S K R 
S K R 
(J48 
for that purpose : to clear it from the oil, it j 
is put into a vessel oi hot soap-water, whence 
being taken out, wrung, and dried, it is spun 
on the wheel. As to the. shorter wool, in- 
tended for the woof, it is only carded on the 
knee, with small line cords, and then spun on ; 
the wheel, without being scoured of its oil: 
and here it is to be observed, that the thread 
for the warp is always to be spun liner, and 
into eh better twisted, than that of the woof. 
The wool both for the warp and woof 
being spun, and the thread reeled intoskains, 
that of the woof is put on spools, fit for the 
cavity of the shuttle; and that for the warp is 
wound on a kind of wooden bobbins, to lit it 
for warping ; and when warped, it is stiffened 
with a size, usually made of the shreds of 
parchments; and when dried, put into the 
loom, and mounted so as to be raised by four 
treadles, placed under the loom, which the 
workman makes to act transversely, equally, 
and alternately, one after another, with his 
feet; and as the threads are raised, throws 
the shuttle. See Weaving. 
The serge, on being taken from the loom, 
is carried to the fuller, who fulls or scours it, 
in the trough of his mill, with fuller’ s-earth ; 
and after tne first fulling, the knots, ends, 
straws, Ac. sticking out on either side of the 
surface, are taken off with a kind of pliers or 
iron pincers, after which it is returned into 
the fulling-trough, where it is worked with 
warm water, in which soap has been dissolv- 
ed; when quite cleared, it is taken out, the 
knots are again pulled off; it is then put on 
the tenter to dry; taking care, as fast as it 
dries, to stretch it out, both in length and 
breadth, till it is brought to its just dimen- 
sions; then being taken off the tenter, it is 
dyed, shorn, and pressed. 
SERGEANT, or Serjeant, at law, is the 
highest degree taken in that profession, as 
that of a doctor is in the civil law. To these 
serjeants, as men of great learning and expe- 
rience, one court is set apart for them to 
plead in by themselves, which is the court of 
common pleas, where the common law of 
England is most strictly observed ; yet though 
they have this court to themselves, they are 
not restrained from pleading in other courts, 
where the judges (who cannot be elevated to 
that dignity till they have taken the degree 
of serjeant at law) call them brothers, ►and 
hear them with great respect, next to the 
king’s attorney and solicitor general. These 
are made by the king’s mandate, or writ. 
There are also serjeants at arms, whose 
office is to attend on the person of the king, 
to arrest persons of condition offending. < 
Sergeant, or Serjeant, in war, is an in- 
ferior officer in a company of foot, or troop of 
dragoons, armed with a halberd, and ap- 
pointed to see discipline observed, to teach 
the soldiers the exercise of their arms, and 
to order, straighten, and form, ranks, riles, Sec. 
SERJEANTY, signifies in law a service 
that cannot be due from a tenant to any lord, 
but to the king only; and it is either grand 
serjeanty or petit serjeanty. 
Grand serjeanty, is a tenure whereby a 
person holds his lands of the king by such 
services as he ought to do m person ; as to 
carry the king’s banner, or ins knee, or to 
ca rv his sword before him at his coronation, 
or to do other like services ; and it is called 
grand serjeanty, because it is a more worthy 
3 E R 
service than the service in the common tenure 
of escuage. 
Petit serjeanty is where a person holds 
his land of the king, to furnish him yearly 
with some small tiring towards his wars, as a 
bo\v. lance, & c. And such service is but 
socage in effect, because such tenant by his 
tenure ought not to go nor do any thing in 
Iris proper person. 
SERIES, in general, denotes a continued 
succession of things in the same order, and 
having the same relation or connection with 
each other : in this sense we say, a series of 
emperors, kings, bishops, Sec. 
Series, in mathematics, is a number of 
terms, whether of numbers or quantities, in- 
creasing or decreasing in a given proportion, 
the doctrine of which has already been given 
under the article Progression. 
Series, infinite, is a series consisting of an 
infinite number of terms, that is, to the end 
of which it is impossible ever to come; so 
that let the series becarried on to any assign- 
able length, or number of terms, it can be 
carried yet farther, without end or limitation. 
