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by imbibing the odour themselves, or inter- Fox-Glove, in botany. See DicitALIS. mixing other odours with it. When the gra- Fox-GLOVE (False), in botany. See Mo. sity of the air suffers the scent to remain buoy- MULUS. ani just breast high, it is a most fortunate cir- FOXFORD, a town in Ireland, in tho cuinstance for the pack. The more rapid the county of Mayo, situate on the river May, 8 animal, again, the less the scent cominuni. miles N. of Castlebar, cated. The scent, however, scarcely ever lies FOX-ISLANDS, a group of islands in the with a north or an east wind; a southerly wind N. Archipelago They are io in number, and. without rain, and a westerly wind that is not are situated between the E. coast of Kautssough, are the best.

chatka and the W. coast of America, between On first finding a fox, the huntsman should 52° and 55° N. lat. Each island has a pecudraw quietly and up the wind; the fox does not, liar name; but this general name is given to in this case, readily hear till the hounds are all the whole group, on account of the great in, noise can then do no hurt, and the hounds number of black, grey, and red foxes with are inspirited by it. While the hounds are which they abound. The dress of the inhadrawing, the company should so place them- bitants consists of a cap, and a fur coat, which selves that a fox cannot go off unseen : upon reaches down to the knee. Some of them such occasions, if two gentlemen keep close wear common caps of a party-coloured birdtogether, instead of assisting in the discovery, skin, upon which they leave part of the wings it is clear that one of them at least, if not both, and tail. On the fore part of their hunting knows nothing of the matter. The true sports- and fishing caps they place a small board, like man will not draw a cover near the kennel in a skreen, adorned with the jawbones of seathe commencement of the season, but will bears, and ornamented with glass beads, which keep this as a reserve when the more distant they receive in barter from tħe Russians. At corers are exhausted; of the first he is sure their festivals and dancing parties, they use a at any tiine.

much more showy sort of caps. They feed A perfect knowledge of feeding and drafting upon the flesh of all sorts of sea animals, and hounds is of essential consequence; for good generally eat it raw. But when they dress their hounds will require but little assistance after- food, they inake use of a hollow stone, in wards. By the first is meant the bringing a which they place the fish or flesh: they thed. hound into the field in his highest vigour, by cover it with another, and close the interstices a full or sparing feed according to his tempera- with lime or clay. They next lay it horizonment; by the second, the taking out no un- tally on two stones, and light a fire under it. steady hound, nor any that are not likely to be The provision intended for keeping is dried of service to the pack.

without salt in the open air. Their weapons With a high scent hounds cannot be pushed are bows, arrows, and darts; and, for their deon too much; screams keep the fox forward, fence, they use wooden shields. The most perfect the hounds together, or let in the tail hounds : equality reigns among them. They have neihalloos are of service when hounds are run- ther chiefs nor superiors, neither laws nor puning up the wind, for then none but the nishments. They live together in families, and tail hounds can hear them ; when running societies of several families united, which form down the wind, on the contrary, there should what they call a race, who, in case of attack or be no more halloos than are necessary to bring defence, mutually aid each other. The inhathe tail hounds forwards. Halloo forward is bitants of the same island always pretend to be a necessary and useful cry, but is employed too of the same race, indiscriminately: the hounds should only FO'XSHIP. s. (from for.) The character know it to signify that a fox is found—they or qualities of a fox; cunning (Shakspeare). will then fly to it. Gone away, is a halloo FOʻXTRAP. s. (fox and trap.Y A gin or that denotes a fox has broke cover, and should snare to catch foxes (Tatler). certainly be restrained to that occasion, when FOY. s. (foi, French.) Faith ; allegiance it cannot be given too loudly. When a fox is (Spenser). killed he should first be 'Aung across the FOYLE (Lough), a lake or bay of Ireland, branch of a tree to be bayed a few minutes, in Londonderry. It is of an oval form, 14 then with a loud Tally ho, the meaning of miles long and eight broad, and communicates which the hounds will thus understand, he with the ocean by a short and narrow strait. should be hurled amongst them to be eaten To FRACT. . a. (fractus, Latin.) To ravenously. It will make them the more break; to violate ; to infringe (Shakspeare). eager. No good country should be hunted FRA'CTION. s. (fraction, French.) 1. aster February : no country at all after March. The act of breaking; the state of being broken

