Recapitulation. The observations presented in this memoir establish the following facts:

1. The production of derived currents in the stems of plants by the aid of platinum needles, inserted, one into the bark, the other into the wood, which currents have a direction from the parenchyma to the pith.

2. The production of similar currents in the bark proceeding from the cambium to the parenchyma, having an inverse direction as compared with the former.

3. The sap of the cortical parenchyma, held exposed to the air for some instants, undergoes such a modification that when put again in contact with the parenchyma sap, it becomes relatively negative.

4. The production of derived terrestrial currents, through the medium of the roots from the pith and other parts of the stem.

5. The direction of the terrestrial currents shows that in the act of vegetation, the earth takes constantly an excess of positive electricity, and the parenchyma of the bark and the leaves an excess of negative electricity which is transmitted to the air through the exhaled water.

6. The distribution of the ascending sap and the sap of the cortical parenchyma leads to the belief that there are currents. circulating continually in plants, directed from the bark to the pith, passing by the roots and earth, and perhaps without passing by these two intermediaries.

7. Chemical reactions are the first cause, beyond doubt, of the electric effects observed in plants. These effects are very varied, and have thus far been observed only in a small number of cases. 8. The opposite electric states of plants and the earth give reason for concluding, that through the great extent of vegetation over the continents and islands, they exert a decided influence upon the electric phenomena of the atmosphere.

ART. XIV. On the Rings of Saturn; By G. P. BOND, Assistant at the Observatory of Harvard University.*

THE question of the multiple divisions of the ring of Saturn has engaged the attention of astronomers from an early period. Cassini appears to have been the first to notice the primary divis ion, though he has placed it midway between the inner and the outer edges.

This interval is always visible with a good telescope, but much nearer to the outer edge than Cassini describes it to be. Short, next, with a telescope of twelve feet focus, probably a reflector,

* Cited from the Astronomical Journal, vol. ii, No. 1 and 2. SECOND SERIES, Vol. XII, No. 34.-July, 1851. 13

saw two or three divisions outside of the center of the ring; a figure is given in Lalande's Astronomy. In June, 1780, Sir W. Herschel noticed, on four different nights, a division near the inner edge. From its never, either previously or subsequently, having been seen by him, it is probable that the subdivisions are not permanent; otherwise they could scarcely have escaped detection under the scrutiny to which he subjected every thing appertaining to the system of Saturn for thirty or forty years. This inner division is figured and described in the Philosophical Transactions for 1792. In Gruithuisen's Astron. Jahrbuch, for 1840, pp. 103-105, mention is made of lines seen on both rings in 1813 and 1814. Quetelet, at Paris, with an achromatic of ten inches' aperture, saw the outer ring divided in December, 1823.

On the 17th of December, 1825, and on the 16th and 17th of January, 1826, at least three divisions were seen on the outer ring by Captain Kater. A full account, illustrated with engravings, has been published in vol. iv, Part II, of the Memoirs of the Royal Astronomical Society. This contains also a collection of the accounts of previous observers. Two reflectors of the Newtonian form were used, of between six and seven inches' aperture.

At Berlin, on the 25th of April, 1837, the outer ring was seen by Professor Encke, with perfect distinctness, divided into two nearly equal parts, and several divisions were recognized on the inner edge of the inner ring. The great equatorial of the Berlin Observatory was used with an achromatic eyepiece.

On the 28th of May, the place of the outer secondary interval was determined. The great optical capacity of the telescope, and the eminence of Professor Encke as an observer, give the highest value to these observations. They are found in the Astr. Nachr., No. 338. No. 357 of the same volume has a notice of several divisions on both rings, seen by De Vico, at Rome, with the equatorial of the Roman College, the object-glass of six inches, by Cauchoix. A letter from M. Decuppis, Comptes Ren dus, vol. vii, gives a description of several divisions seen at Rome, in May, June, and July, 1838.

On the 7th of September, 1843, a division of the outer ring was detected by Messrs. Lassel and Dawes, at Starfield. They employed a Newtonian reflector of nine inches' aperture; the details are to be found in vol. vi, of the Monthly Notices of the Royal Astronomical Society.

The newly discovered inner ring of Saturn cannot properly be classed with the subdivisions of the old ring, as it lies within its inner edge.

We have, then, the best assurance in the number and reputaof those who have described the phenomena in question,

that to set aside these appearances by referring them to some optical deception on the part of the observer, or to some defect in his instrument, is an explanation altogether insufficient and unsatisfactory. On the other hand, we know that some of the best telescopes in the world, in the hands of Struve, Bessel, Sir John Herschel, and others, have given no indication of more than one division, when the planet has appeared under the most perfect definition. The fact, also, that the divisions on both rings have not usually been visible together, and that the telescopes which have shown distinctly several intervals in the old ring have failed to reveal the new inner ring, while the latter is now seen, but not the former, may be taken as some evidence that the difference is not probably owing to any extraordinary tranquillity or purity of the atmosphere, nor to any peculiarly favorable condition of the eye or instrument, but rather to some real alterations in the disposition of the material of the rings.

