ROGERIO

ROGERIO. NICOLAI. F. BOSCOVICHIO,
Summi. Ingenii. Viro. Philosopho. Et Mathematico. Præstantissimo
Scriptori. Operum. Egregiorum
Res. Physicas. Geometricas. Astronomicas
Plurimis. Inventis. Suis. Auctas. Continentium
Celebriorum. Europæ. Academiarum. Socio
Qui. In. Soc. Jesu. Cum. Effet. Ac. Romæ. Mathefim. Profiteretur
Benedicto. XIV. Mandante
Multo. Labore. Singulari. Industria
Dimensus. Est. Gradum. Terrestris. Circuli
Boream. Versus. Per. Pontificiam. Ditionem. Transeuntis
Ejusdemque. Ditionis. In. Nova. Tabula. Situs. Omnes. Descripsit.
Stabilitati. Vaticano. Tholo. Reddundæ
Portibus. Superi. Et. Inferi. Maris. Ad. Justam. Altitudinem. Redigendis
Resurgentibus. Per. Campos. Aquis. Emittendis. Commonstravit. Viam
Legatus. A. Lucensibus. Ad. Franciscum. I. Cæsarum. M. Etrurizæ. Ducem
Ut. Amnes. Ab. Eorum. Agro. Averterentur. Obtinuit
Merito. Ab. Iis. Inter. Patricios. Coopatus
Mediolanum. Ad. Docendum. Mathematicas. Disciplinas, Evocatus
Braidensem. Extruxit. Instruxitque. Servandis. Astris. Speculam
Deletæ. Tura. Societati. Sux. Superstes
Lutetiz. Parisiorum. Inter. Galliz. Indigenas. Relatus
Commissum. Sibi. Perficiundæ. In. Usus. Maritimos.
Opticæ. Munus. Adecuravit
Ampla. A. Ludovico. XV. Rege. Xmo. Attributa. Pensione
Inter. Hæc. Et. Poësim. Mira. Ubertate. Et. Facilitate. Excoluit
Doctus. Non. Semel. Suscepit. Per. Europam. Peregrinationes
Multorum. Amicitias. Gratia. Virorum. Principum. Ubique. Floruit
Ubique. Animum. Christianarum. Virtutum
Veræque. Religionis. Studiofum. Præse-tulit
Ex. Gallia. Italiam. Revicens. Jam. Senex
Cum. Ibi. In. Elaborandis. Edendisque. Postremis. Operibus
Plurimum. Contendisset. Et. Novis. Inchoandis. Ac. Veteribus. Absolvendis
Sese. Adeingeret
In. Diuturnum. Incidit. Morbum. Eoque. Obiit. Mediolani
Id. Feb. An. MDCCLXXXVII. Natus. Annos. LXXV. Mensis. IX. Dies. II.
Huic. Optime. Merito. De. Republica. Civi
Quod. Fidem. Atque. Operam. Suam. Eidem. Sæpe. Probaverit
In. Arduis. Apud. Exteras. Nationes
Bene. Utiliterque. Expediendis. Negotiis
Quodque. Sui. Nominis. Celebritate. Novum. Patriæ. Decus. Adtulit
Post. Funebrem. Honorem. In. Hoc. Templo. Cum. Sacro. Et. Laudatione
Publice. Delatum
Ejusdem. Templi. Curatores
Ex. Senatus. Consulto
M. P. P.

This inscription was composed by his friend and countryman the celebrated poet Benedict Stay. Zamagna, another of his countrymen, who had likewise been his fellow-jesuit, published a panegyric on him in elegant Latin. A short encomium of him is to be found in the Effratto della Letteratura Europea; and another, in form of a letter, was directed by M. de la Lande to the Parisian journalists, and by them given to the public. A more full elogium has been written by M. Fabroni; and another is to be met with in the journal of Modena; a third was published at Milan by the Abbate Ricca; and a fourth at Naples by the Dr Julius Bajamonti, of which a second edition was made in the year 1790. Of this last chiefly use has been made here.

But what must secure to Boscovich the esteem of posterity are his works, of the greater part of which we

have already taken notice. We have mentioned, 1. His Elements of Mathematics, with his Treatise on Conic Sections; 2. His many dissertations published during his professorship in the Roman college; 3. His account of his Survey of the Pope's Estate; 4. His Theory of Natural Philosophy; 5. His Poem on the Eclipses; 6. His five volumes printed at Bassano.

To these we may add his hydrodynamical pieces. He had made a particular study of the force of running water, and of its effects in rivers; and he was often consulted concerning the best means to prevent rivers from corroding their banks, and from overflowing the neighbouring plains, which often happens in Italy, where the Alps and Apennines pour down so many impetuous streams. He gave a writing on the damages done by the Tiber at Porto Felice; another on the project of turning

Boscovich: turning the navigation to Rome from Fiumicino to Mac-
carese; a third on two torrents in the territory of Pe-
rugia; a fourth on the bulwarks on the river Panaro;
a fifth on the river Sidone, in the territory of Placentia;
a sixth on the entrance into the sea of the Adige.
He wrote other such works on the bulwarks of the
Po; on the harbours of Ancona, of Rimini, of Magna
Vaca, and Savona, besides others, almost all which were
printed. He had likewise received a commission from
Clement XIII. to visit the Pemptin lakes, on the drain-
ing of which he drew up his opinion in writing, to
which he added further elucidations at the desire of
Pius VI. On these occasions he showed how useful
philosophy may be to the public; and of this he gave
another proof when it was referred entirely to his judg-
ment to determine whether or not the cupola of the ca-
thedral of Milan could bear the weight of a very high
spire, which it was proposed to raise on it, and which
was actually erected according to his directions.

His application to abstruse studies did not hinder
him from paying some attention to what is more plea-
sant. We have seen that he was a poet: he was also
well acquainted with history, and particularly with that
of the Greeks and Romans, and with their antiquities.
He wrote a dissertation on an ancient villa discovered in
his time upon the Tuscan Hill, and on an ancient dial
found there, which dissertation was published at Rome
in a literary journal. He wrote likewise three letters
on the obelisk of Cæsar Augustus, two of which were
printed with his own name, and the third under the
name of another.

Besides all these works that were given to the public
in his lifetime, many writings of his remained in manu-
script in the hands of different persons, and particularly
with his friend M. Gaetani, and many more with Count
Michael de Sargo, a Ragusan senator, who inherited
all his papers that were in his own hands at his death.
These, it is hoped, have either been already sent to the
press or will be so; as nothing came from the pen of
Boscovich which was not useful and deserving to see
the light.

