assumes the sum of the latter to be infinite.

In the work of a celebrated political economist there is the following argument, to show that a tax on wages must fall on the labourers; for if it did not so fall, wages would rise, whence the price of goods would rise, which would again cause a rise of wages, and this again a rise in goods, and so on ad infinitum, which is inferred to be absurd. This is of course precisely a repetition of the preceding case; and granting all the premises, the conclusion by no means follows. For that conclusion is that the rise would go on without limit, which need not be the case.

PROHIBITION, a writ to prohibit a court and parties to a cause then depending before it from further proceeding in the cause. It will be convenient to define,-1, out of what courts it may issue; 2, to what courts it may be addressed; 3, under what circumstances it is grantable; 4, at whose instance it may be obtained; 5, at what time it may be obtained; 6, the form and incidents of the proceeding.

1. A writ of prohibition may issue from any of the three superior courts of common law at Westminster, and also from each of the common-law courts of Chester and Lancaster. It is generally stated that a writ of prohibition may issue from the Court of Chancery; but the Court of Chancery acts by injunction addressed only to the parties, and does not interfere with the court. [INJUNCTION.]

2. It may be addressed by any of the three superior courts to any other temporal court; such as to the Admiralty courts, to courts-martial, a court baron, any other inferior court in a city or borough, to the Cinque-Ports courts, the duchy or county palatine courts, the chancery of Chester, the Stannary courts, the Court of Honour of the EarlMarshal, to the Commissioners of Appeals of Excise, to any court by usurpation without lawful authority, or to a court whose authority has expired. When any one has a citation to a court out of the realm, a prohibition lies to prevent his answering. It seems also that it might issue to the Court of Exchequer and to the Court of Common Pleas; but not to the Court of Chancery, nor is there any instance of a prohibition to the King's Bench. It may be granted by any of the three superior common-law courts to any spiritual court, and by the common-law courts of Chester and Lancaster to the spiritual courts within the county palatine and duchy.

3. The writ is grantable in all cases where a court entertains matter not within its jurisdiction; or where, though the matter is within its jurisdiction, it attempts to try by rules other than those recognised by the law of England. Matter may be said to be not within the jurisdiction of a court in two senses: 1, when the subject-matter entertained is in its nature not cognizable by the court; 2, where the subject-matter is in its nature cognizable by the court, but lies out of the local district where only that court has jurisdiction; or, in the case of a court whose jurisdiction is general, when the subject-matter lies in a local district exempt from the general jurisdiction of the court or where the subject-matter of the cause relates to persons over whom the court has no jurisdiction.

In order to ascertain those cases which fall under the first head, we must consider the nature and character of the subject-matters over which the jurisdiction of the court extends. It is obvious, that if we have those clearly defined, we shall see whether the subject-matter in question is or is not within that jurisdiction. This general rule may be useful, because the cases that may occur in which a prohibition will lie, are endless. The examples of cases which have occurred will assist in the application of it. To begin with those relating to temporal courts. A prohibition will lie if one sue another in a court-baron, or other court not a court of record, for charters concerning inheritance or freehold; or in the county court for trespass vi et armis; or in the county courts or courts baron for a matter of 40s. or upwards, and the plaintiff cannot evade the prohibition by dividing his demand into smaller sums; to the courts of Admiralty, if they entertain questions of a contract made or to be executed within the kingdom; to an inferior court, if an action be brought in it on a judgment in one of the superior courts; to the court of honour of the earl-marshal, it holds plea of things determinable by the common law. To a spiritual court a prohibition will lie, if

it takes cognizance of any plea concerning a title to lands or tenements, or an advowson of a church, or an office, or goods, money, or chattels; and this applies even in the case of goods or ornaments given to a church, or matters of a criminal nature punishable only temporally: in short, as it has been said, anything for which a remedy exists at common law. Yet it has been held that a pension which commenced by the grant of the patron or ordinary may be sued for either in the temporal or spiritual court. Lord Coke however goes further, and says that prohibition lies to a spiritual court in any case, though of a spiritual nature, where a remedy is given by statute in a temporal court, unless the jurisdiction of the spiritual court is saved by the same statute. Perhaps this assertion cannot be maintained to the full extent. In some cases it has been so held, as where a suit in an ecclesiastical court was instituted for preaching without licence or marrying without banns, these having been created offences by act of parliament. Still a prohibition does not lie in a suit for small tithes or for contribution to the repairs of the church, though other remedies are given in these cases by statute (7 and 8 Wm. III., c. 6, and c. 34), and perhaps in some other cases. In cases where no remedy exists elsewhere, a spiritual court may still be restrained from entertaining questions as to matters not within its jurisdiction.

