VAR 



Sauriam, arranged by Linnaeus under 

 the great genus Lacerta. 



VAREC. The French name for help, 

 or incinerated sea-weed. 



VARIABLE MOTION. In Mecha- 

 nics, a variable motion is that which is 

 produced by the action of a force which 

 varies in intensity, or which continues 

 to act after motion has been communi- 

 cated to it. 



VARIABLE QUANTITY. In Ma- 

 thematics, a quantity is called variable, 

 which continually increases or decreases, 

 asdistinguished from a constant quantity, 

 which remains always the same. Thus, 

 the abscissas and the ordinates of an 

 ellipsis, or other curve line, are variable 

 quantities, because they vary or change 

 their magnitudes together. The dia- 

 meter of a circle and the parameter of a 

 conic section are constant, while their 

 abscissas are variable. Variable quan- 

 tities are usually denoted by the last 

 letters of the alphabet, x, y, z, while the 

 constant are denoted by the first a, b, c. 

 VARIABLE STARS. Stars which 

 undergo a periodical increase and dimi- 

 nution of their lustre. The star called 

 Algol, or (3 Persei, is usually visible as a 

 star of the second magnitude, and such it 

 continues for the space of 2d. 14h., when 

 it suddenly begins to diminish in splen- 

 dour, and in about 3^ hours is reduced to 

 the fourth magnitude. It then begins 

 again to increase, and in 3^ hours more 

 is restored to its usual brightness, going 

 through all its changes in 2d. 20h. 48m., 

 or thereabouts. This remarkable law of 

 variation suggests the revolution round 

 it of some opaque body, which, when in- 

 terposed between us and Algol, cuts oflT 

 a large portion of its light. Herschel. 



VARIATION. An algebraical rule 

 for investigating the relation which vary- 

 ing and dependent quantities bear to 

 each other. When one quantity y de- 

 pends upon another x, in such a manner 

 that if X is changed in value, the value 

 of y is changed in the same proportion, 

 then y is said to vary directly as x, or, 

 shortly, to vary as x. Variation is merely 

 an abridgment of Proportion ; for one 

 quantity is said to " vary " as another, 

 not because the two increase and de- 

 crease together, but because as one in- 

 creases or decreases, the other increases 

 or decreases in the same proportion. The 

 sign used to denote variation is a (read 

 varies as). Thus, x^ + 3x a 2x^ + 6x, 

 x^ + 3x ^ ^^ whatever be the 



since 



2x^ + 6x 



358 



VAR 



value of X. Single and Double Rule of 

 Three sums are solved upon the prin- 

 ciples of Variation and Proportion. 



1. One quantity is said to vary directly 

 as another, when the two quantities de- 

 pend wholly upon each other, and in 

 such a manner, that, if one be changed, 

 the other is changed in the same propor- 

 tion. If the altitude of a triangle be in- 

 variable, the area varies as the base. 



2. One quantity is said to vary in- 

 versely as another, when the former can- 

 not be changed in any manner, but the 

 reciprocal of the latter is changed in the 

 same proportion. If the area of a triangle 

 be given, the base varies inversely as the 

 perpendicular altitude. 



3. One quantity is said to vary as two 

 others jointly, if, when the former is 

 changed in any manner, the product of 

 the other two be changed in the same 

 proportion. The area of a triangle varies 

 as its base and perpendicular altitude 

 jointly. 



4. One quantity is said to vary directly 

 as a second and inversely as a third, when 

 the first cannot be changed in any man- 

 ner, but the second multiplied by the 

 reciprocal of the third is changed in the 

 same proportion. The base of a triangle 

 varies as the area directly and the per- 

 pendicular altitude inversely. 



VARIATION OF THE COMPASS. 

 This term, as well as the expressions, 

 " variation of the needle " and " declina- 

 tion of the needle," denotes the angle 

 which a vertical plane passing through 

 the axis of a magnetized needle makes 

 with the geographical meridian of a ship 

 or station ; and as, for the purposes of 

 navigation, the needle is made to traverse 

 horizontally, the variation becomes the 

 angle between the magnetic axis of the 

 needle and a meridian line passing par- 

 allel to the horizon through the centre 

 of the compass. 



VARIATION OF CURVATURE. 

 The change of curvature which takes 

 place in passing from one point of a 

 curve to another. In the conic sections, 

 the variation of curvature at any point 

 is proportional to the tangent of the angle 

 included between the diameter and the 

 normal both of these passing through 

 that point. The circle is the only curve 

 in which the curvature is uniform at 

 every point. 



VARIATIONS, BAROMETRICAL. 

 The changes in the altitude of the baro- 

 meter at the same place are in part regu- 

 lar, and in part extremely irregular. 