A fox-hunting establishment consists, when (Burnet). 2. A broken part of an integral complete, of a first and second huntsman, (Brown). first and second whipper-in, three horses

FRACTION, in arithmetic, and algebra, is for each of the first, and two for each of the last: from twenty-five to thirty-five ber considered as a whole but divided into a cer.

a part or some parts of another quantity or numcouples of hounds, terriers, helpers, earth- taiu number of parts: as 3-4ths of any quantity, stoppers, and dog-feeders.

a pound, for instance, which denotes 3 parts out Fox-CHASE. See CHASE.

of 4, or 15 shillings. Fox-EVIL, a disease in which the hair Fractions are usually divided into vulgar, dedrops off from the head.

cimal, duodecimal, xexagesimal. The first

ad

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kind is what we speak of here; for the last three either equal to, or greater than, the denominator; sorts, see Decimal, &c.

and consequently the fraction either equal to, or "The definitions of fractions,' says bishop Horse greater than, the whole integer, as $, which is ley, 'which we find in the common books of arith equal to the whole; or }, which is greater than metic, that a fraction is a broken number, or that the whole. it is a number less than unity, are absurd and un- Simple Fractions, or Single Fractions, are such as intelligible. Number, in its own abstract nature, consist of only one numerator, and one denomi. is coinposed of unity; and unity, in the abstract, nator; as 3, or, or in is indivisible: a number, therefore, cannot other- Compound Fractions are fractions of fractions, wise be broken, than into less numbers; or into and consist of several fractions, connected togethe units of which it is composed. The ultimate ther by the word of: as off, or of of $. division of number is into units; and below A Mixt Number consists of an integer and a a unit there is no number. But, considering fraction joined together : as 11, or 123 number not in the abstract, but as existing in the The arithmetic

of fractions consists in the Rei things numbered, the unit of these embodied DUCTION, ADDITION, SUBTRACTION, MULTIPLI. numbers exists in the individuals, of which the CATion, and Division of them. See the various multitude is composed ; that is, in each indivi. articles; see also ALGEBRA and ARITHMETIC. dual separately taken. Each individual is no Algebraic Fractions, or Fractions in Species, are exotherwise one, or no otherwise partakes of unity, actly similar to vulgar fractions, in numbers, and than as it is a whole. And, as a whole, it must all the operations are performed exactly in the be composed of parts, for to be composed of parts same way; therefore the rules need not be reis essential to a whole; for a whole is that from peated, and it may be sufficient here to set down which no part is absent. A whole, therefore, as a few exainples to the foregoing rules. Thus, a whole, is one; but as composed of parts, it is

aab

1. The fraction abbreviates to many. The unit, therefore, of embodied num

bc bers, is many in one; and, by dividing the whole

03-ax+ ar-** a2 + into its parts, this concrete one is resolved into 2.

by dividing by

ad - ax its many. And these many parts among them

See COMMON MEASURE. selves, and with relation to the whole, are no less

ad bc the subject of numeration, than the wholes mak- 3. and is become and

when reing multitudes. These parts, considered in their

bd bd' relation to the whole, are called fractions, the duced to a common denominator. whole being usually called an integer. And the

ad + bc

See ADDITION. drithmetic of fractions is the art of numbering

d bd them as parts of a whole, and of performing the

bir like operations upon them, for combining or se. 5.

See SUBTRACTIOX. parating them; as are performed by the rules of common arithmetic upon numbers properly so

6.

See MULTIPLICATION, called, that is, upon integral numbers.' (Elementary Treatises on Practical Math.) Nearly to the

1 7.

See Division. same purpose speaks Malcolm at pp. 19, 20, of

bx' his Arithmetic.

