seriema 
the legs are bare above the suffrage; the head is crested 
with a f ron till egret; the bill is red ; the bare orbit bluish ; 
the iris yellow; the 
plumage is dark, but 
somewhat variegat- 
ed with lighter col- 
ors, and the tail is 
tipped with white. 
The seriema inhabits 
the compos of Brazil 
and northern Para- 
guay, and may be do- 
mesticated. Fur its 
technical names, see 
Cariama and Caria- 
5509 
. . . Bemoulllan series. See Benwul- 
i . 
linn. Bluet's series, the series 
* w= \J "<*- 
"l 
Seriema (Cllr ,- ama .*,,,,,;. 
series (se'rez or 
se'ri-ez), n. ; pi. 
si-ries. [In earlier 
use (ME.) serie, 
< OF. 'serie, F. 
serie = Sp. Pg. It. 
m-rie; < L. series, 
a row, succes- 
sion, course, se- 
ries, connection, 
etc., < iterere, pp. 
sertim, join toge- 
ther, bind, = Gr. 
elpeiv, fasten, bind; cf. aeipd, a rope, Skt. -^ si, 
bind. From the same L. verb are also ult. E. as- 
sert, ilrsert, dixsert, exert, exscrt, insert, seraglio, 
Kcrinl, etc.] 1 . A continued succession of simi- 
lar things, or of things bearing a similar rela- 
tion to oue another; an extended order, line, or 
course ; sequence ; succession : as, a series of 
kings; a series of calamitous events; defini- 
tions arranged in several distinct series. 
A dreadful series of intestine wars, 
Inglorious triumphs and dishonest scars. 
Pope, Windsor Forest, 1. 325. 
A series of unmerited mischances had pursued him from 
that moment. Sterne, Tristram Shandy, vi. 13. 
2. In geol., a set of strata possessing some com- 
mon mineral or fossil characteristic : as, the 
greeusand aeries; the Wenlock scries. 3. In 
diem., a number of elements or compounds 
which have certain common properties and re- 
lations, or which exhibit, when arranged in or- 
derly succession, a constant difference from 
member to member. Thus, the elements lithium, 
sodium, potassium, rubidium, and ctesium form a natural 
series having the familiar properties of the alkalis, and 
certain striking physical relations to the other elements. 
The hydrocarbons methane (CH 4 ), ethane (C 2 H 6 ), propane 
(CsHa), etc., form a series having the constant difference 
CHg between successive members, but all the members 
having in common great chemical stability, slight reac- 
tive properties, and incapacity to unite directly with any 
element or radical. 
4. In numis., a set of coins made at any one 
place or time, or issued by any one sovereign 
or government. 
In the Thracian Chersonese the most important series 
is one of small autonomous silver pieces, probably of the 
town of Cardia. Encyc. Brit., XVII. 640. 
5. In i>kilately, a set of similar postage- or reve- 
nue-stamps. 6. In math., a progression; also, 
more usually, an algebraic expression appear- 
ing as a sum of a succession of terms subject 
to a regular law. In many cases the number of terms 
is infinite, in which case the addition cannot actually be 
performed ; it is, however, indicated. 
7. In systematic bot., according to Gray, the 
first group below kingdom and the next above 
class: equivalent to subkingdom or division 
(which see). In actual usage, however, this rule is by 
no means always observed. In Bentham and Hooker's 
"Genera" it is a group of cohorts with two stages be- 
tween it and kingdom ; and in the same and other good 
works it may be found denoting the first subdivision of an 
order, a tribe, a subtribe, a genus, and doubtless still other 
groups. It appears, however, always to mark a compre- 
hensive and not very strongly accentuated division. 
8. In zool., a number of genera in a family, of 
families in an order, etc.; a section or division 
of a taxonomic group, containing two or more 
groups of a lower grade : loosely and variably 
used, like grade, group, cohort, phalanx, etc. 
9. In anc. pros., same as colon^, 2. 10. In 
bibliography, a set of volumes, as of periodical 
publications or transactions of societies, sepa- 
rately numbered from another set of the same 
publication. Abbreviated ser Abel's series, the 
series xt x 9B\ 
i-^-i f"(2/3)+ 
where <(>(n) is denned by the equation 
rw^-^^-'e -*'">. 
Binomial series, the series of the binomial theorem. 
Burmann's series the series of Burmann's theorem 
(which see, under theorem). Cayley's series, the series 
t(x + o + b -r c + e . . .) = t(x f- 6 + c + e i ) 
+ / do. t'(x + c + e + . . .) 
seringa 
That the nth differential coefficient relatively to x should 
be equal to lu ! is the necessary and sutlick-nt condition 
of n being prime. Lame's series, hanif a- nimnum"* 
-Laplace's series, the series of Laplace's theorem 
< whirh see, under theorem). Law of a series, that rela- 
tion which subsists between the successive terms of a se- 
ries, and by which their general term may be expressed. 
