upon the diameter a b 

 Jescri.be a semicircle a z b, and erect 

 the perpendicular z x, which will be 

 the. required mean proportional; for, 

 by a well-known theorem in geometry, 

 a x x x b is equal to x z 2 , or ax : x z :: 

 x Z : x b. 



To find two mean proportionals be- 

 vsveen two given extremes : " Multiply 

 each extreme 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 each product, and the two 

 roots will be the two mean proportionals 

 sought. Thus the two mean proportionals 

 between a and b are \/ a- b and \/afr 

 or between 2 and 16 the mean pro. 

 portionals are \/64, and ^/3T2 = 4 

 and 8. 



MEAN distance of a planet from the SUH, 

 in astronomy, is the right line drawn 

 from the sun to the extremity of the con- 

 jugate axis of the ellipsis the planet moves 

 in ; and this is equal to the semi-trans- 

 verse axis, and is so called, because it is 

 a mean between the planet's greatest and 

 least distance from the sun. See DIS- 

 TANCE. 



MEAN motion, in astronomv, that \\ here- 

 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 quanti- 

 ty, estimated as one, to which the propor- 

 tion of other similar quantities may be 

 expressed. 



Measure is classed under a variety of 

 heads, of which the following are illustra- 

 tions. 



MEASURE of velocity, is the interval ot 

 space between two points, regularly pass- 

 ed through by a substance in constant and 

 uniform motion, within a certain period 

 of time. 



MEASUIIE 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. 



MK VSUIIE of a line, is the extension of a 

 right line at pleasure, which is to be con- 

 sidered as unity ; for instance, an inch, a 

 foot, or a yard. 



MKASUUE of a figure, or a surface per- 

 fectly level, thence called a plane survive?, 

 is a square inch, foot, or yard. This 

 square is termed the measuring unit, be- 

 cause the side is an inch, a foot, a yard, 

 or any other determinate extent. 



MKASUHE of a certain portion or quantity 

 of matter, is its weight. 



MEASURE of a number, applies thus : 2 is 

 the measure of 4, 3 of 6, &c. ; in fact, it is 

 any number which divides without a re- 

 mainder. 



It has long been wished by the learn- 

 ed, that an universal measure, secured by 

 penalties in an unalterable state, hadt 

 hitherto been, or may hereafter be adopt- 

 ed, which would prove of incalculable, 

 advantage to mankind in their philosophi- 

 cal and even less exalted pursuits. Pre- 

 judices are, however, far too numerous 

 and powerful to be easily overcome, or 

 removed, in matters of infinitely less mo- 

 ment. \Ve cannot, therefore, entertain 

 the slightest hope that national partiality 

 will be subdued in every quarter of the 

 globe, so as to produce a general resigna- 

 tion of favourite methods, in order to 

 adopt a new one recommended by a con-. 

 ^TCSS of philosophers, whfirh it would bo 