Continued Fraction, is a fraction whose denoVulgar Fractions are usually denoted by two

minator is an integer with a fraction, which latter numbers, the one set under the other, with a fraction has for its denominator an integer and a small line between them: thus denotes the fraction, and the same for this last fraction again, fraction three fourths of some whole quantity and so on, to any extent, whether supposed to be considered as divided into four equal parts. The lower number 4, is called the denominator number of terms. Euler, Analys. Inf. vol. 1. pi

infinitely continued, or broken off after any of the fraction, shewing into how many parts the 295. whole or integer is divided ; and the upper num

As & + 2 + 7 + 7 + &c. ber 3, is called the numerator, and shews how many of those equal parts are contained in the fraction. Hence it follows, that as the numerator is to the denominator, so is the fraction it

Or using letters instead of numbers, self to the whole of which it is a fraction; or as the denominator is to the numerator, so is the whole or integer to the fraction: thus, the inte

f + &c. ger being denoted by 1, as 4 : 3 :: : the

e + &c. fraction. And hence there may be innumerable

These continued fractions may be reduced to fractions all of the same value, as there may be those of the common form by an easy application innumerable quantities all in the same ratio, viz.

of the usual rules for fractions; for an example of 4 to 3 ; such as 8 to 6, or 12 to 9, &c. So that

we will take that continued fraction which exif the two terms of any fraction, i. e. the numerator and denominator, be either both multiplied presses the ratio of the circumference of a circle,

to the diameter, namely, or both divided by any number, the resulting

with

15+ each other.

1 +

292 + Fractional expressions are usually distinguished into proper and improper, simple and compound,

1 + &c. and mixt numbers. less than the denominator; and consequently the

21+1 fraction is less than the whole or integer; ass.

If we stop at Improper Fraction, is when the aumerator is

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A Proper Fraction, is that whose numerator is Here, if we stop at“, we shall have 3 +

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+ 1

t', we have

15 + 1

when »

15 318 + 15 333 1 = 3 + =3+

more general method, however, is that of substi. + 106 106 106

106 tuting for the variable quantity its magnitude, 15

when the numerator and denominator vanish, in 15 But if we stop at }, which is convenient on ac. posing this latter to decrease without limit, the

creased by another variable quantity; then

supcount of the small fraction zba, added to the last value of the proposed fraction will be known: denominator, 1, we shall then find,

taking again the same example, and putting i + 353 $+

The first of the 113:

X-25=1+2-1+35

1-534 for 1

1-5 reductions gives the proportion of Archimedes,

nearly =4, as before. and the last that of Adrian Metius.

These vanishing fractions have led to some The doctrine of continued fractions does not sharp contests among algebraists; as between Vaappear to have been so much cultivated as it de- rignon and Rolle, between Maseres and Waring, serves: the best treatises upon it, however, and &c. And in one instance, it is said, a superior the best exemplifications of its use, are given in knowledge of such fractions was the means of obWallis's Arith. Infin, Euler's Analys. Infin. Hut- taining a professorship: though we trust appointton's Tracts; and Lagrange's Additions to Euler's ments to professorships seldom depend upon such Algebra.

equivocal proofs of merit. Vanishing Fractions. Such fractions as have Mr. Woodhouse, in his Principles of Analytical both their numerator and denominator vanish, Calculation, a work in which he has taken great or equal to 0, at the same time, may be called va- pains to unsettle every thing, but to settle nonishing fractions. We are not hastily to conclude hing, has revived some of the objections formerthat such fractions are equal to nothing, or have ly brought against vanishing fractions : he prono value; for that they have a certain determinate

x2-a value, has been shewn by some very able mathe- duces the instance among others, and as. maticians. Different methods have been adopted for valu- reasons, that this fraction is not =rta, in the

serts, not, as appears to us, from the most cogent ing these fractions. One is to divide the fluxion particular case when r=a. His mistake, we of the numerator by that of the denominator for think, lies in this, that he takes the cyphers to

*-75 the value: thus, in the fraction

which both the numerator and denominator re

duce, as like and equal quantities, which cannot -1; the furion of the numerator is 8–51, and be the case ; for since x-a? may be considered that of the denominator is -r: hence,

as a plane and i-a as a line, the cyphers must be

Jooked upon as cyphers of different orders. For i-5541_1-584 1-5

=4, the value of this matter a little more particularly. Let us ex

the sake of the young student, we will consider the fraction. A second method is by common

amine an instance like that above mentioned, division: thus, in the same example,

-= x + namely,
namely, -

and let us suppose q=10, consi* +33+*+= (when x=1) 1+1+1+1=4. A dering x as a varying quantity.