It now remains that we give an account of his
THEORY OF NATURAL PHILOSOPHY; and in doing
this we shall, in the first place, lay before our readers a
view of this system. We shall, in the second place, re-
late, from what principles and by what steps it was de-
rived. We shall, thirdly, take notice of the principal
objections made to it, and subjoin the author's answers
to the same. We shall, finally, shew how happily it
may be applied to explain the general properties of mat-
ter, as well as the particular qualities of all the classes
of bodies, which have been examined according to what
it teaches.

I. In this system, therefore, the whole mass of matter,
of which all the bodies of the universe are composed,
consists of an exceeding great, yet still finite, number of
simple, indivisible, inextended, atoms. These atoms are
endowed with repulsive and attractive forces, which vary
and change from the one to the other, according to the
distance between them, in the following manner: In
the least and innermost distances they repel one ano-
ther; and this repulsive force increases beyond all li-

mits as the distances are diminished, and is consequent-
ly sufficient for extinguishing the greatest velocity, and
for preventing the contact of the atoms. In the sen-
sible distances, this force is attractive, and decreases, at
least sensibly, as the squares of the distances increase,
constituting universal gravity, and extending beyond
the sphere of the most distant comets. Between this
innermost repulsive force and the outermost attractive
one, in the insensible distances, many varieties and chan-
ges of the force, or determination to motion, take
place: for the repulsive force decreases as the distance
increases. At a certain distance it comes to vanish en-
tirely; and, when that distance is increased, attraction
begins, increases, becomes less, vanishes; and the distance
becoming greater, the force becomes repulsive, increases,
lessens, and vanishes as before. Many varieties and chan-
ges of this kind happen in the insensible distances, some-
times more rapidly, sometimes more slowly, and some-
times one of the forces may come to nothing, and then
return back to the same without passing to the other. For
all this there is full room in the distances that are in-
sensible to us, seeing the least part of space is divisible
in infinitum. Besides these repulsive and attractive for-
ces, our atoms have that vis inertiae which is admitted
by almost all modern philosophers. These atoms, en-
dued with these forces, constitute the whole substance
of Boscovich's system; which, however simple and short
it may appear to be, has numberless and very wonder-
ful consequences, as we shall see afterwards.

But, that the whole theory ex-
pressed by a geometri-
cal curve,
is an axis, from which, in the point A, is drawn the
right line AB at right angles. AB is considered as an
asymptote; on each side of which the two curves, quite
similar and equal, DEFGHIKLMNOPQRSTVU on
the one side, and DEFG on the other, are placed.
Now, if ED be supposed to be asymptotical, and be ex-
tended, it will still approach to BA, but will never
come to touch it. This curve ED approaches to the
axis CC, comes to it in E, cuts it and departs to a
certain distance in F, after which it again approaches
the same axis and cuts it in G. In like manner it
forms the arches GHI, IKL, LMN, NOP, PQL.
At last it goes on in TVU, which is asymptoti-
cal, and approaches to the axis; so that the distan-
ces from it are in a duplicate reciprocal proportion
of the distances from the right line BA. If from
any points of the axis, as from a, b, d, we raise the
perpendiculars ag, br, db, the segments of the axis
Aa, Ab, Ad, are called abscissæ, and represent the dis-
tances of any two points of matter from one another;
and the perpendiculars ag, br, db, are called ordinates,
and exhibit the repulsive or attractive force, according
as it lies on the same side with D, or on the other side
of the axis.

Now it is evident that, in this form of the curve line,
the ordinate ag will be increased beyond whatever li-
mits, if the abscissæ Aa be lessened likewise beyond what-
ever limits; that if this abscissa be increased to Ab, the
ordinate will be lessened, and will pass into br, which
will still be lessened as it approaches from b to E, where
it will come to nothing; that then, the axis being in-
creased to Ad, the ordinate will change its direction in-
to bb, and, on the opposite side, will increase at first

Boseovich's to F, then it will decrease through $i$ as far as G, where it will again vanish, and again change its direction in $m$ to the former, and that, in the same manner, it will vanish and change its directions in all the sections I, L, N, P, R, until the ordinates $op,\; vs.$ become of a constant direction, and decrease, at least sensibly, in a reciprocal duplicate proportion of the abscisses $Ao,\; Av.$ Wherefore, it is manifest, that by such a curve are expressed our forces; at first repulsive, and increasing beyond all limits, the distances being lessened in like manner, and which decrease, the same distances being augmented; then vanish, change their direction, and become attractive; vanish again, and become repulsive; till at last, at sensible distances, they remain on the side opposite to D, and are attractive in a duplicate reciprocal proportion of the distances.

We may also observe, that the ordinates may increase or decrease rapidly, as in $yo,\; zi$, or slowly, as in $vx,\; wc$; and, consequently, that the forces may increase or decrease in like manner. We may add, that the curve may return back without intersecting, or even touching, the axis, as in $f$, and may return after having touched the same axis.

Although this curve expresses very clearly the repulsive and attractive forces of our system, yet, at first sight, it may appear to be a complicated irregular line. But the author shews that his curve is uniform and regular, and may be expressed by one uniform algebraical equation; which it will be necessary for us to consider, in order to give satisfaction to our readers, and to do justice to the theory.

The simplicity of this curve proved. Wherefore, from what we have seen, the curve must have the following six conditions: 1^st, It must be regular and simple, and not composed of an aggregate of arches of different curves. 2^dly, It is necessary that it cut the axis CAC in certain given points only, at two equal distances on each side AE, AE, AG, AG, and so on. 3^dly, That to every abscissa an ordinate correspond. 4^thly, That if we take equal abscisses on each side of A, they have equal ordinates. 5^thly, That the right line AB be an asymptote, the area BAED being asymptotical, and consequently infinite. 6^thly, That the arches terminated by any two intersections may be varied at pleasure, and recede to any distance from the axis CAC, and approach at pleasure to whatever arches of whatever curves, cutting them, touching them, or osculating them, in any place and manner.

In order to find an algebraical formula expressing the nature of a curve line that would answer all these six conditions, let us call the ordinate $y$, the abscissa $x$, and let it be made $x\; =\; z$. Then let us take the values of all the abscisses AE, AG, AI, &c. with the negative sign, and let the sum of the squares of all these values be called $a$, the sum of the products of every two squares $b$, the sum of the products of every three, $c$, and so on; and let the product of all of them be called $f$, and the number of the same values $m$. All this being supposed, let it be made $z^m\; +\; az^\{m-1\}\; +\; bz^\{m-2\}\; +\; cz^\{m-3\}\; +\; \backslash dots\; +\; f\; =\; P$. If we suppose $P$ equal to nothing, it is clear that all the roots of that equation will be real and positive; that is, the squares only of the quantities AE, AG, AI, &c. which will be the values of $z$; and therefore, as it is $z\; =\; \backslash pm\; \backslash sqrt\{x\}$, because it is $x\; =\; z^2$, it is likewise clear that the values of $x$ will be

both AE, AG, AI, positive, and AE', AG', &c. negative. Boseovich's System of Natural Philosophy.

