PROJECTILES, THEORY OP. 



PROJECTILES, THEORY OF. 



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modus, or that the lands are discharged by statute, or tithes are 

 claimed of thing* for which no tithe* are due, or the dfftmdant makes 

 title by lease, Ac., a prohibition will lie immediately. And a pro- 

 hibition is in all oases grantable where a court allows illegal or disallows 

 legal evidence, as where the Commissioners of Appeals for the Excise 

 determine by the minutes of evidence taken by a justice of the peace, 

 instead of examining the witnesses rinl rocr, or a spiritual court 

 disallows proof of payment, Ac., because proof of it is made only by a 

 single witness, or where it has misconstrued an Act of Parliament, or 

 disallows an award when it is good by law. 



A prohibition will also lie where a court attempts to extend its 

 jurisdiction to parties over whom it has none, as where a court-martial 

 inquires into the conduct of a person not a soldier or sailor; the 

 Stannary courts, where neither parties are tinners, nor the matter in 

 question respecting tin, Ac. 



4. A prohibition may be obtained at the instance of either party to 

 an ecclesiastical suit. In the case of a unit for tithes against a lessee 

 it may be obtained by the revcreioner. Where a court has no juris- 

 diction over the matter of the suit, a prohibition is grantable at the 

 request of a mere stranger. 



6. Ha court has no cognisance of the matter of a suit, prohibition 

 will lie immediately after appearance, and it may be obtained by either 

 plaintiff or defendant at any future time, even after sentence, appeal, 

 and affirmation ; or after judgment and execution, provided it appears 

 by the proceedings that the court had no jurisdiction. When the 

 court has cognisance of a cause, prohibition will not lie until the 

 matter out of its jurisdiction has not only arisen, but is also clearly in 

 progress of being tried. If the matter is then admitted by the litigant 

 parties, the court is still entitled to certain cognisance of the suit. If 

 not admitted, and these circumstances, though not appearing on the 

 face of the proceedings, are duly brought forward before judgment, a 

 prohibitiuu will then lie. If, however, a prohibition is not then applied 

 for, but the party submit to the trial in the court where the suit has 

 been commenced and judgment is pronounced, no prohibition will lie 

 unless it appear on the proceedings, not only that matter out of the 

 jurisdiction of the court has arisen, but also that the matter has been 

 wrongly decided. These observations only apply to permanent courts, 

 and where something still remains to be done. In the case of an occa- 

 sional court, as a court-martial, it would be impossible to carry the 

 principle into execution. 



0. A writ of prohibition is applied for by motion in court, which 

 Beta out the proceedings in the suit. If the proceedings are not suffi- 

 cient to show the want of jurisdiction in the court against which 

 prohibition is prayed, suggestions must be added, verified by affidavit, 

 showing such want of jurisdiction. 



If the court grants a rule, the other party is heard in answer. The 

 court may then decide, either to refuse the prohibition 1 , or, if they 

 incline to grant it, direct the party applying to declare in prohibition. 

 'I i .' must contain a concise statement of the grounds of 



the application, and conclude by praying that the writ may issue. To 

 this the other party may demur on the ground that no suflicient cause 

 appears fur a prohibition, or he may plead such matters as he thinks 

 proper to show that the writ ought not to issue, and conclude by 

 praying that it may not issue. If matters of fact are put in issue, 

 they are tried by a jury. Judgment is given either on the demurrer 

 or after nonsuit or verdict. The party succeeding is entitled to the 

 costs of these proceedings, and, if a trial takes place, the jury may 

 ttSSQHi damages. If the court decide in favour of the party applying, 

 the writ issues and forbids the court and other party from further 

 proceeding. In such casea, if the ground of application was that the 

 court had no jurisdiction at all in the suit, the writ of prohibition is 

 final. But if the ground is that something had arisen not cognisable 

 by the court, during the progress of a suit, concerning a matter pro- 

 perly within its jurisdiction, the prohibition is not final. In such case 

 the question is referred to the proper tribunal for trial, and if found 

 against the applicant, the suit may be then resumed. In either case, 

 where the court decides in favour of the party against whom prohibition 

 is prayed, or the verdict has been afterwards in his favour, the court 

 awards a consultation, as it is called, by which the cause is again 

 rcuiitu-d to the original court. If parties proceed after a writ of pro- 

 hibition has been obtained and served, they are liable to an attachment 

 ntempt. No prohibition for the same matter lies after a con- 

 nutation Lou been awarded upon the merits. 



re can be no pleadings in a prohibition to the County Courts, 

 the merits of which must be determined on the application for the 

 writ. 



