VARIATION. 



VARIATION'. 



to tad that it hod rapidly Increased in brightness. It was now equal 

 to a ( Yntaiiri, ami far surpassed in brightness all the other Axed atari 

 except Oinopas and Sirlus. It attained ita maximum brightness on 

 the and of January. IMS. Shortly afterward, it grew fainter, and it 

 ontimwd to dinunwh in brightness till March, 1843. In the following 

 in nth it again rapidly increased in brightness. According to the ob- 

 servations of XaoW at the Cape of Good Hope, and of Maokay at 

 Calcutta, it now surpassed Oanopu! in brightness, and ahnott rivalled 

 Siriiim, It eontinned (or several yean to exhibit this great degree of 

 brightness, when it began to fluctuate at before. 



The new (tan which hare appeared in tlie ixv.vcns, and of wlikli 

 several instances an reeorded in hutory, probably belong to the elan 

 of variable stars. The mort notable objecU of this description, are the 

 new tar which appeared in 1572, of which Tyolio lirohe baa given a 

 detailed account, and the new star of 1004, which wai observed by 

 Galileo and Kepler. 



The following table of variable stare, drawn up by Mr. 1'ogson, in 

 extracted from vol. xvii. of the ' Observation! made at the HaiU-lillo 

 Observatory,' Oxford. Mr. 1'ogson is known aa oue of the moat suc- 

 cessful expioren of thia interesting field of astronomy. 



The epochs marked thus f are epochs of minimum. 



No mtUfactory explanntion of the phenomena of variable stars ho 

 hitherto been advanced by any inquirer. Borne astronomers have 

 oggerted that the variation! of light may be due to dark bodies 

 circulating around the rtar". According to others, the fluctuations of 

 brightneM may ariae from the presence of dark tracts on the surfaces 

 of the atan, which are periodically turned towards the earth by the 

 revolution of the star* on their axes. The phenomena, however, are in 

 general so irregular, that neither of them hypotheses is capable of 

 atUactorily accounting for them. 



VARIATION. Under thia bead come* the explanation of a part of 

 the language of proportion which is much used, and which was once 

 very prominent in Kngluh mathematical writing*. We refer to such 

 pbraw* a* the following : A variee M B A varies inversely aa B-the 

 gravitation of particles varies inversely as the square* of their distances 

 -. time of oscillation of a pendulum varies as the square root of its 

 Matt, Ac. 



When w* ny that one thing varies as Mother, we mean that there 

 are two variable magnitudes which have this property, that if when 

 the Brat change* from A to n the second change from o to 6, then A 

 is to in the same proportion a* a to . And when we say that one 

 thing varies inversely as another, we mean that if when the first 

 ihanges from A to B the second changes from a to J, then 



1 I 

 A : B :: -: or : : 6 : . 



The modes of denoting these laws of eormertioi n- .1 to ta, In Kngli-h 



A a o 



A <* _. 



a 



These were in fact but modes of writing the equations 



ea 



in a manner which should recognise tlicir exiftinr 

 us to think of the particular value of the coukint c. According tn the 

 preceding equation.*, if we take the first, and suppose that A changes 

 into D when a, changes into b, we see obviously that A-=-B is the same 

 sut a~-b, both being equal to c. And A oc a informs us that A -4- a ia 

 always the same quantity, without faying what it is. 



When one quantity varies as both of two others jointly, it means 

 that if either of Iho second and third mentioned remain constant, tho 

 first varies as the other. Thus tho price of a quantity of goods varies 

 jointly as tho number of things and the price of each. At a given 

 price per article, the whole price varies as the number of things ; for a 

 given number of things, the whole price varies as the price of ono. 

 When x varies as y and; jointly, tho o|ii:iticni .r = cy: if implied. 



We arc rather inclined to regret tho complete disappearance of tho 

 notation of variations which has taken place within the last thirty 

 years, though the phrtucology is itill iii *ome degree of use. It in now 

 usual either to write equations at full length, or to make an equation 

 of tho variation itself, which can always be done by a proper choice of 

 units. Thus A oc a, or A = c a, can always be made A = a, if such choice 

 of units be made in which to measure tho magnitudes A and a as will 

 make e = 1. Thi! must be done by contriving that A and nhall 

 become unity together. But this, 1> Mvenient for men- calcu- 



lation, is likely enough to produce confusion in the mind of the 

 learner, and actually docs so in in.iny inntances. It is ol)\ i 

 that of two different kinds of magnitude one may ran/ as the other : 