This being done, let any quantity be multiplied by $z$, providing it hath no common divisor with $P$, lest $z$ vanishing, it likewise might vanish; and having made $z$ an infinitesim of the first order, it may become an infinitesim of the same, or of a lower order, as will be whatever formula $z^r\; +\; g\; z^\{r-1\}\; +\; h\; z^\{r-2\}\; +\; \backslash dots\; +\; l$; which, being supposed equal to $o$, may have as many imaginary, and as many and whatever real roots, providing none of them be those of AG, AE, AI, &c. either positive or negative. If then the whole formula be multiplied by $z$, let this product be called $Q$.

If we make $P\; -\; Q\; =\; o$, this equation will satisfy the five first conditions above mentioned; and the value of $Q$ being properly determined, the sixth condition also may be complied with.

For, in the first place, seeing the value $P$ and $Q$ are made equal to $o$, they have no common root, and therefore no common divisor. Hence this equation cannot be reduced to two by division; and therefore it is not composed of two equations, but is simple, and therefore exhibits one simple continued curve, which is not composed of any others; which is the first condition.

Secondly, The curve thus expressed will cut the axis CAC in all the points E, G, I, &c. G', &c. and in them only: for it will cut that axis only in those points in which $y\; =\; o$, and in all of them. Moreover, where it will be $y\; =\; o$, it will also be $Q\; =\; o$; and therefore, because of $P\; -\; Q\; =\; o$, it will be $P\; =\; o$. But this will happen only in those points in which $z$ will be one of the roots of the equation $P\; =\; o$; that is, as we have seen above, in the points E, G, I, or E', G', &c.: wherefore, only in those points will $y$ vanish, and the curve cut the axis. Again, that the same curve will cut it in all these points, is clear from this, that in them all it will be $P\; =\; o$. Wherefore it will likewise be $Q\; =\; o$; but it will not be $Q\; =\; o$, seeing there is no common root of the equations $P\; =\; o$ and $Q\; =\; o$: it must therefore be $y\; =\; o$, and the curve will cut the axis: and thus the second condition is satisfied.

Besides, whereas it is $P\; -\; Q\; =\; o$, it will be $y\; =\; \backslash frac\{P\}\{Q\}$: the abscissa $x$ being, however, determined, we will have a certain determinate quantity for $z$; and thus $P,\; Q$, will be determined, and the only two of the kind. Wherefore $y$ also will be sole and determined; and therefore to every abscissa $z$, one only ordinate $y$ will correspond. This is the third condition.

Again, whether $x$ be assumed positive or negative, providing it be of the same length, still the value $z\; =\; \backslash sqrt\{x\}$ will be the same, and therefore the values of both $P$ and $Q$ will be the same: wherefore $y$ will still be the same. Taking, therefore, equal abscisses $z$ on both sides of A, the one positive, the other negative, they will have equal corresponding ordinates. This is the fourth condition.

If $x$ be lessened beyond all limits, whether it be positive or negative, $z$ likewise will be lessened beyond all limits, and will become an infinitesim of the second order: wherefore, in the value $P$, all the terms will decrease in infinitum, except in $y$, because all the rest besides it are multiplied by $z$; and thus the value $P$ will be as yet finite. But the value $Q$, which has the formula

with's mula multiplied by $z$, will be lessened in infinitum, and will be an infinitesim of the second order: therefore $\backslash frac\{P\}\{Q\}$ will be augmented in infinitum, so as to become an infinite of the second order. Wherefore the curve will have the right line AB for an asymptote, and the area BAED will increase in infinitum: and if the ordinate $y$ be assumed positive on the side AB, and express repulsive forces, the asymptotic arch ED will lie on the same side AB. This is the fifth condition.

Now the value $Q$ can be varied in infinite manners; so that still the conditions for which it was assumed may be fulfilled; and therefore the arches of the curve intercepted by the intersections may be varied in infinite manners; so that the first five conditions of the curve may be implemented: whence it follows, that they may be so varied that the sixth condition may also be answered.

For if there be given, however many, and whatever arches of whatever curve, providing they be such that they recede always from the asymptote AB, and thus no right line parallel to that asymptote cut these arches in more than one point, and in them let there be taken as many points as you please, and as near one another; it will be easy to assume such a value of $P$, that the curve shall pass through all these points, and the same may be varied infinitely; so that still the curve will pass through all the same points.

Let the number of points assumed be what you please $=\; r$, and, from every one of such points, let right lines be drawn parallel to AB, as far as the axis CAC, which must be the ordinates of the curve that is sought; and let the abscissæ from A to the said ordinates be called $M^1,\; M^2,\; M^3,\; \backslash dots$ and the ordinates $N^1,\; N^2,\; N^3,\; \backslash dots$. Let there now be taken a certain quantity $Ax^r\; +\; Bx^\{r-1\}\; +\; Cx^\{r-2\}\; +\; Gx$, and let this quantity be supposed equal to $R$. Then let another such quantity $T$ be assumed, so that $z$ vanishing, whatsoever term of it may vanish, and so that there be no common divisor of the value of $P$, and of the value of $R+T$; which may be easily done, seeing all the divisors of the quantity $P$ are known. Let it now be made $Q=R+T$, and then the equation of the curve will be $P-Ry-Ty=0$. After this, let there be put in the equation $M\_1,\; M\_2,\; M\_3$, successively for $x$, and $N\_1,\; N\_2,\; N\_3$, &c. for $y$; we will have a number of equations equal to $r$, which will contain the values of $A,\; B,\; C,\; \backslash dots,\; G$, each of them of one dimension, in number likewise equal to $r$; and, besides, we will have the given values of $M\_1,\; M\_2,\; \backslash dots,\; N\_1,\; N\_2,\; N\_3,\; \backslash dots$ and the arbitrary values which in $T$ are the coefficients of $z$.

By these equations, which are in number $r$, it will be easy to determine the values $A,\; B,\; C,\; \backslash dots,\; G$, which are likewise in number $r$, assuming in the first equation, according to the usual method, the value $A$, and substituting it in all the following equations: by which means the equations will become $r-1$. These, again, by throwing out the value $B$, will be reduced to $r-2$, and so on until we come to one only; in which the value $Q$ being determined by means of it, going back, all the preceding values will be determined, one by each equation.