(Comyns 1 * Digal ; 2 /*., 699 ; 3 BUckst.'Com., Mr. Korr's cd., c. 7.) 



The right of the common-law courts to issue writs of prohibition. 

 and the mode in which they exercised that right, have often be 

 subject of great dispute between the common-law judges and the eccle- 

 siastics. The latter have several times exhibited many articles of 

 grievance before the parliament and privy council against the former. 

 TTie most famous of these are the Articuli cleri,' exhibited by Arch- 

 bishop Bancroft, in the name of the whole clergy, in the third year of 

 the reign of Jama I. Tl,ry are given at length by Lord Coke (2 

 Inst, 699), with a full view of the nature of the controversy between 

 the parties and the unanimous answers of the judges. 



PROJECTILES, THEORY OF. This subject usually compre- 



bends the investigation of the relations between the space described, 

 the time of motion, and the velocity acquired by a body when impelled 

 in any direction by some motive force. 



The circumstances of a body descending from a high place towards 

 the earth by the action of gravity, and those of a body projected 

 vertically upwards from the earth, on the supposition, in both cases, 

 that the body moves in a non-resisting medium, have been noticed in 

 the article FALL OF BODIES ; and the circumstances attending the 



M. both in a resisting and a non-resisting medium, of ., 

 imjiolled by fired gunpowder, when the impulse is in 

 parallel or oblique to the horizon, have been investigated in the article 



IIT. It is intended therefore in this place only to e 

 laws of the vertical ascent and descent of bodies in resisting media, the 

 force of gravity, or of terrestrial attraction, being supposed to lie 

 constant; and in non-resisting media, under the condition that the 

 force of gravity is variable. 



Let a spherical body descend vertically from a state of rest in a 

 resisting medium (air, water, Ac.) supposed to be of uniform density ; 

 and let it be admitted, agreeably to the Newtonian hypothesis 

 (' Priucip.', lib. ii sea. 1 ; Schol.), that the resistance of the medium 

 in pro] lortional to the square of the velocity, , acquired at any moment 

 in the descent ; then, if we suppose u to be the velocity which a body 

 falling towards the earth in the resisting medium would acquire wln-n 

 that resistance becomes equal to the accelerative force of gravity. : h<- 

 Utter being, as usual, represented by g ( = 82'2 feet), we shall have 



V 1 : g : : u 3 : -g ; and the last term represents the resistance of the 



medium at the instant when the velocity is v ; hence the accel. 

 force by which the falling; body is urged at such moment 'a e.\j 



*>y0--^!/- 



Now < being the space descended by the body in the time t, and r 

 being the velocity as before, an accelerative force is represented 



dv d? s dv <'- 



ky<FT an< ^ ky -jj^j-. [FoBCE.] Therefore ^7 =g - ,y; whence gdt = 



- ; and integrating this equation, observing that v = when 





U U + v 2yt o + ti 



t = 0, we have t = ^- hyp. log. ^-^ , or = hyp. log. ;j~3~ ; or 



u + 



again, passing from logarithms to numbers, = c u (c being the 



base of the hyperbolic logarithms) ; whence v = v 



u 



c -I 

 S 



l+c U 



.'/''* 



, and this 



second member being developed, gives t> = gt jr- 5 + Ac. Substi- 



* 

 tuting, in this equation, -3; for v, and again integrating, we have 



These equations for s and v give the space descended and the velocity 

 acquired at the end of any given time t from the moment when the 

 motion commenced. For tables of the values of D (the terminal velo- 

 cities) for iron bolls, see Dr. Hutton's Tracts, tract 37. 



Next, let a body bo projected vertically upwards in a uniformly 

 resisting medium with an initial velocity = v ; and let the body be of 

 a spherical form so that u may be the same as before : then, the force 

 of gravity and the resistance of the medium acting in a di: 



dv 

 opposite to that of the projectile force, we have now -r = g ' ; 



whence gdt 



This equation, being integrated, gives 



gt = u arc tan. = - + const. ; and considering that v = v v.h. n 



y 



t = 0, tho constant is equal to u arc tan. = - ; putting - c to 

 sent this term, we have - = arc tan. - ; and passing from arcs to 

 tangents, wo havo ^ = tan."^-", or v = U tan. ;'. Multiplying 



u 

 v c gt 



u = taD -~iT"' " o 



both members of the last equation by <lt, and putting dx for it* 



r ' 

 nit, this c |iiation becomes dx = u tan. 



gives x = - hyp. log. cos.- p g - 



dl; which integrated 



+ comt. The constant is determined 