With regard however to the spiritual courts, various exceptions and restrictions must be applied to what has been said. A spiritual court can hold plea for goods, money, and chattels to which a spiritual character attaches; as for instance, tithes, provided they are under a fourth part of the value of the church, or oblations, mortuaries, &c., that is, payments by communicants, or payments for marriages, christenings, churchings, and burials, or pensions; or a sum promised to be given as a marriage portion. It can also hold plea for matters testamentary, such as a legacy, even of a chattel real. Though a will disposes of land as well as personalty, the granting of probate belongs to the spiritual court; but this grant in no way determines the validity of the will so far as relates to the land. A spiritual court has also jurisdiction as to offices merely spiritual, but not for lay offices, even though they are in the spiritual court. It has also jurisdiction over offences committed within the spiritual court itself, as perjury or extortion in all officers of the court, or for brawling and committing a nuisance within a churchyard, or for defamation where no damages are demanded, or where a crime either merely or in part spiritual is imputed, or the words spoken are mere words of passion. Where violence has been done to a spiritual person, he may maintain a suit in the ecclesiastical court, to punish the party by ecclesiastical censures. The spiritual court also has cognizance of a suit for maintaining a way to the church, or where the question is not of a right of way generally, but solely as to the right of way to a church, or a way by which a parson carries off his tithes.

Prohibition lies equally both where the matter of the suit is not cognizable by the court, and where, though the substance is cognizable, matter arises during the progress of it, and is clearly about to be tried, over which the court has no cognizance. As to this, perhaps some confusion and contradiction will be found in the authorities. It has been said that where a suit is brought in the spiritual court for a thing within the cognizance of that court, and temporal matter becomes incident, it shall be determined there, and there can be no prohibition. (12 Co., 65.) However this must always have been understood with the condition, that as to such things the ecclesiastical court was bound to try according to course of common law. Perhaps it was only applicable to cases where parties neglected to apply for prohibition till after sentence, and where no want of jurisdiction appeared on the face of the proceedings. More recent cases have clearly established that if in a cause properly cognizable by a spiritual court a question arises and is necessarily about to be tried as to the existence of a custom, or a prescription, or the limits of a parish, or where in a suit for tithes there is plea of a modus, or that the lands are discharged by statute, or tithes are claimed of things for which no tithes are due, or the defendant makes title by lease, &c., a prohibition will lie immediately.

It has been laid down broadly that the ecclesiastical courts cannot try any matter triable at common law. It is otherwise however where the construction of a statute may come in question: prohibition will not lie on the mere suggestion that the spiritual court is not competent to construe it.

6. A writ of prohibition is applied for by motion in court, which sets out the proceedings in the suit. If the proceedings are not sufficient 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 juris-term represents the resistance of the medium at the instant diction. when the velocity is v; hence the accelerative force by which the falling body is urged at such moment is expressed by g-g.

If the court grants a rule, the other party is heard in answer. The court may then decide, either to refuse the prohibition, or, if they incline to grant it, direct the party applying to declare in prohibition. The mode of doing this is regulated by 1 Will. IV., c. 21. The declaration must Now s being the space descended by the body in the time contain a concise statement of the grounds of the applica-, and v being the velocity as before, an accelerative force

tion, and conclude by praying that the writ may issue. To is represented by this the other party may demur on the ground that no suffi

8-; whence gd:=

equation, observing that v=0 when t=0, we have t=
U+v
U+v
or again, pas-
U-v
2gt

U

2g

hyp. log. U-v

sing from logarithras to numbers, =e

base of the hyperbolic logarithms); whence v=U

and this second member being developed, gives v=gt-b

ds

U+&c. Substituting, in this equation, for v, and

again integrating, we have sg

dt

0314
12Us+ &c.

cos. t. Now, in the equation for x, making æ=

r' (any given distance from the centre) when t=0, we have
dx
dx
dt
dt

a=r'; and in the equation for , making (the velocity)
=0 when t=0, we have b=0. Consequently x=r' cos. t

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 have t the values of U (the terminal, velocities) for iron balls, see Dr. Hutton's 'Tracts,' tract 37.