The values $A,\; B,\; C,\; \backslash dots,\; G$, being in this manner determined, in the equation $P-Ry-Ty=0$, or $P-Qy=0$, it is clear that, the values $M\_1,\; M\_2,\; M\_3,\; \backslash dots$

being successively put for $x$, the values of the ordinate Boscovich's $y$ must successively be $N\_1,\; N\_2,\; N\_3,\; \backslash dots$; and, therefore, that the curve must pass through these given points in those given curves; and still the value $Q$ will have all the preceding conditions. For $z$ being lessened beyond whatever limits, every one of its terms will be lessened beyond whatever limits, seeing all the terms of the value of $T$ are lessened which were thus assumed, and likewise the terms of the value $R$ are lessened, which are all multiplied by $z$; and, besides this, there will be no common divisor of the quantities $P$ and $Q$, seeing there is none of the quantity $P$ and $R+T$.

But if two of the nearest of the points assumed in the arches of the curves, on the same side of the axis, be supposed to accede to one another beyond whatever limits, and at last to coincide, which will be done by making two $M$ equal, and likewise two $N$ equal; then the curve sought will touch the arch of the given curve; and if three such points coincide, they will osculate it: nay, as many points as we please may be made to meet together where we please; and thus we may have osculations of what order we please, and as near one another as we please, the arch of the given curve approaching as we please, and at whatever distances we please, to whatever arches of whatever curves, and yet still preserving all the six conditions required for expressing the law of the repulsive and attractive forces. And whereas the value of $T$ can be varied in infinite manners, the same may be done in an infinite number of ways; and therefore a simple curve, answering the given conditions, may be found out in an infinite number of ways. Q. E. F.

What we have said will, we hope, satisfy our readers, and especially those of them who are in the least acquainted with high geometry, that Boscovich's curve is simple, regular, and uniform; and that therefore the law of repulsive and attractive forces, expressed by it, is simple and regular.

II. If this system were a mere hypothesis, it would still be very ingenious, and, from what we shall say afterwards, would still be well adapted for explaining the phenomena of nature. But its author is far from looking upon it as an arbitrary supposition; he assures us that he was led to it by a chain of strict reasoning, from evident principles. We shall now give an abridgement of that reasoning from his Dissertations on the Law of Continuity, and from his Theory of Natural Philosophy.

He tells us, then, that in the examination of Leibniz's opinion of the vires vitæ, he came to consider the theory of the collision of bodies, and took for example two equal bodies, A proceeding with six degrees of velocity, and B following with the velocity of 12: after the collision, they proceed jointly with the common velocity 9. Now, in the moment of collision, it either happens that A passes abruptly from the velocity 6 to the velocity 9, without passing through the velocity 7 and 8, and B passes from 12 of velocity to 9, without passing through 11 and 10; or else there must be some cause which accelerates the one and retards the other before they come to contact. In the first case, the law of continuity is broken; in the second, immediate contact of bodies would be rejected. Maclaurin saw this difficulty, and mentioned it in his work on Newton's Discoveries, l. i. c. 4. He, not having courage to recede from the common opinion, allowed a breach, in such cases, of the law of continuity; but Boscovich maintains

Boscovich's maintains the universality of the law of continuity; and holds, that no bodies touch one another really and materially, but only physically and sensibly to us.

⁵ The law of continuity is that by which variable quantities, passing from one magnitude to another, pass through all the intermediate magnitudes, without ever abruptly passing over any of them. This law Boscovich proves to be universal, in the first place, from induction. Thus we see that the distances of two bodies can never be changed without their passing through all the intermediate distances. We see the planets move with different velocities and directions; but in this they still observe the law of continuity. In heavy bodies projected, the velocity decreases and increases through all the intermediate velocities: the same happens with regard to elasticity and magnetism. No body becomes more or less dense without passing through the intermediate densities. The light of the day increases in the morning and decreases at night through all the intermediate possible degrees. In a word, if we go through all nature, we shall see the law of continuity strictly take place, if all things be rightly considered. It is true, we sometimes make abrupt passages in our minds; as when we compare the length of one day with that of another immediately following, and say that the second is two or three minutes longer or shorter than the former, passing all at once, in our way of speaking, round the globe; but if we take all the longitudes, we shall find days of all the intermediate lengths. We likewise sometimes confound a quick motion with an instantaneous one: thus, we are apt to imagine that the ball is thrown abruptly out of the gun; but, in truth, some space of time is required for the gradual inflammation of the powder, for the rarefaction of the air, and for the communication of motion to the ball. In like manner, all the objections made against the law of continuity may be solved to satisfaction.

⁶ A breach of this law may appear to be, yet Boscovich goes farther, and maintains, that a breach of this law, in the proper cases, is metaphysically impossible. This argument he draws from the very nature of continuity. It is essential to continuity that, where one part of the thing continued ends and another part begins, the limit be common to both. Thus, when a geometrical line is divided into two, an indivisible point is the common limit of both: thus time is continued; and therefore where one hour ends, another immediately begins, and the common limit is an indivisible instant. Now, as all variations in variable quantities are made in time, they all partake of its continuity; and hence none of them can hasten by an abrupt passage from one magnitude to another, without passing through the intermediate magnitudes. As we cannot pass from the sixth hour to the ninth without passing through the seventh, and eighth; because, if we did, there would be a common limit between the sixth hour and the ninth, which is impossible; so likewise you cannot go from the distance 6 to the distance 9 without passing through the distances 7 and 8; because, if you did, in the instant of passage you would be both at the distance 6 and at the distance 9, which is impossible. In like manner, a body that is condensed or rarefied cannot pass from the density 6 to the density 9, or vice versa, without passing through the densities 7 and 8; because, in the abrupt passage, there

would be two densities, 6 and 9, in the same instant. The body must pass through all the intermediate densities. This it may do quickly or slowly, but still it must evidently pass through them all. The like may be said of all variable quantities; and thence we may conclude, that the law of continuity is universal.

But, in creation, is there not an instance of an abrupt passage from non-existence to existence? No, there is not; because before existence a being is nothing, and therefore incapable of any state. In creation, a being does not pass from one state to another abruptly; it passes over no intermediate state: it begins to exist and to have a state, and existence is not divisible. Do we not, at least, allow of an abrupt passage from repulsive to attractive forces in our very theory itself? We do not. Our repulsive forces diminish, through all the intermediate magnitudes, down to nothing; through which, as a limit, they pass to attraction. In the building of a house or ship, neither of them is augmented abruptly; because the additions made to them are effected solely by a change of distances between the parts of which they are composed; and all the intermediate distances are gone through. The like may be said of many other such cases; and still the law of continuity remains firm and constant.