- * <=101

In the tablet in the margin, we have placed several different values

= 4+ * of a, passing on from – 13 through 0 to + 13. The third column 13

10-15 contains the several values of the fraction, as they result from sup. 12

10-12 plying the values of x and a, and actually performing the opera. -11

al_*? 100-25 - 10

Thus, when x=-5, then 10-10

-=5: again when

10+ 5
9
10-9

e-*2 100-25
8
10- 8 *= + 5,

-=15. But when x=10, we have not

10–5 7

10- 7

placed the value of the fraction in this third column, because since 6

- 6 both numerator and denominator then become =0, and the ciphers 5 5 10- 51

are of different orders, we must have recourse to some other inethod 6 10-4

of ascertaining the quotient. Here then we go to the fourth column, 10- 3

which contains the several values of a + x, the universal and accurate 10- 2

algebraic representation of the quotient equivalent to the fraction 9

10-1 10+ 0

proposed. We find the value of a+x in this column exactly cor

responding with the different values of the fraction obtained by 10+ 1

actual division in the third column, in every instance given both 12 10+ 2

above and below the case when x and a are both = 10). Now surely 3 13 10+ 3

we ought not to be accused of adopting any unfair or unwarrant4 14

10+ 4 able species of induction, that in this case as well as the others the 5 15 10 + 5

value of the fraction is truly expressed by the alyebraic representa6 16 10+ 6

tion a + x. We know not what magical infuence may be hid under 17 10 + 7

the symbol =, which should when this mark is placed between x 18

10+ 8 and a cause the value of the proposed fraction to be absolutely un. 19 10+ 9

assignable, though it may be readily assigned in every other con10

10+ 19 ceivable instance. The question, in fact, amounts to this : either 21 10 + 11

we can perform the fundamental algebraical operations (as addition, 12 22

10+12 multiplication, division, &c.) correctly and safely, without knowing 13

10+ 13.the real quineral values of the characters employed (a, b, c, 1, y, s, &c. &c. &c.

&c.); or we cannot. If we cannot, the boasted universality of algebra

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is gone, we must abandon it altogether, and reo it, in order to give more room for the motion turn to our arithmetic and geometry. But, if we of the tongue. can,-if, for example, we can affirm universally, FRÆNUM, or FRENUM, bridle, in anathat = a + *, whatever a and x may be, tomy, a name given to divers ligaments, from

their office in retaining and curbing the mowhy then the sum of e and * will represent tions of the parts they are fitted to. the quotient uf al-** divided by e-*, whatever FRÆNUM LINGUÆ, or BRIDLE OF THE be the relation subsisting between a and *. There TONGUE; a membranous ligament, which is no alternative between admitting this and aban- connects the tongue with the muscles about doning all that is useful and valuable in modern the fauces, and lower parts of the mouth. In analysis. Should not this manner of considering the sub

some subjects the frænum runs the whole ject remove all the scruples of Mr. Woodhouse, length of the tongue to the very tip; in which and others who have adopted similar notions, we cases, if it were not cut, it has been erronewill endeavour to place it in another point of ously supposed, that there would be no possi

bility of speech. Sec TONGUE-TIED. view. Let us conceive y= and let us con- FRÆNUM PENIS, a slender ligament, struct a figure which shall exhibit the different whereby the prepuce is tied to the lower part values of y. Since y, or its equal a +1, has all its of the glans of the penis. Nature varies in variations in a ratio of equality with those of x, the make of this part; it being so short in (a being constant) it is manifest that the locus of some, that unless divided it would not admit this equation is a right line making an angle of of perfect erection. There is also a kind of 45° with the axis of the figure. Let mAMMM, frænum, fastened to the lower part of the clie &c. be such locus, (fig. 12. Pl. 68.) and draw the toris in women. several ordinates pm, pm, PM, PM, &c. Now at FRAGA, a town of Spain, in Arragon, the point P, where x=0, we have y=a +x=10= with a handsome castle. It is strongly situPM; and AP being = 10, the ordinates gradually ated among the mountains, having the river diminish until at the point A, a + I, being = 10–10 Cinca before it. Lat. 41.46 N. Lon. 0.28 E. =0, the ordinate vanishes, and the locus crosses the axis: when x becomes - 12,-14, &c, the or

FRAGARIA. Strawberry. In botany, dinate is truly expressed by —2,-4, &c. being genus of the class icosandria, order polygynia