Leibnitz's series, the series 
D'"uv = wD'"o 
/a /*+ b 
do/ d(o i b) t"(x i e + ...) + ... 
o 
Circular series, a series whose terms depend on circular 
functions, as sines, cosines, etc. Contact series of the 
metals. Same as electromotive series. Continued se- 
ries, a continued fraction. Convergent or converging 
series. See converging. Descending series. See de- 
scending. De Stairville's series, the series 
+ o(a + *)(o T 2*)z=/3! + .-. 
Determinate series, a series whose terms depend on 
different powers or other functions of a constant. Di- 
richlet's series, the series 2( 1-, where I j is the 
Legendrian symbol. Discontinuous series, a series 
the value of the sum of which does not vary continuously 
with the independent variable, so that for certain values 
of the variable the series represents one function and for 
other values another. Thus, the series 
Arithmetical series, a succession of quantities each dif- 
fering from the preceding by the addition or subtraction 
of a constant difference, as 1, 3, 5, 7, 9. 11, etc., or 10, 8, , 
4, 2, 0, 2, 4, 6, etc.; algebraically, a, a - d, a + 2d, 
a + 3d, a + 4d, etc., or z, zd, z 2d, z 3d, z 4d, etc., 
where o represents the least term, z the greatest, and d the 
common difference.- Ascending series, a series accord- 
ing to ascending powers of the variable, as <1 + a t x + ajc* 
is equal to J4> for values of <t> between - it and + it ; but 
for values between IT and 2ir, it is equal to *<ir </>). Di- 
vergent series. See divergent. Double series, a series 
the general term of which contains two variable integers. 
Such a series is the following : 
a 00 +,* -<-a a .,x* + 
-hO, COSJ! +01,3 COS* \a,,X-COSX +... 
+ a 20 cos2a; raj,* cos 2ZJ-032* 5 cos 2* r. . . 
Eisenstein's series, the double series the general term 
of which is 1 /(M 3 + N 3 + . . .X, where M, N, are integers 
varying independently from 1 to oc. Electrochemical, 
electromotive, equidifferent series. See the adjec- 
tives. Exponential series, a series whose terms depend 
on exponential quantities. Factorial series, a series 
proceeding by factorials instead of powers of the variable. 
Farey series, a succession of all proper vulgar frac- 
tions whose tenns do not exceed a given limit, arranged 
in order of their magnitudes. Fibonacci's series, the 
phyllotactic succession of numbers : 0, 1, 1, 2, 3, 5, 8, 13, 21, 
34, 55, 89, etc. These numbers are such that the sum of any 
two successive ones gives the next, a property possessed 
also by the series 2, 1, 3, 4, 7, 11, 18, 29, 47, 78, etc., and by 
no other series except derivatives of these. The series is 
named from the Italian mathematician Fibonacci or Leo- 
nardo of Pisa (first part of the thirteenth century), who 
first considered it. Also called Lami 'i series. Figurate 
series, a regular succession of flgurate numbers. Finite 
series, a polynomial consisting of all the terms which sat- 
isfy a certain general condition, especially when, by virtue 
of that condition, they have a determinate linear order. 
Fluent by series. See fluent. Fourier's series, the 
series 
, fir i /"IT 
to = - / f(0)ds + cos x. - / f(3) cos p.ds 
air*/ TT itffTT 
- / " 
II J If 
.~ / f(/3)co820.d/3 
"' ~ " 
Logarithmic series, a series whose terms depend on 
logarithms. Maclaurin's series, the series of Mac- 
laurin's theorem (which see, under theorem). Halaco- 
ZOic series. See malacozoic. Mixed series, a series 
whose summation partly depends on the quadrature of 
the circle and partly on that of the hyperbola. Num- 
mulitic series. See nmnamlitic. politic series. See 
oolite. Osborne series, in yed., a division of the Lower 
Tertiary series, forming a subgroup in the Older Miocene, 
or Oligocene, of the Hampshire basin, England, and the 
Isle of Wight. It consists of clays, marls, sands, and 
limestones, with fresh-water shells, and is about 70 feet 
in thickness. Also called St. Helen's beds. Pea-grit 
series. See pea-grit. Reciprocal series, a series each 
term of which is the reciprocal of the corresponding 
term of another stries. Recurrent series, a series in 
which each term is a given linear function of a certain 
number of those which precede it. Recurring series. 
See recMrrinjr.-Red Marl series. See warn. -Rever- 
sion of series. See reversion. Rhizoristlc series. 
See rhizoriatit. Schwab's series, the succession of posi- 
tive numbers A, B, C = J(A H B), D = /BC, E = j(C D), 
F = V/DE, etc. Semi-convergent series, (o) A series 
which is at first convergent and afterward divergent. 
Such series are of great value, and frequently afford ex- 
tremely close approximations, (b) A series which is con- 
vergent although if the signs of all the terms were the 
same (or their arguments considered as imaginaries were 
the same) it would be divergent Series dynamo. See 
electric machine, under electric. Summation of series, 
the method of finding the sum of a series whether the 
number of terms is finite or infinite. See profession. 