Let us now apply this doctrine to the case above mentioned of the collision of two bodies. We say that the body B cannot pass from the velocity 6 to the velocity 9 without passing through the velocities 6 and 7; because if it did, in the moment of contact of the two superficies it would have the velocities 6 and 9. Now a body cannot have two velocities at the same instant. For if it had two equal velocities at the same time, it would be in two different places at the same time: if it had two different potential velocities or determinations to a certain velocity, it would be capable of being, after a given time, in two places at once—both which are impossible. It is therefore necessary that it go through the velocities 7 and 8, and through all the parts of them. What we have said of the bodies A and B may be said universally of all bodies. Therefore no two bodies in motion can come to immediate contact; but their velocities must undergo the successive necessary change before contact. And as the velocity to be extinguished may be increased beyond all limits, an adequate cause to effect this extinction must be admitted.

This naturally leads us to the interior repulsive forces of our system. for the cause retarding the one body forces and accelerating the other must be a force, because by this we mean a determination to motion; and it must be repulsive, because it acts from the body; and it must increase beyond all limits, seeing the velocity of the incurring bodies may be increased beyond all limits. It must likewise be mutual, because action and reaction are always equal, as may be proved by induction.

From these repulsive forces Boscovich deduces the inextension of his atoms: for this repulsion being common to all matter, must cause a perfect simplicity in the first elements of body. If these elements were extended, and consequently compounded of particles of an inferior order, these particles might possibly be separated, and then they might meet, and an abrupt passage from one velocity to another might take place, which we have excluded from nature by induction, and by a positive argument.

Boscovich's
System of
Natural
Philosophy

Besides this, by rejecting the extension of the elements of matter, we get rid at once of all the difficulties arising from continued extension in body, which have always perplexed the philosophers, and have never been satisfactorily explained. If the elements of matter are extended, each of them may be divided in infinitum, and each part may still be divided in infinitum. Can this division be actually made by the power of God or not? Can there be one infinite in number greater than another? Can there be a compound without a simple of the same kind? These difficulties regard not space, which is no real being; but they would regard matter if it had continued extension. All these perplexities are removed by maintaining, as Boscovich does, that the first elements of bodies are perfectly simple, and therefore inextended (A).

With regard to the exterior attractive forces of our system, there can be no question; seeing they constitute universal gravity, the effects of which we see and feel every day. But between the interior repulsive and exterior attractive forces we must admit many transitions from repulsion to attraction, and from attraction back to repulsion, in insensible distances, which are indicated to us by cohesion, fermentation, evaporation, and other phenomena of nature. And thus we have given, in short, Boscovich's proofs of his whole system.

III. This system has been well received by the learned in Europe, and has contributed much to render its author famous; yet many objections against it have been proposed. Some are startled at the rejection of all immediate contact between bodies; and indeed Boscovich is perhaps the first of mankind who advanced that opinion; but he allows that bodies approach so near to one another, as to leave no sensible distance between them; and his repulsive forces make the same impression on the nerves of our senses as the solid bodies could do. And therefore this opinion of his, however new, is no wise contrary to the testimony of our senses. He only removes a prejudice which was before universal.

Some say, that they cannot even form an idea of an inextended atom, and that Boscovich reduces all matter to nothing: but certainly extension is not necessary for the essence of a being, as must be allowed by all those who hold that spirits are inextended. Because all the bodies that fall under our senses are extended, we are apt to look upon extension as essential to matter: but this error may be corrected by reflection, and an idea of an inextended atom may be formed, by considering the nature of a mathematical point, which is the limit of any two contiguous parts of a line.

Others again have said, that if the elements of matter were void of extension, there would be no difference between body and spirit. But the difference between body and spirit does not consist in the having or not having extension; but in this, that the atoms of

matter are endowed with repulsive and attractive forces, which spirit has not; and spirit has a capacity of thought and volition which bodies have not.

We may here observe, that among the ancients Zeno, and among the moderns Leibnitz, held, that the first principles of matter are inextended points. But both held this opinion with the inconsistency, that they maintained the continued extension of bodies, without ever being able to show how continued extension could arise from inextended elements.

It has been objected likewise, that our repulsive and attractive forces are no better than the occult qualities of the Peripatetics. The like objection has been made to Newton's attraction: but the answer is easy. We observe the effects, and take notice of them: for them we must admit an adequate cause, without being able to determine, whether that cause is an immediate law of the Creator, or some mediate instrument that he makes use of for that purpose.

Some are unwilling to give up the idea of motion occasioned by immediate impulse: but can they show a good reason why some distance may not occasion motion as well as no distance? These are the principal objections that have been made against the Boscovichian system.

IV. Before we proceed to the explication of phenomena by means of our theory, we must advert, that in the curve expressing this theory, the abscissæ denote the distances between the atoms that are under consideration; the ordinates give the present force, and the area between any two of these ordinates gives the square of the velocity generated between them: the arches are either repulsive or attractive, according as they fall upon the same side with the asymptotic curve EG, or on the opposite side.

We must, in the next place, consider the passages from one side of the axis to the other. Sometimes the passage is from repulsion to attraction, at other times from attraction to repulsion. The first are called limits of cohesion, because a particle removed from that limit returns back to it; because if it is removed to a greater distance it is attracted back, and if it is removed nearer it is repelled back. The second are called limits of non-cohesion; because a particle removed thence to a greater distance is repelled still further, and if removed nearer it is attracted still nearer. Of the first kind are E, I, N; of the second are G, L. Likewise, when the curve touches the axis, it may either be an attractive part of the curve, or a repulsive part. These limits may be nearer one another, or farther away; and the limits of cohesion may be stronger or weaker, according as the forces near them are greater or less.

Boscovich considers minutely the effects of these varieties of limits and forces; first with regard to two points, then with regard to three and four, demonstrating

(A) If a particle of matter is not extended, in what respect does it differ from a point of space? Says Boscovich, it is endowed with attractive and repulsive forces. What is this it before it is thus endowed? Does it then differ from a point of space? We can form no notion of any such difference. But a point of space, considered as an individual, is distinguished from another individual only by its situation; it is therefore immovable, but matter is moveable. Have these forces, then, which make matter an object of sense, any substratum, any thing in which they are inherent as qualities? What are the things which these qualities distinguish from each other as individuals?