. found on the contrary side of the axis. But, to Calyx ten-cleft, inferior; petals five; seeds proceed with the increasing ordinates on the right smooth, imbedded in an ovate berry-like hand part of the figure: when PP=5, 6, 7, 8, or Aeshy receptacle. Seven species-two of Ame9 respectively, it is manifest that PM, the ordinate, rica, one somewhat shrubby; the rest natives becoines = 15, 16, 17, 18, or 19 respectively; and of Europe ; two of which, E. vesca, common when PP=11, 12, 13, 14, &c., the ordinate PM = strawberry, and E. sterilis, barren of fruit, 21, 22, 23, 24, &c. Since then the different values of y, or the proposed fraction, are exhibited, and we trust fairly and accurately exhibited, by this cultivated for use; and its varieties are very

The common strawberry is the only species figure, both in the cases when x is less than a, and when it is greater than a, we trust there will be no

numerous. The following are the chief : great impropriety in adopting the species of rea

a F. sylvestris, woodşstrawberry. soning which is the foundation of the differential

6 F. virginiana. Virginian scarlet. method, (and which is so admirably elucidated in

F. moschatta. Hautboy, or musky strawa prop. 87 of Hartley on Man) and thus determining

berry. the value of y in the particular case of r=4. By

8 F. Chiloensis. Chili, or Carolina. this method then we find the ordinate (which in F. alpina. Alpine, or monthly. the figure we have presumed to represent by a

The mode of cultivation in respect to all 19 +21 dotted line) =21, which is equivalent tially. They may be transplanted in Septein

:

the species and varietjes does not differ essento a+ t, and furnishes another reason for believing ber or February: the former is the best month; that the value of the vanishing fraction is truly ase for if the spring be dry, the February transsigned. FRA'CTIONAL. a. (from fraction.) Be- much watering. The proper soil is a light

plantation will require great attention and longing to a broken number (Cocker).

loam, and not peculiarly rich. The ground FRACTURE. s. (fructura, Latin.) 1. must be well dug and cleared of all noxious Breach; separation of continuous parts (Hale). weeds ; and when levelled it should be marked 2. The separation of the continuity of a bone in out into beds about three feet and a half wide, living bodies (Herbert).

leaving a pathway between each bed two feet To Fr A'CTURE. ú. a. (from the noun.) broad. In each of these beds should be plantTo break a bone (Wiseman).

ed four rows of plants, so that they may stand Fracture, in surgery, a rupture of a about a foot distant from each other in the bone, or a solution of continuity in a bone rows, and at about eight inches plant from when it is crushed or broken by some external plant in each. This is the proper distance for cause. See SURGERY.

the wood strawberry, which is of the least FRÆNULUM. The cutaneous fold, un- growth of any, but the scarlet strawberry der the apex of the tongue, that connects the must be planted at a fost distance every way longue to the infralingual cavity. It is some and the hautboy sixteen inches ; and finally

, times, in infancy, so short as to prevent the the large Chili strawberry, which is the largest child from sucking, when it is necessary to cut grower of all, must be set at twenty-five

are common to our own country.

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inches distant plant from plant. In the spring, Fraises differ from palisades chiefly in this, when the strawberries begin to flower, if the that the latter stand perpendicular to ihe horiseason be dry, they must be very plentifully zon, or nearly so, being usually made a little watered, and kept cleared from weeds. At sloping, or with the points hanging down. Michaelmas the beds should be dressed, the Fraises are chiefly used in retrenchments and Weeds all very carefully taken up, all the other works thrown up of earth; sometimes strings or runners taken from the roots, and they are found under the parapet of a rampart, the weak plants, which stand too close, be serving instead of the cordon of stone used in pulledfup; a little fine earth, at the same time, stone-works. should be thrown near the plants, which will FRAMBOESIA, (frambæsia, from framgreatly strengthen their roots. These beds, boise, French for a raspberry.) The yaws. however, will not continue good above three A genus of disease arranged by Cullen in the years; and the beds of the first year bearing class cachexiæ, and order impetigines. It is but few fruit, it is necessary to new plant somewhat similar in its nature to the lues some fresh ground every third year, and destroy venerea, and is endemial to the Antilla the old beds ; but the new ones must be first islands. It appears with excrescences, like of one year's growth. Different palates prefer mulberries, growing out of the skin in various different sorts of strawberries, but the white- parts of the body, which discharge an ichorous fruited one is, of all others, the best favoured ; Auid. though it is but a very bad bearer. The great Some of our best and most approved writers Chili strawberry is cultivated in the field in upon this subject, however, assign it to the that country; it is a much stronger and larger family of fevers, with the general syınptoms of plant than any of our indigenous kinds; and its which they affirm it is always accompanied ; fruit is as large as a walnut, but not so well that like the small pox, it has an accession, tasted as our own strawberries. They grow height and decline, may be propagated by inobest in a loamy soil, under the shade of trees. culation, and is never known to occur a second FRAGILE. a.

