There still remains the second way of looking at the course of nature: it is such as it is, and no reason therefor can be given. What is the exact meaning of this statement? Simply that the upholder of the doctrine resolves, so far as concerns the gaining of truth, to put trust in the testimony of his eyes, ears, touch, and other physical senses, and in nothing else. He is a strict positivist; he says: "I see x, feel y, and hear z; to me, then, x, y, and z exist as things seen, felt and heard, respectively. To me there is no causation, for I do not directly perceive it. I believe in memory, it tells me what I have formerly seen; I believe in the axiom, cogito ergo sum, because the very denial of thought implies the action of thought. My duty is to clearly understand and to tabulate all the observations I have made; but there it stops; I may make many inductions and may use them for convenience, but am not sure of them. One induction tells me the sun will rise to-morrow: for my convenience I say it will; but of this I am not sure; perhaps it will not:-it is a thing of the future and the future I cannot see. I attempt to explain nothing:-you attempt to explain, and you come to no certain results:-I am more modest. By my individual observation I know certain things, and all other things are to me only as what may be. The earth may, or may not, turn again on its axis; causation may, or may not, exist; there may, or may not, be a God."

The holder of this theory, when compared with the believers in kindred opinions, is, in a certain sense, consistent; because he only makes statements, which are true as far as they go; and does not attempt explanations, which must in the end prove unsatisfactory. But his theory is incomplete and therefore onesided and untrue. On the one hand, he acknowledges consciousness, and through consciousness believes in all the phenomena of the outer world (non-ego) as isolated facts; while, on the other, he ignores the properties of self (ego) which are also given by consciousness, and are as reliable as any of its data. Thus, he acknowledges the motions of his voluntary muscles, of which he is conscious, but refuses to acknowledge his own power to move them, or to leave them at rest, of which he is also conscious. We need go no further than the idea of intelligent power, to find the whole trouble in this, and in many other theories.*

What interest does a true conception of the ever-working Creative Intellect give to science! This correspondence of the human with the Divine mind! The astronomer works out, with pencil and paper, the possible answers to a certain problem of

* For able presentations of the doctrines of free will and of necessity, consult the writings of Prof. Francis Bowen, and of J. S. Mill. The idea of causation has been carried to its last analysis by Sir William Hamilton.

motion; he looks at the heavens, and there sees these answers, illustrated in the orbits of celestial bodies. The zoologist, marking the changes of the embryo, thinks of these changes as so many different animals; deep in the rocks he finds all stages of this embryo, each represented by a species, perfect in its kind! On the other hand, how dead the science, that puts "force" as its first cause! What is this force that makes the star-fish and the oyster, the medusa and the cuttle-fish, the crab and the whale, the tufted sea worm and the shark, each in its kind, and each telling its own story of manifold relations with animal creation, that is, that has been, and that is to come? Nature is no such simple thing that she should be dictated to by light, or heat, or electricity. These are her servants, not her masters! Boston, Nov., 1859.

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ART. XVII. On the causes of deviation in Elongated Projectiles; by Maj. J. G. BARNARD, Corps of Engineers, U. S. A.

THE various and somewhat conflicting explanations given of the deviation of projectiles, both spherical and elongated, arising from their own rotary motions, leave room for a few additional words on this subject.

B

A b

1.

D

If the plane surface ab moves, in an elastic medium in the direction of its normal, with a velocity A B, that medium will oppose a force to which we apply the term "resistance" and which is measured by a function of the veloC city A B.

If, at the same time, the surface has a velocity A C, in its own plane, the result will be an actual velocity of each point of the surface, represented by the diagonal AD; but the velocity of impact of the surface with the air, is the same in both cases, being due only to the normal velocity A B. The motion AC in its own plane, would displace, in no degree, the atmo. spheric particles, (except through the agency of that action known as friction-not now considered,) and would therefore generate no component of "resistance."

E

F

2.

F'

If the sphere, whose great circle is A DEF, move through the air in the direction CB, with Ka velocity V, a resistance will be opposed to its motion which will, in magnitude, be a function of the diameter, and of the

velocity V. If we leave out of consideration the force of friction, the character and intensity of the impact of the sphere with the

air will be identically the same, whether it possesses or not rotary motion: for in either case, the surface, considered as a whole, advances in identically the same manner-the displacement of atmospheric particles is the same, and the resulting resistance, the same.

Let the rotation be supposed about a horizontal axis, perpendicular to the line of flight, and in the direction A D. The velocity of the individual points, m, n-or if you choose-elementary surface, mn, will be the resultant of the rotary and translative velocities, and the little surface m n, instead of moving (at the instant) in the direction no, will move in an oblique direction n p. But the rotary component of velocity lies in the plane of this elementary surface, and has, (as in the case of the lateral velocity AC of the plane, Fig. 1) no agency whatever in displacing the air, or in affecting the intensity or character of its impact.

These considerations will, perhaps, be rendered more clear by reflecting that the resistance of a fluid, is due and due only to the displacement of its particles-that when the centre of the sphere has advanced from C to B, the anterior surface has advanced from FAD to F'A' D', and displaced the air in identically the same manner, whether the sphere revolves or not.

These considerations are so obvious that it seems superfluous to insist on them; yet few of the writers on this subject have exhibited a clear understanding of them; or rather it may be said that they exhibit the reverse.