Boscovich's great variety of forces that may arise from these various combinations, and shewing how from simple atoms a great variety of bodies may be formed. He particularly proves, that, from the various position of the atoms, they may either always repel or always attract other atoms, or do neither. Four atoms may form a pyramid, eight may form a cube, and so on, in regular or irregular figures. Particles of the lowest order may compose particles of a second order, these of a third, and so on. This he exemplifies by a library, in which the letters of the books should be composed of small points, placed so near one another as that their distance could not be perceived without the help of a microscope. Here the letters will be composed of points, the words of letters, and all the variety of books on different subjects, and in different languages, would be composed of words. In like manner, he says, his atoms may compose particles, these may compose others of different orders, of which may be formed various bodies, animal, vegetable, air, fire, water, earth, whole planets, central bodies, the whole universe.

15 Composition of bodies. 16 The system applied to account for

But to be more particular, our author proceeds to apply his system to mechanics, and demonstrates, with his usual accuracy and originality, what regards the centre of gravity, action and reaction, the collision of bodies, the centre of equilibrium, and of oscillation. Of these subjects he treats in the second part of his Theoria; to which we must refer our learned readers, as it cannot be easily abridged.

17 Impenetrability.

In the third part of the same work he proceeds to account for the general properties of matter, beginning with impenetrability. This naturally flows from the interior repulsive forces, which prevent the compensation of any two points. Besides, as the least part of space is divisible in infinitum, it is infinitely improbable that any two points should ever meet, seeing they have an infinite number of other lines in which they can move, besides the one that would join them. But an apparent compensation might take place, if one body should meet another with so great a velocity as not to give time to the repulsive forces to exert their action. Thus an iron ball may pass swiftly near a strong magnet, without being sensibly attracted by it, which it would be if it moved more slowly. Thus a ball from a gun passes through a piece of wood so quickly as to make only a passage for itself, without breaking the neighbouring parts, which it would do were its motion more slow. Of this kind of compensation we have a resemblance in light passing through pellucid bodies.

18 Cohesion.

Cohesion has never been well accounted for by any philosopher before Boscovich. From his system it follows naturally, as we have seen in speaking of the limits of cohesion; for when two atoms are placed in a limit of that kind, they necessarily cohere more or less strongly, according as that limit is stronger or weaker. From the cohesion of the atoms arises the cohesion of compounded particles, and consequently of sensible bodies.

19 Extension.

From the cohesion of particles arises the extension of bodies; because there must always be space between the particles. However, it is evident that this extension is not formed of a continuity of matter; though it may appear to be so to our senses, which cannot perceive the small intermediate distance between the parts of

some bodies, and much less the distances between the simple elements of which they are composed.

Extension of bodies involves figurability; because every extended body must be surrounded by some superficies of a certain figure; but the superficies of bodies can never be accurately determined, upon account of the inequalities in all surfaces. We take, however, that figure for the true one which the body appears to come nearest. Thus we call the earth a globe, notwithstanding the hills and valleys that are on it.

Under the same figure, and of the same magnitude, there may be contained very different quantities of matter. Hence we come to the consideration of density. That body is most dense which contains in the same space the greatest number of atoms, and vice versa.

This density may be increased beyond any given limits by the nearer approach of the atoms to one another. Hence a body of any given magnitude, however small, may come to be divisible beyond any given limits.

Mobility, which is likewise reckoned among the general properties of body, is essential to our system, seeing an essential part of it consists in forces, which are determinations to motion, at least in certain distances.

Universal gravity in sensible distances is likewise a branch of our theory. On which subject it may be observed, that perhaps our curve, after it has extended beyond the sphere of the comets most distant from the sun, may depart from its asymptotical nature, and approach to the axis, intersect it, and pass to repulsion. This would effectually answer the objection made by some against Newton's attraction, when they allege, that, from his opinion, it would follow, that the fixed stars, and all matter, would be drawn together into one mass. If such a repulsion takes place, it may soon pass again into attraction, and form limits of coelition; so that our sun may be in such a limit with regard to the fixed stars, and our planetary system make only a small part of the whole universe. And this may suffice concerning the general properties of matter.

Let us now descend to some particular classes of bodies, of which some are fluid, others solid. The parts of fluid bodies are easily separated, and easily moved round one another, because they are spherical and very homogeneous; and hence their forces are directed more to their centres than to one another, and their motions through one another are less obstructed. Between the particles of some of them there is very little attraction, as in fine sand or small grains of seed, which approach much to fluidity. The particles of some others of them attract one another sensibly, as do those of water, and still more those of mercury. This variety arises from the various combinations of the particles themselves, of which we have already taken notice. But in air the particles repel one another very strongly; and hence comes that great rarefaction, when it is not compressed by an external force. Its particles must be placed in ample limits of repulsion.

Solid bodies are formed of parallelopipeds, fibres, and of irregular figures. This occasions a greater cohesion than in fluids, and prevents the motion of the parts round one another; so that when one part is moved all the rest follow. Of these bodies some are harder, whose particles are placed in limits which have strong repulsive

Bovcovich's five arches within them; others are softer, whose particles have those arches of repulsion weaker. Some are flexible, the particles of which are placed in limits that have weak arches of repulsion and attraction on each side; and if those arches are short, the particles may come to new limits of cohesion, and remain bent: but if the arches are longer, the former repulsion and attraction will continue to act, and bring back the body to its former position; nay, in doing this with an accelerated velocity, the parts will pass their former limits, and vibrate backwards and forwards, as may be seen in a bended spring. Thus elasticity is accounted for.

Viscous bodies stand in the middle between solid and fluid. Their particles have less cohesion than the first, and more than the second: they stick to other bodies by an attraction which their particles have from their composition. In like manner water itself sticks to some bodies, and is repelled by others. All which arises from the different composition of the particles, which gives a variety of respective forces.

What appears very wonderful in nature, is the composition of organic bodies. But if we consider that particles may be so formed, that they may repel some and attract others, the whole of vegetation, nutrition, and secretion, may be understood, and follows from our system. And as one particle may attract another in one part only, and repel it in every other situation, hence may be gathered the orderly situation of the particles in many crystallizations. The great variety of repulsive and attractive forces, or limits of cohesion, of the position of atoms, and of combinations of particles, will account for all these phenomena.