Next, let a body be 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 direction opposite to that of the gvi whence U

projectile force, we have now

time of falling from the surface to the centre of the earth.

Let it now be required to investigate the relations between the times, the spaces described, and the acquired velocities when a body falls in vacuo from a point at such a distance from the earth that the attraction of gravity upon it may be considered as variable; and when, agreeably to This equation, being integrated, gives the law of nature, its intensity is inversely proportional to

the square of the distance. (Princip., lib. i., prop. 74.)
Then, if r be the radius of the earth, p the distance from
the centre of the earth to the point above the latter from
whence the body is let fall; and if x be the space descended
in any time t: also if g be the force of gravity at the earth's
1
2g
surface, we shall have
:g::
and
2.2
(p-x) (p-x)2;
the last term expresses the force of gravity at the place of
the body when the space descended is x and the time of
d2x
gri
descent is t: therefore
dt (p-x)2

1

:

C-gt
U
C-gt
U

dt; which in

+ const.

+ const.
dx
dt

In order to integrate this equation, multiply both sides of dx2 it by 2dx; and then the first integral will be de 2gp2 The constant may be found on conp-x sidering that

=

(the velocity) = 0 when t = 0, when also

Making v 0 in the above equation for v, we get the value of t when the body has attained its greatest height; and substituting the value of t so found in the last equation for x, we have that greatest height.

equation may be put in the form

dx2 and = 2gr2 dta

2gr2 x )

.

P p -x

(p-x) dx
√px-x2
2gr

by the rules of integration we have t

When arrived at the greatest height, the body would begin to return towards the earth; and it may be shown that the velocity acquired by the body on arriving at the place from whence it was projected would be less than the initial velo-be city; also that the time of the descent would differ from the time of ascent.

If we imagine the earth to be perforated in the direction of a diameter; and if a body be allowed to descend towards the centre in a non-resisting medium from any point in the line of perforation: the law of attraction being in such a case directly proportional to the distance of the body at any time from the centre of the earth (Newton. lib. i., prop. 73),

1

2gp2

=

Ρ

dt; and

√xx-x

p-2x +p arc cos. = : there is no constant to be added, 2 P because x=0 when t=0. From this equation t may easily found when x is given: likewise from the equation for we have the velocity when x is given. And if x be made equal to p-r, the whole distance of the body from the surface of the earth, we shall obtain the whole time of the descent and the velocity acquired at the end of that time.

dx

dt

Again: let it be supposed that a body may be projected vertically upwards in vacuo from the surface of the earth, and be subject to a variably accelerative force of attraction

downwards. Let r be the semidiameter of the earth as before; and now let a be the height ascended from the surface at the end of the time t: also let h be the height due to the initial velocity, supposing the latter to have been acquired by a body falling in vacuo with a uniformly accelerative force; then 2gh will express the square of that velocity. By the law of attraction we have

1
: g :

1

: (r+x) gr3 ; and the last term expresses the intensity of the (r+x)* attractive force at the end of the time t from the comdox g° = dt2 (r+x)**

mencement of the ascent. Hence

In order to integrate this equation, multiply both sides by
dx 2grå
+ const.: and to find the
r+x

=

2dx; then we get a
constant, it must be observed that x=0 when =2gh;

dr
dte

therefore const. = 2g (h+r) and = 2g (h+r)

2gr

that point, insomuch that, given a point of the surface, the curve which passes through that point is given. If any second surface be taken, which is cut by all the curves emanating from the points of the first, every point of the first surface has a point corresponding to it on the second. Thus if the curve passing through A on the first surface cut the second surface in a, the point A is said to be projected on the second surface at a by means of the projecting curve Aa. Similarly any line on the first surface is projected into a line on the second, which last contains the projections of all the points on the first; and the projections of the several boundaries of a figure on the first surface are boundaries of a figure on the second, which is the projection* of the first figure.

