376 ALT 
proper to any medicines, all of them may be ufed as al¬ 
teratives, and the molt powerful alteratives are evacuants, 
given in diminilhed dofes, if repeated at proper intervals; 
by adminiltering them thus, or mixed with fuch alteratives 
as the cafe may indicate; though the difcharge they pro¬ 
mote, when given in full dofes, is not encreafed, they pafs 
into the blood, and the fecretions are promoted whereby 
the faulty natural excretions are regulated. 
ALTERC A'TION, f. [altercation, Yv. altercor, Lat.] 
Debate; controvcrly ; wrangle.—Our whole life is little 
elfe than a perpetual wrangling and altercation-, and that, 
many times, rather for victory and oflentation of wit, than 
a fober and ferious fearch of truth. Hahcwitl. 
ALTE'RN, ad]. [alternus , Lat.] Acting by turns, in 
fucceflion each to the other: 
And God made two great lights, great for their life 
To man; the greater to have rule by day. 
The lefs by night, allcrn. Milton. 
ALTE'RNACY, f. Action performed by turns. 
AI.TE'RN-BASE,yi in trigonometry, a term ufed in 
contradilr.inftion to the true bale. Thus in oblique trian¬ 
gles, the true bale is either the fum of the tides, and then 
the difference of the lides is called the altern-bafe ; or the 
true bafe is the difference of the lides, and then the fum of 
the (ides is called the altern-bafe. 
ALTE'RNATE, adj. [ alternus , Lat.] Being by turns ; 
one after another; reciprocal.—Friendlhip conlills pro¬ 
perly in mutual offices, and a generous ftrife in alternate 
;t6bs of kindnefs. South. 
Hear how Timotheus’ various lays furprife, 
And bid alternate paffions fall and rife! 
While, at each change, the foil of Lybian Jove 
Now burns with glory, and then melts with love. Pope. 
At.tern ate, f. That which happens alternately; vi- 
ciflitude -. 
And rais’d in pleafure, or repos’d in eafe, 
Grateful alternates of fubllantial peace, 
They bids the long nocturnal influence Hied 
On the crown’d goblet, and the genial bed. Prior. 
Alternate, in heraldry, is faid in refpeft of the fitu- 
ation of the quarters. Thus, the fir ft and fourth quarters, 
and the fecond and third, are ufually of the fame nature, 
and are called alternate quarters. 
Alternate, in botany, when the leaves or branches 
of plants arife higher on oppolite lides alternately. 
Alternate Angles, in geometry, are the internal 
angles made by a line cutting two parallels, and lying on 
the oppolite lides of the cutting line ; the one below the 
firft parallel, and the other above the fecond. 
To Alternate, v. a. f altcrno, Lat.] To perform al¬ 
ternately. To change one thing for another reciprocally. 
-—The molt high God, in all things appertaining unto this 
life, for fundry wife ends, alternates the difpolition of good 
^indevil. Grew. 
ALTERNATELY, a do. In reciprocal fucceflion, fo 
that each (hall be fucceeded by that which it fucceeds, as 
light follows darknefs and darknefs follows light.—The 
rays of light are, by fume caufe or other, alternately difpo- 
fed to be reflected or refracted for many vicillitudes. Newton. 
Unhappy man! whom forrow thus and rage 
To different ills alternately engage. Prior. 
ALTE'RN ATENESS,yi The quality of being alter¬ 
nate, or of happening in reciprocal fucceflion. 
ALTERNA'TION, f. The reciprocal fucceflion of 
things.—The one would be opptelled with conflant heat, 
the other with infufferable cold; and fo the deleft of al- 
temation would utterly impugn the generation of all things. 
Brown. 
