176 ROC 
ROC 
Hence snpd 2 — [m — is the motive force, 
snpd 2 —(m — —^ . 
' \ a ) a snp a 2 
and 
c t 
a 
am — ct 
1, the accelerating 
force. Therefore, from the known formulae for variable 
forces, we have v = 2 gf t, which hence becomes 
Hagsnpd 2 t 
am — ct 
— 2gt; 
the fluent of which is 
v = — ^ *r hyp. log. {f-g- — — 2 g t, or 
v = — hyp. log. ( am ~~ c ^ —2 gt-, 
wher ei a iM£^. 
This fluent, corrected for the case in which t 
the correct fluent, 
v = b . hyp. log-—2gi; 
am —ct 
which, when t = a, becomes 
v = b. hyp. log. —~ —2ga, 
0, gives 
m — c 
the velocity required. 
Again, to find the space described in the same time, we 
a m 
have s=vt, oxx = bty. hyp. log. ~ 2 S ft - 
b a m\ 
The correct fluent of this is x 
bt ■ 
-) hyp- log. 
a m + — lam — ct) . hyp. log. [am — c t) + b t — gt 2 ; 
c 
and in the case when t = a, it becomes x = — + 
c 
Um — c) hyp. log. 
c — j the space sought. 
It will be observed, however, that in both these cases, 
gravity has been supposed to act directly in opposition to 
the motion of the rocket; but had we considered the flight 
uninterrupted by gravity (as we must suppose, in estimating 
its flight, when projected at any given angle, where gravity 
is not considered as in any respect retarding the rocket’s 
motion in the first line of projection), then the last terms in 
each of the above expressions will disappear, and we shall 
have simply 
v = b . hyp. log. ———, and 
x = ~ + m — c) hyp. log. 
+ c' 
Having thus detennined the height of the rocket, and its 
velocity, when the composition is just consumed, it follows 
that its whole height may be determined in the usual manner, 
by the known formula for the ascent and descent of heavy 
bodies. 
ROCKET is the popular name of the plant Eruca ,— 
Bastard Rocket of Reseda;—Corn, Sea or Square 
Podded Rocket of Bunias;—Garden Rocket of Hes- 
peris;—Water Rocket of Sysymbrium. See the 
classical names. 
ROCKFIELD, a parish of England, in Monmouthshire; 
2 miles north-west of Monmouth. 
ROCKFORD, a post village of the United States, in Sur¬ 
rey county, North Carolina. 
ROCKHAMPTON, a parish of England, in Gloucester¬ 
shire, near Thornbury, where there is a ferry over the 
Severn. 
RO'CKINESS, s. State of being rocky.—This rockiness 
in the highest parts proves his fine earth to be but a figment. 
Bp. If. Croft. 
RO'CKING, s. State of being shaken. — I like this 
rocking of the battlements. Young. 
ROCKINGHAM, a market-town and parish in the hun¬ 
dred of Corby, and county of Northampton, England, is 
situated close to the river Welland, at the distance of 26 
miles north-north-east from Northampton, and 84 miles 
north-north-west from London. In former times it was a 
place of some note on account of its castle and appendant 
forest. This castle was built by William the Conqueror, on 
the summit of a hill overlooking the town, and appears to 
have been occasionally the residence of several of our early 
monarchs In the reign of William Rufus, a great council 
of the nobility, bishops, and clergy, was assembled here to 
terminate the dispute between the king and Anselm, arch¬ 
bishop of Canterbury, respecting the right of investiture, and 
obedience to the see of Rome. The council sat on Sunday 
the 11th of March, 1094, in the chapel belonging to the 
castle. Edward III. frequently honoured this fortress with 
his presence, as is evident from the numerous dispatches, and 
other instruments of royal authority, which are dated at 
Rockingham, in different years of his reign, Edward IV. 
settled the manor here, together with the castle and forest, 
on his queen, Elizabeth, for her life-time. These afterwards 
formed part of the duchy of Cornwall, and continued so till 
the reign of Edward VI., when they were granted to Edward, 
lord Clynton, from whose family they passed to the Wat¬ 
sons, one of whom, sir Lewis Watson, was created baron 
Rockingham, of Rockingham castle, in the year 1644. At 
what period the castle was dismantled is uncertain ; but it is 
probable that event happened early in the reign of Henry III., 
as in the 34th year of that monarch, it is described as being 
in a ruinous condition. Leland, who visited it in the time 
of Henry VIII., gives the following account of this structure 
in the first volume of his Itinerary. “ The castelle of Rok- 
ingham standith on the toppe of an hill, right stately, and 
hath a mighte diche, and bulwarkes agayne withoute the 
diche. The uttur waulls of it yet stond. The kepe is exce- 
ding fair and strong - and in the waulls be certein strong 
towers. The lodgings that were within the area of the 
castelle be discovered and faul to ruine. One thing in the 
waulls of this castlle is much to be notid ; that is, that they 
be embatelid on booth the sides. So that if the area of the 
castelle were won by cumming in at either of the 2 greate 
gates of the castelle, yet the keepers of the waulls might defende 
the castelle. I marked that there is a stronge tower in the 
area of the castelle, and from it over the dungeon dike is a 
drawbridge to the dungeon toure.” All that now remains 
of the original building is the arched gateway of ithe grand 
entrance, which is flanked by two massy bastion towers. 
Rockingham forest extended about 29 miles in length, from 
Oxenden bridge to Stamford bridge, and four or five miles in 
breadth. Leland says there were only “ fallow dere in it” 
“ with diverslodges for kepers” in histime. 
The town of Rockingham consists chiefly of one irregular 
street. The market day is Thursday, weekly; and there is an 
annual fair on the 25t’h of September. These privileges w ere 
granted by Henry III., at the request of Edmund, earl of 
Cornwall, the then possessor of the manor; but they are at 
present only nominal. According to the population of 1811, 
this parish contains 49 houses, and 230 inhabitants. The 
church is not remarkable except for some handsome monu¬ 
ments, erected to commemorate different individuals of the 
Watson ’family. An altar-tomb, in the chancel, bears the 
recumbent statue of a man in armour, with that of a female 
by his side; and on the entablatures are the figures of nine 
children, sculptured in relief. This tomb was erected in 
memory of Edward Watson, grandfather cf the first lord 
Rockingham, and his wife, one of the daughters of Sir Edward 
Montague, lord chief justice of the court of king’s bench. 
Another 