The chemical operations, which are so curious in themselves, and so useful to society, are well explained by Boscovich's system, and serve as a confirmation of its truth. Of this we shall give some instances. When some solids are thrown into some liquids, there happens to be a greater attraction between the particles of the solid and of the liquid than there is between the particles of the solid itself. Hence the particles of the solid are detached and surrounded by the fluid; this mixture retaining the form of globules, and therefore continuing to be fluid. This is called solution. But when the solid particles are covered to a certain depth, the attractive forces cease on account of the different distances, and no more of the solid is detached. Then the fluid is said to be saturated. If into this mixture another solid be put, the particles of which attract the fluid more strongly, and perhaps at greater distances than the particles of the former; then the fluid will abandon the former and cleave to the latter, dissolving them, and the particles of the former will fall to the bottom in the form of powder, into which they had been reduced by the solution. This separation is called precipitation. Perhaps rain arises from a precipitation of this kind, when the aqueous particles are left by the air, which is more strongly attracted by some other particles floating in the atmosphere.

Fluids of the same specific gravity are easily mixed; and even though the specific gravity be different, the particles of the one attract those of the other, in such a manner that they seem to form one fluid by a kind of solution. Nay, it happens, that two fluids mixed together form a solid, because their particles come to be in

the limits of cohesion. They may even occupy less space than they did before, by being attracted into less distances between their parts.

Fermentation is a necessary consequence of our system. For when bodies, whose particles, by the variety of their composition, are endowed with different forces, come to be mixed, there must arise an agitation of the parts, and an oscillation among them; sometimes greater, sometimes less, according to the nature of the particles. This agitation is stopped by the expulsion of some particles, by the intrusion of others into vacant spaces, and by the impression of external bodies; but always there is a change in what remains, because there is a new disposition of particles.

Fire consists in a violent fermentation of sulphureous matter, especially when it meets with the matter of light in any quantity. This fermentation agitates strongly the parts of other bodies, separates them from one another, and often throws them into a state of fusion; the cohesion between their parts being broken, and they being thrown into a circular motion. In this state they may be often mixed together, so as to form one body; they may be again separated by the action of the same fire, which evaporates some of them sooner, some later. Hence the art of smelting metals.

When, in the agitation occasioned by fire, some of the particles are thrown out into an arch of repulsion, they may fly off and evaporate. Sometimes the whole body may be thrown into a strong repulsion and volatilization, or a sudden explosion take place; when, before the particles are near an equilibrium, a small force may occasion a great change; as the foot of a bird may occasion the fall of a great rock, which was before almost detached from a mountain. In evaporation, the bodies that remain assume a particular figure, as all salts do; and this upon account of their particles having certain parts only that attract one another, and consequently occasion a particular disposition. All these chemical operations evidently prove that there are in nature repulsive and attractive forces between the particles of bodies at small distances; which greatly confirms our whole system.

Boscovich holds, that light is an effluvium, emitted with great velocity from the luminous bodies by a strong repulsion. He explains all the most remarkable properties of this extraordinary matter according to his own principles, and that with great acuteness. On this subject it is observable, that Newton law the necessity of admitting repulsive forces for the reflexion of light, which extend at some distance from the reflecting surface, and therefore resemble the repulsive forces of our theory.

Our author gives likewise a probable explication of electricity, according to Franklin's ingenious hypothesis, and likewise of magnetism, deducing the whole of the appearances from various attractions and repulsions. He supposes that fire and the electrical fluid differ only in this, that fire is in actual fermentation, and not so the electrical fluid.

Finally, he explains our bodily sensations, in which he agrees pretty much with other philosophers; excepting in this, that what they attribute to the immediate contact of bodies, or of certain particles emitted from them, he ascribes to attractions and repulsions; which indeed

Boscovich's System of Natural Philosophy indeed are particularly fit for causing that motion in our nerves, which is supposed to take place in the organs of sensation, and to be thence communicated to the brain.

It is to be observed, that although Boscovich maintains, that the very first elements of matter are void of extension; yet he allows, that of these elements, combined in a certain manner, may be formed extended particles of various figures, the parts of which may be so coherent as to be inseparable by any power in nature. By these means the opinion of those philosophers, who are so fond of extended particles, may be in so far gratified. Nay, the Peripatetics may, if they please, adopt Boscovich's inextended atoms for their Materia Prima without any inconsistency; and his repulsive and attractive forces may serve for their substantial forms. And as God can make impressions on our senses independently of the atoms, their absolute accidents may in some sense be admitted. Nor would some such extraordinary exertions of Divine Power favour idealism in the ordinary course of nature.

But what is of more consequence, it is more than probable, that had Newton lived to be acquainted with the Boscovichian theory, he would have paid to it a very great regard. This we may conjecture from what he says in his last question of optics; where, after having mentioned those things which might be explained by an attractive force, succeeded by a repulsive one on a change of the distances, he adds, "And if all these things are so, then all nature will be very simple, and consistent with itself, effecting all the great motions of the heavenly bodies by the attraction of gravity, which is mutual between all those bodies, and almost all the less motions of its particles by another certain attractive and repulsive force, which is mutual between those particles." And a little after, treating of the elementary particles, he says: "Now it seems that these elementary particles not only have in themselves the vis inertia, and those passive laws of motion which necessarily arise from that force, but that they likewise perpetually receive a motion from certain active principles; such as gravity, and the cause of fermentation, and of the cohesion of bodies. And I consider these principles, not as occult qualities, which are feigned to flow from the specific forms of things, but as universal laws of nature, by which the things themselves were formed. For that truly such principles exist, the phenomena of nature shew, although what may be their causes has not as yet been explained. To affirm that every species of things is endowed with specific occult qualities, by which they have a certain power, is indeed to say nothing; but to deduce two or three general principles of motion from the phenomena of nature, and then to explain how the properties and action of all corporeal things follow from those principles, this truly would be to have made a great advancement in philosophy, although the causes of those principles were not as yet known. Wherefore I do not hesitate to maintain the above said principles of motion, seeing they extend widely through all nature." From this passage we may safely conclude, that the great British philosopher would have been highly pleased, had he seen all nature so well explained by the one simple law of forces proposed by the Ragusan.

Boscovich himself was so fully convinced of the truth

of his system, that he was wont to make use of the following comparison: When a letter has been written in occult characters, and we are endeavouring to decipher it, we make various suppositions of alphabets; and when we have found one according to which the whole letter comes to have a reasonable meaning, agreeable to all the circumstances of time, place, persons, and things, we can entertain no doubt of our having discovered the true key of the cypher—so, said he, my system explains so well all the phenomena to which it has been properly applied, that I must flatter myself that I have discovered the true key of nature.

The being accustomed to contemplate so deeply the universe and the materials of which it is composed, made of God. Boscovich sees most clearly the evident necessity of admitting an all-powerful, intelligent, self-existent Being, for the creation of those materials, and for the arrangement of them into their present beautiful form. He was at a loss to find words strong enough to express his surprise, that there should be any man, not to say any one pretending to the name of philosopher, who could be so deaf as not to hear the voice of nature loudly proclaiming its Author from all, even the least of its parts. He gives us his sentiments on this, the most important of all subjects, in the appendix to his Theoria, in which he treats of God and of the soul of man.