Alternation is alfo ufed to exprefs the different 
changes or alterations of orders in any number of things 
propofed. This is alfo called permutation, Sc. and is ealily 
found by a continual multiplication of ali the numbers, 
ALT 
beginning at unity. As fuppofe two things a and b ; thefe 
may be placed either thus ab or ba, that is, two ways, or 
1X2. If there be three things, a, b, c, then the third 
thing c, may be placed three different ways with refpeft 
to each of the two pofitions ( ab and ba) of the other two 
things, it may fraud either before them, or between them, 
or after them both, that is, it may Hand either firft, fe¬ 
cund, or third; and therefore with three things there will 
be three times as many changes as with two, that is, 
1X2X3, or fix changes with three things. Again, if 
there be four things, a, b, c, d, then the fourth thing cl, 
may be placed in four different ways with refpeft to each 
of the fix politions of the other three ; for it may be fet 
either firft, or fecond, or third, or fourth, in the order of 
each polition ; confequently, from four things there will 
be four times as many alternations as there are from three 
things; and therefore 1X 2 X 3X4=24, is the number of 
changes with four things. And lo on, always multiply¬ 
ing the laft-found number of alternations by the next num¬ 
ber of things; or to find the number of changes for any 
number of things, as n, multiply the l’eries of natural 
numbers 1, 3, 4, 5, &c. to n, continually together, and 
the la ft product will be the number of alternations fought; 
fo 1 X 2 X 3 X4X 5-• ••«, is the number of changes in n 
things. So if, for example, it were required to find how 
many changes may be rung on 1? bells; it would be 
1X2X3X4X5X6X7X8X9X10X11 X 12=479001600, 
the number of changes. Now fuppofing there might be 
rung 10 changes in one minute, that is, 10X12 or 120 
Itrokes in a minute, or two (trokes in each fecond of time ; 
then, according to this rate, it would take upwards of 91 
years to ring over all thefe changes on the 12 bells only. 
Alfo, if but two more bells were added, making 14 bells ; 
then, at the fame rate of ringing, it would require about 
16575 years to ring all the changes on 14 bells but once 
over. And, if the number of bells were 24, it would re¬ 
quire more than 11700000000000000a years to ring all the 
different changes upon them ! 
ALTERNATIVE, J'. [alterndtif, Fr.] The choice 
given of two things; lo that, if one be rejected, the other 
mult be taken: 
A ftrange alternative - - 
Mult ladies have a doftor, or a dance ? Young. 
ALTERNATIVELY, adv. In alternate manner; by 
turns; reciprocally.—An appeal alternatively wroAt may be 
tolerated by the civil law as valid. Aylijfe. 
ALTE'RNATIVENESS, f. The quality or ftate of 
being alternative; reciprocation. 
ALTE'RNITY,yi [from altern. ] Reciprocal fuccef- 
fion; vicifiitude; turn; mutual change of one thing for 
another; reciprocation.—They imagine that an animal of 
the vafteft dimenlions, and longeft duration, ihouldlive in 
a continual motion, without the altcrnity and viciffitude of 
reft, whereby all other animals continue. Brown. 
AI.TH/E'A,/! [aASai«, from ulTtavuv, Gr. to heal.] 
In botany, a genus of the monadelphia polyandria clafs, 
ranking in the natural order of coin mni ferae. The gene¬ 
ric charafters are—•£alvx : perianthium double; outer 
fmaller, one-leafed, unequally novemfid; divifions very 
narrow; inner femiquinquefid, divifions broader, fharper. 
Corolla: five-petalled, united at the bafe, obcordate, pra?- 
morfe, flat. Stamina: filaments many, inferted into the 
corolla; anthene fubreniform. Piftillum: germ orbicu- 
late ; ftyle cylindrical, Ihort; ftigmas many (twenty), fe- 
taceous, the length of the ftyle. Periparpium: conliftsof 
arils not jointed, forming a flat ring about a columnar re¬ 
ceptacle ; they are deciduous, and open on the infide. 
Seed: one, flat-kidney-fhaped in each aril.— F.JJcntialCha- 
rafter. Calyx double; outer nine-cleft. Arils many, 
one-leeded. 
Species. 1. Althica officinalis^ or common marfli-mal- 
low : leaves Ample, downy. Common or officinal marffi- 
mallow grows naturally in fait marfties, and on the banks 
of rivers and ditches in Cambridgelhire, Norfolk, and 
Suffolk; 
