S E R
S E R
Bollard Sena, in botany, a name by which authors call
caljia. See the article Cassia, Suppl. Bladder-fen A, theEnghfh. name of a genus of plants., called
by botanifts colutea. See the article Colutea, Suppl. Padded-fen A) the name by which the coron'dla of botanical waiters is fometimes called. See the article Coronilla, Suppl. Scorpion- fern a, the name of a genus of plants, called by authors emerus, See the article Em erus, Suppl.
SENGREEN, a name fometimes given to fedum, or houfeleek. See the article Sedum, Suppl.
SENNA, in botany, &c. ' See Sena, Cycl. and Suppl. SENSITIVE- plant, mimofa, in botany, the Englifh name of a.diftinct genus of plants. See the article Mimosa, Suppl. SEPELAER. See Platea, Suppl.
SEPIA, in zoology, the name of a genus of fea-infects of the gymnarthria. kind, called by us the cuttle- fijh, and ink-fifl). See lNK-fA Append.
The body of the fpia is of an oblong figure, and depreffed ; it is furnifhed with ten tentacula, two of which are longer than the others, and. are pedunculated. It is often fix inches in length, and three and a. half in diameter. Itiis fupported by an oblong, light and fpungy fubftance, of a friable texture, and lined with a light fungous pith. This is ufed by the filver-fmiths, and as a dentifrice under the name of. os fpittm, os fepiec, or cuttle-fifh-bpne. Hill s Hift. of Anim. p. 97. SEPTICS, among phyficians, an appellation given to all fuch fubftances as pmmote. putrefaction. See Putrefaction, Jppend.
From the. many curious experiments, made by Dr. Pr ingle to afcertain die. feptic and antifeptic virtues of natural bodies, it appears that there are very few fubftances of a truly feptic nature. Thofe commonly reputed fuch by authors, as the alcaline and volatile falts, he found to be no wife feptic. How- ever, lie difcovered fome, where it itemed Icaft likely to find any fuch quality: thefe were chalk, common fait, and the teftaceous powders. He mixed twenty grains of crabs eyes, prepared with fix drachms of ox's gall, and an equal quantity of water. Into another phial he ptit an equal quan- tity of gall and water but no crabs-eyes. Both thefe mix- tures being placed in the furnace, the putrefaction began much fooner, where the powder was, than in the other phial. On making a like experiment with chalk, its feptic virtue was found to be much greater than that of the crabs- eyes : nay, what the doctor had never met with before, in a mixture of two drachms of flefh, with two ounces of wa- ter and thirty grains of prepared chalk, the flefti was refolved into a perfect mucus in a few days.
To try whether the teftaceous powders would alfo diffolve vegetable fubftances, the doctor mixed them with barley and water, and compared this mixture with another of barley and water alone. After a long maceration by a fire the plain water was found to fwell the barley, and turn mucilaginous and four j but that with the powder kept the grain to its natural fize, and though it foftencd it, yet made no mucilage and remained fweet.
Nothing could be mnre unexpected, than tq find fea-falt a hafrener of putrefaction ; but the fact is thus. One drachm of fait preferves two drachms of frefh beef in two ounces of water, above thirty hours, uncorrupted, in a heat equal to that of the human body ; or, which is the fame thing, this quantity of fait keeps flefh fweet twenty hours longer than pure water. But then half a drachm of fait does not preferve it above two hours longer. Twenty five grains have little or no antifeptic virtue,' and ten, fifteen, or even twenty grains manifeftly both haft en and heighten the cor- ruption. The quantity, which had the moft putrefying quality, was found to be about ten grains to, the above pro- portion of flefh and water.
Many inferences might be drawn from this experiment. One is, that fince fait is never taken In aliment beyond the propor- tion of the corrupting quantities, it would appear that it is fubfervient to digeftion, chiefly by it's, feptic virtue, that is, by foftening and reiolving meats; an action very different from what is commonly believed.
It is to be obferved that the above experiments were made with the fait kept for domeftic ufes. See Pringle, Obferv. on thedifeafes of the army, p. 848, feq.
SERAPH (Cycl.)— Seraph is alfo the name of a Turkifli gold- coin, worth about five {hillings fterling. Diet. Ruff, invoc. SERCIL feathers of a hawk, the fame with thofe called pini- ons in other fowl. Diet. Ruft. in voc.
SERE, in falconry, the yellow between the beak and eyes of a hawk. Diet. Ruff, in voc.
SERJEANT of the acatery, See.AcATERY, Cycl
SERIES, in algebra {Cycl.) — The notion" of a fries given in the Cyclopedia is too limited, when confined to ranks or pro- greflions of quantities increafing or decreafing in fome con- ftant ratio: for the term feries is indifferently ufed whether the terms of any number of quantities following each other liave a conftant ratio, or even relation or not. And, ftrictly fpeaking, a feries if quantities increafing or decreafing in a conftant ratio is no more than what is commonly called a geometric progreffion.