(fragile, French; fragilis, time. Latin.) 1. Brittle; easily snapped or broken TO FRAME. v. Q. 1. To form or fabricate (Denham). 2. Weak ; uncertain; easily de- by orderly construction (Spenser). 2. To fit one stroyed (Milton).

to another (Abbot). 3. To make; to compose FRAGILITY.s. (from fragile.) 1. Brit- (Shakspeare). 4. To regulate; to adjust (Tillottleness ; easiness to be broken (Bacon). 2. son). 5. To form any rule or method by study Weakness; uncertainty (Knolles). 3. Frailty; or precept (Shakspeare). 6. To form and diliableness to fault (Wotton).

gest by thought (Granville). 7. To contrive; FRAGMENT. s. (fragmentum, Latin.) A to plan (Clarendon). 8. To settle; to scheme part broken from the whole; an imperfect oui (Shakspeare). 9. To invent; to fabricate piece (Newton).

(Bacon). FRAGMENTARY. a. (from fragment.) FRAME. s. (from the verb.) 1. A fabric; Composed of fragments : not used (Donne). any thing constructed of various parts or mem

FRA GOR. s. (Latin.) A noise; a creak; a bers (Tillotson). 2. Any thing made so as to crash: not used (Sandys).

enclose or admit something else (Newton). FRAGRANCE. FRAGRANCY S. (fra- 3. Order; regularity; adjusted series

or dispogrentio, Latin.) Sweetness of smell; pleasing sition (Swift). 4. Scheme; order (Clarendon). scent; grateful odour (Garth).

5. Contrivance; projection (Shakspeare). 6. FRA GRANT. a. (fragrans, Latin.) Odor- Mechanical construction. 7. Shape; form; ous; sweet of smell (Prior).

proportion (Hudibras). FRAGRANTLY. ad. With sweet scent, FRAME, among painters, a kind of square,

FRAIL. s. 1. A basket made of rushes. consisting of four long slips of wood joined 2. A rush for weaving, baskets.

together, whose intermediate space is divided Prail. a. (fragilis, Latin.) 1. Weak; by threads into several little squares like a net; easily decaying; subject to casualties; easily and hence sonetimes called reticula. It serves destroyed (Rogers.) 2. Weak of resolution to reduce figures from great to small; or, on liable to errour or seduction (Taylor). the contrary, to augment their size from small FRAPLNESS. S. Weakness; instability to great.

FRA'MER. s. (from frame; 'fremman, S.) FRAI'LTY. s. (from frail.) 1. Weakness Maker; former; contriver ; schemer (Arl). of resolution; instability of mind; infirmity

FRAMING OF A HOUSE, all the tim. (Milton.) 2. Fault proceeding from weakness; ber-work therein, riz. the carcase, flooring, sins of infirmity (Dryden).

partitioning, roofing, cieling, beams, &c. FRAISCHEUR. s. (French.) Freshness; FRAMLINGHAM, a large town of Sufconlness ( Dryden).

folk, with a market on Saturday. It is seated FRAISE. s. (French.) A pancake with near the head of a small rivulet, and has the bacon in it.

remains of a castle, said to have been built in FRAISE, in fortification, a kind of defence, the time of the Saxon heptarchy. To this consisting of pointed stakes, six or seven feet castle the princess Mary, afterward Mary I. long, driven parallel to the horizon into the retired, when lady Jane Grey was proclaimed fetrenchments of a camp, a half-moon, or the queen; and here she found that powerful suplike, to prevent any approach or scalade. port of the people of Suffolk, which so soon

(Nor.)

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