SER
infinite — t. If then, idly, that Tetffl in the
Quotient continually decreaie ; the Series will give a Quo- tient as near the Truth as poffible. _E. gr. If b=i, c=i and a =2; thefe Values fubftituted in the gene- ral Series, or the Divifion performed as in the general
Example; we ihall find f=s —L_ = i— ^-fi— T V + TJ
2+1 — sV+ri-Ti Bfc. Suppofe then, the Series to be broke off in the Fourth Term ; there will be a Deficiency : but 'twill be left than ~. If it be broke off in the Sixth, there will be a Deficiency, but that lefs than T J e , The further there- fore the Series is continued, the nearer it approaches to Truth, but never arrives at it*
16: ]
SER
After the like Manner we find | = — — =
tt -J- r' T) &c, In infinit. $ =,
3+1 1 .
4+1'
14 — rrr, (3c-. In Infinitum £= L_ ==',
5+'
xi T > *$ c - ' n Infinitum. This is a conftant Law, where- by all Fractions, whofe Numerator is Unity, may be ex- preffed by infinite Series : Thofe Series being all Geome- trical Progreflions, decreafing in fuch Manner as that the Numerator is always Unity ; and the Denominator of the firft Term, which is alfo the Exponent of the Ratio, differs by Unity from the Denominator of the Fraction to be refblved.
If the Terms of the Quotient be continually increafing, the Series recedes lb much the farther from the Quotient as it is continued longer; nor does it ever become equal to the Quotient, unlefs it be terminated ; and the laft Remainder be added under its Sign. XZ.gr, Suppofe
A= — — ; the Quotient will be found 1 — 2+4 — 8+
1+2 16 — 64+1281 iSc One Term, 1 exceeds | by an Ex- cels of -J- ; Two Terms come fhort by ±. Three Terms exceed by | ; Four fall fhott by ' T ', &c.' If the Series be
fuppofed to terminate in — 8 ; then will — L. = 1 — 1-4~
4— 8+'/- But ' — * + 4 8= — j =y. Therefore,
— L_ = \f — y =J, Suppofe the General Series to ter-
minate in —c 3 ; then
will ^,- i+c
f+c
.1+0
The Stars in the Conftellation Serpens, in 'Ptolemy's Catalogue are 17 ; in Tycho's 19 ; in the Britannic Cata- logue 59. The Longitudes, Latitudes, Magnitudes, &c. whereof are as follow.
Stars in the Conftellation Serpens Ophidchi.
flams and Situations of ^.Longitude the Stars. "3
m
To find an Infinite Series -\ r by extracting of Roots - - S See ^Quadrature if tie
To find an Infinite Series f \ Circle. by preiuppofed Series ) C
To extract the Roots of? „ ^Extraction of an Infinite Series i £ Roots.
SERMOLOGIES, in Church Hifiory, Books of Ser- mons, or Homilies of Popes and other Perfons of Emi- nence and SanSity, read at the Feafts of the Confef- fors, the Purification, All Saints, and on every Day from Chripnas totheOflaveof the Epiphany. See Homily. SERMONES, the Title Horace gives his Satyrs. The Criticks are divided about the Real'on of the Name. The Opinion of Father Boffil ftems well grounded. A mere Obfervation of Feet, and Meafure, iuch as we find in 'Terence, Tlautus, and in Horace's Satyrs, he thinks, is not fufficient to conftitute Verfe; to determine the Work to be Poetical ; or to diftinguilh it from Profc : unlefs it have fome further Air, or Character of Poetry ; fomewhat of the Fable, or the Sublime. See Poetrv. Hence it is, that Horace calls his Satyrs, 'Profe, Sermcnes. His Odes have qui te another Air, and ate therefore called, Teems, Carmina. See Poem, Prose, and Versification.
SERMONIUM, in Old Records, a kind of Interlude ot Hiftorical Play, which the Inferior Orders of Cleroy, affifted by Boys, (£c. ufed to act in the Body of the Church, fuitable to the Solemnity of fbme Feftival or high Proceflion Day. This is fuppofed to have been the Origin of the Modern Drama. See Comedy.
SERON OF ALMONDS, is the Quantity of Two Hundred Weight ; of Anife-feeds from 3 to 400 ; of Ca- flle Soap, from 200 and a Half, to 300 and 3 Quatters.
SEROSITY, in Medicine, an aqueous Liquor, mixed with the Blood and other Humours. tDegori defines it, a (harp, bilious Juice, approaching nearly the Nature of Blood ; but which, being extravafated, does not coagulate »*e the Blood. See Serum. Diforders of the Spleen ar = attended with Serofities. The Kidneys help to purge olt Serofities.