Thiroux, rejecting friction entirely, or rather considering its effects inappreciable, bases his reasoning on the higher velocity with which the points of the surface on the side AF impinge on the air, over that belonging to points on the side A D; an idea, as just shown, entirely fallacious. Capt. Neumann (Prussian artillery), in a theory as pretentious as it is unmeaning (Delobel's Révue de Technologie Militaire, vol. i.), carries this absurdity to the extreme of considering each elementary surface mn, sepa rately, with its combined motion of translation and rotation, and, applying to each the ordinary expression for resistance of a plane surface impinging obliquely upon an elastic medium, integrates through each half of the anterior surface, to obtain the total action on each side.

Not only are the conventional expressions for the resistance of isolated oblique plane surfaces found most inaccurate in practice, but they lose all applicability when they cease to be isolated, and form part of another larger surface (not plane); and this problem, of which the knot is so expertly cut by Capt. Neumann, who proceeds to apply his results to the criticism or test of Magnus' and other theories, is the very "pièce de résistance" which has defied the analysis of d'Alembert, Poisson and Poncelet-per

haps I might add of Newton and Laplace; one of those problems of mechanics to which the term difficult would be misapplied, for analysis has never yet been able to grasp it at all.

I have said that without the consideration of friction, the ac tion upon the air of a rotating and non-rotating ball are iden tically the same. But friction materially alters the character of this action. Whatever may be the immediate cause of this force -whether simply a collision of the inequalities of the surface with the particles of the fluid-or whether it is due to adhesion, the effect is that the moving surface puts in motion with it, the adjacent fluid particles, and in so doing, developes forces tangential and opposed to its own motion.

3.

Thus the anterior surface of the sphere C, revolving from F to D, and advancing from A to B, creates, at each point, forces, p, p', p" &c., tangential and opposed to its rotary moв tion, the resultant of which is a force acting from D towards F and tending to deflect the flight of the ball in that direction. This is the point of view, and the sole one, in which Poisson has considered the effects of friction.

But there is another effect which proves to be very powerful. Force cannot be applied to an elastic fluid, neither can motion be imparted or destroyed, without effecting, at the same time, its density and pressure. To retard a flowing current is to increase its pressure; to accelerate it is to diminish the same.

Applying this to the ball, the air, displaced and compressed in front, escapes along the surfaces A F and AD. Near its surface, the action of friction is to retard the escaping currents on the side A F, and to accelerate them on the side A D, and in consequence, an increase of pressure ensues on the side AF, and a diminution on the side AD; and therefore, a resulting

m

4.

pressure tending to deflect the ball from F towards D. If we divide the great circle ADF into four quadrants by the lines mo and np, drawn at angles of 45° with the direction of translation A B, we may better analyze the effects of friction, in the two forms in which I have presented them.

The posterior quadrant op is in air so highly rarified that its action is insensible or nearly so.* On the side quadrant mp the resultant of the forces of friction (the forces p, p', &c., of Fig. 3) are parallel (or nearly so) and opposed to the motion of translation. They have no effect (or but trifling) to deflect the ball from its course, but acting upon the air, in direct opposition to

* The high velocities of translation of military projectiles is supposed.

the escaping currents, their whole force is expended in destroying velocity and generating pressure. On the anterior quadrant mn the resultant of the forces p, p', &c., is from n towards m, and tends, almost entirely, to deflect the ball in that direction.

On the quadrant no the resultant of the forces p, p', is parallel to the motion of translation, and co-incident in direction with the escaping current whose motion it accelerates and whose pressure it diminishes. Thus, taking the four quadrants, in one, op, the forces of friction are absent; in two, mp and no, they are expended in producing an inequality of pressure on the two sides of the ball, tending to deflect the ball towards the side D (right); while in the anterior quadrant m n, they act to deflect the ball in the opposite direction F (left).

It would have been difficult to decide a priori, which of these forces would prevail, though, while the force of friction is nugatory in one quadrant, in two (mp and on) it expends itself in developing forces tending to deflect to the right, and in only one, mn, does its direct action tend to deflect to the left; yet it must be remarked that in this quadrant the air is most dense, friction the greatest, and that it acts directly upon the projectile.

In the two lateral quadrants the air is less dense, and it is only through pressures developed in the air that it produces its effect; a loss of effect ensuing in the medium through which it acts.

Experience has shown, however, that the forces developed in the two lateral quadrants prevail, and the projectile is deflected to the right; and the experiments of Dr. Magnus give the same result when, instead of a projectile moving through the air, a current of air is directed upon a revolving cylinder.*

The deviation of elongated projectiles, having rotary motion about their axis of figure, though many authors, Thiroux, Panôt, Tamissier, &c., have attempted to refer it to the same causes which produce the deviation in spherical balls, is evidently governed by other causes.

Not only do such writers have to make, as to the direction. which the axis maintains, assumptions which conflict with each

*Of course the division into quadrants which I have made is arbitrary, and only used as a simple means of illustrating how the conflicting effects are produced from one and the same cause. I comprehend under the term friction, all the forces by which a solid surface acts upon a fluid flowing along it, whether by adhesion or simple mechanical collision of particles; and this is the usual meaning of the word in this connection. Poisson has considered friction only in its direct action, i. e., as the resultant of the forces p, p', &c., of Fig. 3, and, deducing therefrom a deviation to the left, he arrives at the conclusion that the magnitude of the force was not sufficient to account for the amount of observed deviation (irrespective, I presume, of direction). If this is true, it is difficult to conceive that the force (overlooked by him) arising from developed pressures (and which I show to have its origin in friction), is sufficient to annihilate the direct effects of friction itself, and to produce the deviations beside. Nevertheless it is all we can account for, and the experiments of Magnus seem to indicate its adequacy.

SECOND SERIES, VOL. XXIX, No. 85.-MARCH, 1860.