It is not perhaps usual to make so wide a definition of projection in general, since the only cases which are commonly considered are those in which the projecting lines are all straight, and either parallel to one another, as in the orthographic projection, or all passing through the same point, as in common perspective. But such a conception of projection is necessary: in Mercator's projection, for exr+xample, the points of a sphere are projected on a circumscribing cylinder, not by straight lines passing through a point, but either by straight lines disposed according to a complicated law, or by curves. If a relation between any dx=2g. dt, and this point and its projection be given, so that either can be found from the other, the passage from one to the other may be made either on a straight lipe or on an infinite variety of curves: but it may happen that the law which the disposi tion of the projecting straight lines follows may be of a more difficult character than that which would be required if a curve, not in itself so simple as a straight line, were substituted.

dr dt2 Taking the square roots and trans√r+x √ {hr+(h+r)x} equation may be put in the form

posing, we have

(r+x)dx

√{hr2+(2h+r)rx+(h+r)x2}

= √2g.dt;

or (h being small compared with r) rejecting h when added to r, the equation becomes

When the foundations of plane geometry were fixed, and the first principles of solid geometry were superadded, it was natural that the very simple idea of the perspective projecfirst principles at least of drawing were practically known, tion should excite attention. In a country in which the the following problem must have suggested itself to the geometers: If through a given point lines be drawn through all the points of the boundary of a plane figure, until they are stopped by another plane, required the figure traced out upon the second plane. A straight line was known thus to

— √ { hr2+r2x+rx® } + hyp. log. {+r+give a straight line: a moment's consideration of the circle,

√{hr2+r3x+rx'}} + const. =√g. t.

The constant may be determined by considering that = 0 when t0; and thus t may be found when x is given. What has been stated respecting the vertical descent and ascent of bodies may be understood to apply also to bodies descending and ascending on inclined planes; the force of gravity on the plane being represented by g sin. a, where a is the inclination of the plane to the horizon.

the only other line then considered, would show that a projection of a circle and a plane section of a cone are the same things. Hence probably the first idea of a conic section; and thus, if the conjecture be correct, the attention was turned from that point, which would, if properly kept in view, have led to the theory of projections in place of one isolated branch of it. The properties of the conic sections, as deduced in the antient manner from the cone, are neither so genera nor so easy as they might be made; and it may be confidently expected, considering the progress which the doctrine of projections has made of late years, that the method of considering the ellipse, hyperbola, and parabola as projections of the circle, will become established in elementary teaching, in preference to the detached geometrical and algebraical methods now in use.

In Dr. Hutton's Tracts there is given a problem for determining the height ascended by a ball when projected vertically upwards with a given velocity, and resisted by the the air; the force of gravity being supposed to be constant, and allowance being made for the decrease in the density of the air as the ball ascends. (Tract 37, prob. v.) In the same tract there is also given (prob. xi.) an investigation of the circumstances attending the motion of a body in air when projected horizontally on a smooth surface so that the action of gravity may produce no effect on the motion of the body, the resistance varying as the square of the velocity. Also in Poisson's Traité de Mécanique,' the following remarkable circumstance is demonstrated:-If a body be projected, as in the last case, and if the resistance of the air vary as the square root of the velocity; the motion of the body will at first diminish gradually till it becomes equal to zero; and afterwards it will go on in-tigation of properties which, being true of a figure, are creasing indefinitely. (Tom. i., no. 136, ed. 1833.) But for the demonstrations of these problems our limits oblige us to refer the reader to the works just mentioned.

We have already spoken of the geometry of projections [GEOMETRY, p. 156]: unfortunately there is no elementary work which gives a general view of its first principles; and until such a work shall appear, the student must search for himself the writings of Monge, Carnôt, Chasles, Poncelet, &c. The History of Geometry,' by M. Chasles, referred to in the article cited, will furnish many more references; and the 'Propriétés Projectives des Figures,' by M. Poncelet, is perhaps the work in which the student may most easily make an advantageous beginning of the subject.

The basis of the theory of projections must be the inves

therefore true of its projections. Some of these are evident enough: thus the projection of an intersection of two lines is the intersection of its projections; if two curves touch PROJECTION. The practical parts of this most im- one another, their projections touch at a point which is the portant application of geometry are noticed in the articles projection of the point of contact. But the following proMAP, PERSPECTIVE, GNOMONIC, GLOBULAR, ORTHOGRA-perty, which is projective, that is, true of the projections of PHIC, STEREOGRAPHIC, MERCATOR, &c. The present every figure of which it is true in the first instance, will give article is merely intended to point out the general principle a good idea of the facility with which certain properties of of all projections, and also to note the theoretical import- the conic sections may be deduced from the circle." ance of the subject.

Imagine a surface of any kind, through every point of which passes a curve the character of which depends upon

The projection of a line or figure has seldom any other name; in astronomy however the projection of a planet's distance from the sun on the piane of the ecliptic is sometimes called the curtate distance.