SERPENS, in Aftronomy, a Conftellation in the -^otthetn Hemilphere, called Serpens Ophimhi.
Inform, preceding the Neck and Head of the Serpent S
Firft of Three under the Jaw That in firft Bend of theNeck Preced. in 2d Bend of Neck
Middle underthe Jaw
Third and Subfequent
ift from the Root of theNeck
20 Preced. in the □ of theHead, or in Extrem. of the Cheek Preced. of 2 bef. the 2d Bend The lucid one of the Neck Pofter. in the 2d Bend
2f That follow. theLucida,toN. by Tycho reckon, the i60ph. S. of Din Root of the Neck
A fmall one under thac
3°
Behind zdBend bef.O^.Hand Subfeq. before the 2d Bend In Mouth, in mid. of DHead Subfeq. behind the 2d Bend That fol. theLucida to the S.
North againfl: the Noftrils in the D of the Head
In Temples, 1 fubfeq. of D That without the Head to N. 40
That follo.preced. Ofij.Hmi 4J
I ft of 3 ,beh. Of It. hind Thigh Thefe 3 Tycho ranks am, Ophi. South of 2 following this
fo North of thefe InlaftBend, behind 0p£.Hand Laft but one of the Tail yp Of Three fmall ones 5 North following that £ Soah
r;
Middle and fubfequenc
In Extremity of the Tail Small one adjacent to this vp
7 3 s 4f
8 42 07 10 33 31 12 04 08
12 30 00
13 17 04
10 oi 04
14 26 37
9 n 2 ° 14 4 r 18
16 49 f7 n 29 3f 14 00 3f
17 3y 18
" n v
14 36 42
I? 00 17
12 40 02
13 57 f4 »f 1* 3 1
12 f i of
13 23 17
18 42 ;o
17 43 "
20 19 46
14 36 34
18 04 $0
if 37 °3
21 31 46
16 21 c6
21 37 08
20 27 oy if 26 47
21 S 7 13
19 f9 22
if 11 21
18 16 18
19 jS 18 18 23 04
17 48 n
23 12 27
23 4f j8
21 23 30
22 29 5-9
29 ij r4
28 11 31
11 07 23
»J n 3? 16 12 46
20 13 23
21 07 of 21 47 32
1 31 03 3 c6 fi
3 38 38
4 19 if
11 31 28 11 26 30 II 31 48
Latitude.
16 00 f2
16 21 30 22 10 00
17 jo 23
19 27 c6
18 32 06 29 J9 "
17 01 48
32 f8 ff
20 07 02
17 27 J4
34 01 f2
28 J4 23
18 17 38 3f48 44
28 31 00
33 24 38
34 23 28 34 36 12
3 1 34 09
?8 08 21 3<> S9 f4
21 4f 03 2f 31 f6 '7 39 2f
3« 02 33 26 34 f3 34 21 30 IT fi 00 33 09 36
16 16 11
21 47 38 37 08 fo 16 41 49 24 02 oy
40 01 39
32 41 18 28 if 34
3f 19 32 42 28 p
30 if 28 ,8 37 if 37 03 22 16
16 6
33 7 4 33 02
28 07 f7
9 44 4f 10 18 11 10 08 f9
7 S9 of
10 32 f2
■9 47 f2
20 31 f6 23 29 si
21 17 24
22 14 04
29 19 27 26 f 4 41 V 13 4f
SERPENT, a Mufical Inftrument, ferving as a Bafle to the Cornet, or fmall Shawm, to iuftain a Chorus of Singers in a large Veffel. It has its Name Serpent, from its Figure ; as confining of feveral Folds or Wreaths, ierving to take off its Length, which would otherwife be Six or Seven Feet. 'Tis ul'ually covered with Leather; and confifts of Three Parts ; a Mouth-piece, a Neck, and a Tail. It has Six Holes, by means whereof, they give it the Compafs of Two Ocfaves
SERPENTARIUS, in Aftronomy, a Conftellation of the Northern Hemifphere, called alfo Ophiuchus, and an- ciently JEfculaphts. See Constellation.
The Stars in the Conftellation Serfemarius in 'Ptolemy's Catalogue are 29 ; in Tycho's 25 ; in the 'Britannic Cata- logue 69. The Longitudes, Latitudes, Magnitudes^-Si.. whereof, ate as follow,
CO.] Start