The doctrine of feries is of extenfive ufe in mathematics, and has been carried far; though not fo far as could be'wifhed; It would far exceed the limits of our defign to enter into a detail of the difcoveries relating to this fubject. Something, however, fhould be added to what has been faid in the Cyclopaedia, to give a notion of the principal kinds of feries, and the method of notation ufed in treating of them. A feries being propofedj one of the principal queftions concerning it, is, to find the law of its continuation. For this no univerfal rule can be given; but it often happens, that the terms of the feries taken two and two, three and three, or in greater numbers have an obvious and fimple relation, by which the feries may be determined and produced indefinitely; Thus if unity be divided by 1— x, the quotient will be a geo- metric progreffion, any term of which will be to the next an- tecedent term as a- to r. And by this property the feries 1 -f- x -f- x* -\~ x l -f- &c. may be diftinguifhed and pro- duced ad infinitum. In like manner in other cafes of divinon* other feries' s will arife, the terms of which will have a con- ftant relation to each other, and this relation recurring al- ways throughout the feries, they have been called recurring feries hy Mr. deMoivre, who firft confidered themj and ap- plied them to the folution of feveral intricate problems. See Recurring Series, infra.
In many cafes, the relation of the terms of a feries is not con- ftant, as it is in thofe arifing from divifion. Yet this relation often varies according to a certain law obvious upon infpecti- on. Thus in the fries 1 + f x -f- T 8 T x* -f- 44 x 3 -4- ,*g| x* -f. &c. The terms may be continued indefinitely by the continued multiplication of thefe fractions -}, 4, | ? -|," &c* And the following feries. 1 -|- ^ V~T 4v x% + -t4t ** + T-f-f-r ** -f* & c * ma y De continued by the multiplication of the fraffions &i, $M |^, 1*2. & c .
2X3 4X5OX78X9
Series's of this kind may be defined by differential equations. The equation defining z feries is that which affigns the rela- tion of the terms generally by their diftances from the be- ginning. To do this Mr. Stirling conceives the terms of the feries to be placed as fo many ordinates on a right line given by pofition, and he, for the fake of Simplicity, takes unity as the common interval of thefe ordinates. The ini- tial terms of the fries he denotes by the initial letters of the alphabet, A, B, C, D, &c. A being the firft, B the fecond, C the third &c. And he denotes any term in general by the letter T, and the reft following it in order, T', T", T'" - , T"", &c. He denotes the diftance of the term T from any given term, or from any given intermediate point be- tween two terms, by the indeterminate quantity as; fo that the diftances of the terms T', T", T'", &c. from the faid term or point, will be, z -f- i, z + 2, z -- 3 &c. for the increment of the abfeifs is the common interval of the ordinates, or terms of the fries applied to the abfeife* Thefe things being premifed let this feries be propofed* 1, 4 a-, 4 a- 3 , -/g a- 3 , T y ? a- 4 ", ~ T \ x s &c. in which the re- lations of the terms are B = \ A a-, C = | B a-, D — | C x, E = ■§ D x &t. The relation in general will be defined by
the equation, T' := — X-3 T x, where z denotes the di- ^ %-f- 1
ftance of T from the firft term of the feries. For by fUb-
ftituting 0, 1, 2,3,4, &c. fucceflively in the place of z, the
relations of the terms of the propofed fries will arife. In like
manner, if z be the diftance of T from the fecond term of the
% -J- 3 feries, the equation will be T' z= — — - T a-, as will an*
SS + -2 r
pear by fubfKtuting the numbers — 1, 0, 1, 2, 3, 4, &c^ fucceflively for %. Or if the indeterminate % denotes the place of the term T in the feries, its fucceffive values will be
I, 2, 3, 4, &c. and the equation will he T' — 1
•Ta*.
It appears therefore that innumerable differential equations may define^onc and the fame fries, according to the diffe- rent points 'from whence the origin of the abfchTa z is taken. And on the contrary the fame equation defines innumerable different feries's by taking different fucceffive values of. z.
For in the equation T' =- ~ - T x, which defines thefe-
ries above mentioned, when 1, 2, 3» 4, &c. are the fuc- ceffive values of the abfeiflse ; if I \, 2 -£> 3 £, 4 4, &c. be fucceflively fubfHtuted for 2, the relations of the terms arifing will be B — 3 A x, C = 4 B x, B—^-Cx, &c. from whence the fries A, | A x, T B T A **, 4| A x l , \*\ B x* t Sec. will arife, which is different from the former. But the equation will always determine the feries from the given values of the abfeiffa and of the firft term, when the equation includes but two terms of the feries; as in the laft example^ where the firft term being given, all will be given. But when the equation includes three terms, two muft be given; and three muff be given, when it includes four, and fo forth. Ifthey^rw A", 4 *a tv**9 tt» x7 > tH» x<) & c - ^ e pi"°pof-
ed, where the relations of the terms are, B = ^ A x\
2x3
I = ^^ 3 B a-% D = Z2JL C x\ &c. the equation defining 4x5 6x7' 6
this