There, in the first place, he shows the absurdity of his opinion, who maintain that this world may have been the work of chance, the effect of a jumble of self-existent, self-moving atoms; because chance is an empty word without a real meaning. Whatever exists has its determinate cause, and can only be called fortuitous by us on account of our ignorance of that cause. Besides this, though the number of atoms composing this world is finite, yet their possible combinations are many times infinitely infinite: for they may be placed in infinite places of an infinite line; of these lines there is an infinite number in every plane, and of these planes there is an infinite number in space. Again, these points may have an infinite number of velocities in an infinite number of directions. From all this it is evident, that the combinations in which the points of matter may be, is infinite in a high degree, whereas duration can be infinite in only one dimension. Hence it is infinitely improbable that ever the present combination of things could come out by chance. And this is so much the more infinitely improbable, because the disorderly, chaotic combinations, are infinitely more than the regular ones. The whole of matter might roll about in a blind motion for a boundless eternity, without ever being capable to produce one single mushroom.

Moreover, had matter been in motion from all eternity, every atom would have described an infinite line, and then a part of that line would be assignable at an infinite distance from the point of space in which the atom is at present: but an infinite line can never be run over; therefore the atom could never have come to its present place; and therefore the supposition is absurd. Nothing successive can be eternal with a past eternity, though it can continue without end. God alone can be eternal and actually infinite; but his eternity and infinity are beyond our comprehension.

Neither can the world have existed of itself in any thing like to its present form from all eternity; for matter is perfectly indifferent to numberless states, and from

34 Reconciliation of this with other systems,

35 Especially that of Newton.

36 Comparison of this system to the key of a cypher.

ovich's to its present state it must be determined. This present state is perfectly incapable of determining itself, because this determination must be previous to its existence. It must be determined by the preceding state, which is also incapable of determining itself, and for its determination we must have recourse to the state before. Thus, though we go back to eternity, we shall still find a nullity of determination: now an infinite sum of nothing is nothing; and therefore as the present state of things could have no determination, it could not possibly exist.

It is therefore evident that there must be a Determiner extrinsic to the material world. This Determiner must have an infinite knowledge of all the possible combinations, and an infinite elective creative power to choose and create freely the combination he pleased, in that point of eternity that he chose, with all the numberless circumstances that are agreeable to him.

And here what a vast field of contemplation is laid open to a philosophic mind! What a truly infinite knowledge was requisite to foresee so many ends, and so many means requisite for obtaining those ends, as are contained in the creation! Let us consider light, for example, which was to be emitted for so many ages from so many luminous bodies, with so great velocity, so as to penetrate so many mediums with different degrees of reflectibility and refrangibility, with so many other wonderful qualities; at the same time, so many bodies were to be perfectly fitted for reflecting this light in a certain manner, and the animal eye was to be so formed as to have a picture of visible objects painted on the bottom of it.—How many particular combinations were necessary for all this? What shall we say of the so many herbs, flowers, trees, and animal bodies, as there are on this our earth? All their kinds and species, all the series of their individuals, all their parts and particles, were foreseen, intended, and contrived, by one act of the Divine Mind. Again, how wonderful are the heavenly bodies, of what surprising magnitude, moving in the most beautiful order, at an immense distance from one another? To say nothing of the numberless creatures that are beyond the reach of the best telescope, or below that of the microscope. He who reflects ever so little on these things, must necessarily see the most evident proofs of an infinite power, wisdom, and providence; and he must be filled with admiration and awful respect for the Creator and Ruler of the universe.

Nor are we unconcerned spectators of this grand scene. God has been pleased to make us enter deeply into his great plan of creation. He singled us out among an infinite number of possible human beings, in order to call us into existence at a fixed period; and he has made a vast number of his creatures contribute to the formation of these wonderful machines, our bodies, as likewise to our nourishment, to our preservation, to our necessities, conveniences, and gratifications. Every moment that we exist we are enjoying a great number of benefits, expressly designed for us by that Supreme Being. This evidently demands from us the highest degree of gratitude, love, and obedience.

Let us go a step still farther: Is it not very reasonable to suppose, that our God, who affords us so many instances of his beneficence towards us in the natural order, will also, out of compassion to our weakness and ignorance, have favoured us with a more full and explicit manifestation of himself, of our duties towards him,

and of his intentions concerning us? According to Boscovich and all true philosophers, reason itself alone, and true philosophy, point out to us the probability at least of God's having given us a still better and surer guide, by whose direction we may attain to that perfect happiness which we naturally thirst after, and to which we must have been designed by our Maker. This is probable from reason alone; and of this great fact we are ascertained by unquestionable authority.

BOSHMEN have been generally described as a distinct race of Hottentots, who are enemies to the pastoral life, (see BOSHMEN-Men, Encycl.) This M. Vaillant affirms to be a mistake; and we think he has completely proved that it is so. "These infamous wretches (says he) do not form a particular nation, nor are they a people who have had their origin in the places where they are now found. Boshmen is a name composed of two Dutch words, which signify bad men, or men of the woods; and it is under this appellation that the inhabitants of the Cape, and all the Dutch in general, whether in Africa or America, distinguish those malefactors or assassins who desert from the colonies, in order to escape punishment. In a word, they are what in the British and French West India islands are called Maroon Negroes. These Boshmen, therefore, far from being a distinct species, are only a promiscuous assemblage of mulattoes, negroes, and miztos, of every species, and sometimes of Hottentots and bastards (see BASTER, Supplement), who all differing in colour, resemble each other in nothing but in villany. They are land pirates, who live without laws and without discipline, abandoned to the utmost misery and despair; base deserters, who have no other resources but plundering and crimes. They retire to the steepest rocks and the most inaccessible caverns, and there they pass their lives. From these elevated places they command an extensive prospect over the surrounding plains, lie in wait for the unwary traveller and the scattered flocks, pour down upon them with the velocity of an arrow, and suddenly falling upon the inhabitants and their cattle, slaughter them without distinction. Loaded with booty, and whatever they can carry with them, they then repair to their gloomy caves, which they never quit till, like the lions, hunger again impels them to fresh massacres. But as treachery always marches with a trembling step, and as the presence of one resolute person is sufficient to overawe whole troops of these banditti, they carefully shun those plantations where they are certain that the owners themselves reside. Artifice and cunning, the usual resources of timid souls, are the only means which they employ, and the only guides that accompany them in their expeditions."—Vaillant's Travels into the Interior Parts of Africa.