A number actually infinite ( i. e. all whose 
units can be assigned, and yet is without 
limits) is a plain contradiction to all our ideas 
about numbers; for whatever number we can 
conceive, or have any proper idea of, is al- 
ways determinate and unite; so that a greater 
after it may be assigned, and a greater after 
this; and so on, without a possibility of ever 
coining to an end of the addition or increase 
of numbers assignable: which inexhaustibility, 
or endless progression in the nature oi num- 
bers, is all we can distinctly understand by 
the infinity of number; and therefore to say 
that the number of any things is infinite, is 
not saying that we comprehend their num- 
ber, but indeed the contrary; the only thing 
positive in this proposition being this, that 
the number of these things is greater than 
any number which we can actually con- 
ceive and assign. But then, whether in things 
that do really exist, it can be truly said that 
their number is greater than any assignable 
number ; or, which is the same tiling, that in 
the numeration of their units one after an- 
other, it is impossible ever to come to an 
end; this is a question about which there are 
different opinions, with which we have no 
business in this place: for all that we are 
concerned here to know is this certain truth ; 
that after one determinate number we can 
conceive a greater, and after this a greater, 
and so on without end. And therefore, whe- 
ther the number of any things that do or call 
really exist all at once, can be such that it 
'exceeds any determinable number, or not, 
this is true ; that of things which exist, or are 
produced successively one after another, the 
number may be greater than any assignable 
one; because, though the number of things 
thus produced that does actually exist at any- 
time is finite, yet it may be increased without 
end. And this is the distinct and true notion 
of the infinity of a series; that is, of the infi- 
nity of the number of its terms, as it is ex- 
pressed in the definition. 
Hence it is plain, that we cannot apply to 
an infinite series the common notion of a sum, 
viz. a collection of several particular numbers 
that are joined and added together one after 
another, for this supposes that these particu- 
lars are all known and determined ; whereas 
tne terms of an infinite series cannot be all 
separately assigned, there being no end iri 
the numeration of its parts, and therefore it 
can have no sum in sense. But again, if we 
consider that the idea of an infinite series 
consists of two parts, viz. the idea of some- 
thing positive and determined, in so far as we 
conceive the series to he actually carried on ; 
and the idea of an inexhaustible remainder 
still behind, or an endless addition of terms 
that can be made to it one after another, 
this is as different from the idea of a finite 
series as two things can be. Hence we may 
conceive it as a whole of its own kind, which 
therefore may be said to have a totai value 
whether that is determinable or not. Now 
in some infinite series this value is finite or 
limited ; that is, a number is assignable be- 
yond which the sum of no assignable number 
of terms of the series can ever read;, nor in- 
deed ever be equal to it, yet.it may approach 
to it in such a manner as to want less than 
any assignable difference ; and this we may 
cai! the value or sum of the series ; not as 
being a number found by the common me- 
thod of addition ; but as being such a limita* 
tion of the value of the series, taken in all its 
infinite capacity, that if it were possible to 
add them all one after another, the sum 
would be equal to this number. 
Again, in other series the value has no limi- 
tation ; and we may express this, by saying 
the sum of the series is infinitely great ; which 
indeed signifies no more than that it has no 
determinate and assignable value; and that 
the series may be carried such a length that its 
sum, so far, shall be greater than any given 
number. In short, in the first case we affirm 
there is a sum, yet not a sum taken in the 
common sense; in the other case we plainly 
deny a determinate sum to any sense. 
Theorem I. In an infinite series of num- 
bers, increasing by an equal difference or 
ratio (that is, an arithmetical or geometrical 
increasing progression) from a given number, 
a term may be found greater than any assign- 
able number. 
Hence, if the series increases by differ- 
ences that continually increase, or by ratios 
that continually increase, comparing each 
term to the preceding, it is manifest that 
the same thing must be true, as if the dif- 
ferences or ratios continued equal. 
Theorem II. In a series decreasing in in- 
finitum in a given ratio, we can find a term 
less than any assignable fraction. 
Hence, if the terms decrease, so as the 
ratios of each term to the preceding do also 
continually decrease, then the same thing is 
also true as when they continue equal. 
Theor. III. The sum of an infinite series 
of numbers all equal, or increasing continu- 
ally, by whatever differences or ratios, is 
infinitely great; that is, such a series has no 
determinate sum but grows so as to exceed 
any assignable number. 
Demons. 1. If the terms are all equal, as 
A ; A ; A, &c. then the sum of any finite 
number of them is the product of A by that 
number, as An ; but the greater n is, the 
greater is Am; and we can take n greater 
than any assignable number, therefore Am 
will be still greater than any assignable num- 
ber. 
Secondly, suppose the series increase 
continually (whether it does so infinitely or 
lfmitedly), then its sum must be infinite] y 