Syllogistic series, a logical sorites. Taylor's series, 
the series of Taylor's theorem (which see, under theorem). 
The general term of a series, a function of some 
indeterminate quantity x, which, on substituting succes- 
sively the numbers 1, 2, 3, etc., for x, produces the terms 
of the series. Thermo-electric series. See thermo- 
electricity. To arrange in series, as voltaic cells. See 
battery, 8 (b). To revert a series. See revert. Trigo- 
nometric series, a series in which the successive terms 
are sines and cosines of successive multiples of the varia- 
bles multiplied by coeflicients - that is, the series 
Ao + A^osa; r A s cos2a! r . 
+ 8,8111 x B 3 sm2a; + . . . 
series-wound (se'rez-wound), a. Noting dyna- 
mos or motors wound in series, or so that the 
wire of the field-magnets forms a part of the 
armature and exterior circuit. See electric ma- 
chine, under electric. 
serif (ser'if ), n. [Also eeriph and serif h ; origin 
obscure.] The short cross-line put as a finish 
at the ends of the terminating or unconnected 
strokes of roman or italic types, as in H, 1, d, 
and y. Its form varies with the style of the type: in 
the Elzevir it is short and stubby ; in some French styles 
IHL IHL IHL 
it is long, flat, and slender ; in the Scotch-face it is curved 
like a bracket on the inner side. See sons-sen/. 
i f* 
+ sin Hx. - I f(/3) sin 2,3.d,3 -f . . . 
17 J Tt 
Functional series, a series in which the general term 
contains a variable operational exponent. Gaussian 
series. See Gaussian. Geometrical series, a series in 
which the terms increase or decrease by a common multi- 
plier or common divisor, termed the common ratio. See 
progression. Gregory's series, the series arc tan x = 
x iz 3 + Jx* }x'+ . . .Harmonic series, the finite 
series 1 + i + J + J +... + !/, which is nearly equal to 
not log vXn~nj-t- 1 /6n(n + 1) + 0.5772156649. Heine's 
series, or Helnean series, the series 
1 oa lo* 1 Q a 1 O1+ 1 1 O* 1 oM- 1 
1 -f - X-i -=-5 = _, 1 iC a -t-. . . , 
invented by Heine in 1847. Hyperbolic series, a series 
whose sum depends upon the quadrature of the hyper- 
bola, as the harmonic series. Hypergeometric series. 
Same as Gaussian series. Indeterminate series: See 
indeterminate. Infinite series, an algebraical expres- 
sion appealing as a sum of terms, but differing therefrom 
in that the terms are infinite in number. The most usual 
way of writing an infinite series is to set down a few of 
the first terms added together, and then to append " + ..., 
or + etc.," which is not addition, certainly, but is the in- 
dication of something analogous to the addition of the 
terms given. Another way is to write a general expression 
for any one of the terms of the series, and to prefix to this 
:, the sign for summation. In series. See in parallel, 
under parallel. Jet-rock series. See >(-. Karoo se- 
ries. See karoo. Lagrange's series, the series of La- 
grange's theorem (which see, under theorem). Lambert's 
series, the series 
_____ 
1 z^l x'^1 x 
Seriform (se'ri-form), a. [< L. Seres, Gr. 
the Chinese, + forma, form.] Noting a section 
of the Altaic family of languages, comprising 
the Chinese, Siamese, Burmese, etc. [Rare.] 
Imp. Diet. 
Serilophus (se-ril'o-fus), . [NL. (Swainson, 
1837), emended to' Sericolophus (Reichenbach, 
1850), < Gr. rnip/K6f, silken, + ~Ao<l>oc, crest.] An 
Indian genus of broadbills of the subfamily 
Eurylsminae, containing such species as 8. lu- 
natus, the lunated broadbill, which ranges from 
Tenasserim to Rangoon. S. ntbropygiiis is a 
Nepaulese species. 
serin (ser'in), . [< F. serin, in., serin?, f. (NL. 
Serinus), OF. serin, serein = Pr. serin (ML. se- 
rena), according to some < L. citrinus, citrine, 
i. e. yellow (see citrine), according to others a 
serin, canary; lit. a siren, = OF. serene: see 
siren.'] A small fringilline bird of central ami 
southern Europe, the finch Fiingilla serin us or 
Serinus hortulanm, closely related to the canary. 
It very closely resembles the wild canary in its natural 
coloration, and the canary is in fact a kind of serin-finch. 
See Serinus (with cut). 
serinette (ser-i-nef), [F., < seriner, teach 
a bird to sing, < serin, a serin: see Mrm.] A 
small hand-organ used in the training of song- 
birds; a bird-organ. 
serin-finch (ser'in-fiuch), H. The serin or other 
finch of the genus .Serin MX, as a canary-bird. 
seringa (se-ring'ga), . [So called because 
caoutchouc was used to make syringes; < Pg. 