Admitting this, the idea that they are in a fluid state, and within certain limits change their form and position in obedience to the laws of equilibrium of rotating bodies, naturally suggests itself. There are considerations to be drawn from the state of the forces acting on the rings which favor this hypothesis. For instance, on the assumption that the matter of which the ring is composed is in a solid state, we may compute for any point on its surface the sum of the attractions of the whole ring and of Saturn. The centrifugal force, generated by its rotation, may then be determined from the condition that the particle must remain on the surface. Now in the case of a solid ring, particles on the inner and outer edges must have the same period of rotation. This condition limits the breadth of the ring, for if it be found necessary for the inner and outer edges to have different times of rotation, this can be accomplished only by a division of the ring into two or more parts. In this way Laplace has inferred the necessity of there being several rings. From a more exact analysis, M. Plana, in the Mem. Acad. Turin, vol. xxiv, concludes that more than one ring is not essential. The data which he assumed we now know to have been very wide of the truth, as regards the mass and thickness of the ring.

Bessel's last determination of the mass derived from the progressive motion of the line of apsides of the satellite Titan, which amounts to a very sensible quantity, makes that assumed by Plana at least thirty times too large. If Bessel's mass be received, the necessity of numerous rings can scarcely be questioned.

If the density of the ring be the same with that of Saturn, and its matter uniformily distributed with Bessel's mass of Saturn's, its thickness, seen from the earth, would only subtend an angle of of a second of arc. It is a confirmation of the

mass adopted, that this does not vary more from that derived from observation, than we can attribute without improbability to a difference of density between the ring and Saturn. Sir John Herschel states, Outlines of Astronomy, p. 315, that it cannot be so large as one twentieth of a second. In the Astronomical Journal for January, 1850, I have given as the result of observations with the great refractor at Cambridge, during the disappearance of the ring in 1848-49, a thickness not exceeding one hundredth of a second. We cannot suppose the mass to be greater than that assigned by Bessel, without also admitting a density much greater than that of Saturn, the smallest observed thickness already requiring a density more than three times that of the planet.

In the calculations which follow, I have supposed the mass of the ring not greatly to exceed of Saturn, and its thickness th of a second. For the other elements I have used Struve's

measurements.

The analysis of the attraction of the ring presents great difficulties. Laplace has taken as an approximation for a very narrow ring the attraction of a cylinder of infinite length, having for its base an ellipse. Plana takes account of the curvature by assuming the breadth to be very small compared with its radius. But if more than the first term is taken into account, the numerical calculations become very complicated. These difficulties may in part be avoided by taking account of the form of the surface only in the immediate neighborhood of the point attracted. In all the parts distant compared with the thickness, it is sufficient to suppose the whole mass collected in the plane of the center of the rings. This plane, considered as made up of parallel straight lines, attracts the particle by the sum of the attractions of its elements. The attraction of each line parallel to its length, y being its perpendicular distance from the radius joining the attracted particle with the center, and r and the distances of its extremities from the same point, will be

From which the attraction of a plane surface is easily computed by quadratures. For the ring on the surface of which the attracted particle is, and for the two next adjacent, I have used Laplace's formula, Mécanique Céleste, vol. ii, [2092]. This as sumes the figure of the surface to be elliptical; in the absence of any certain knowledge of its form, this has the recommendation of simplicity and of satisfying also the conditions of equilibrium. The hypothesis of any other figure would not materially affect the conclusions arrived at, provided the mass and density be not altered. The numbers thus obtained are only approximations to the truth, but are sufficient for the object in view.

If we adopt for unity the radius of the outer edge of the outer ring, we have from observation the thickness of the ring=26<.. Let r and r' be the radii of the inner and outer edges, and i the interval between two adjacent rings,

Any intervals permanently existing so large as one half, or even one third, of that usually seen, could not escape observation. Moreover, if the subdivisions are numerous, the width of the intervals must be proportionally diminished, because the whole area occupied by them goes to diminish the amount of light reflected, and to increase the density of each ring, both of which are already large. The light of the ring being sensibly brighter than that from an equal area on the ball, it is not probable that any considerable part of the light of the sun is transmitted through intervals. And to preserve the same mass, if the intervals are large, the matter must be compressed, as it is not allowable to give a thickness greater than is indicated by observation. To avoid the hypothesis of a reflective power, and a density greater than we are warranted in assuming, we must, therefore, consider the intervals to be very narrow. We may take, then, the width of all but the known interval as certainly less than 001, which is one half of the width of the known interval. From the blackness of the shadow of the ring upon the ball, which would be diminished in intensity were a considerable part of the sun's rays transmitted, we may infer that the intervals which reflect no light at all cannot occupy an area so large as one fourth of the average breadth of the rings; that is, r-r>0·04.

The above are very liberal allowances, but it is important to assume the intervals as large as possible, so as to diminish the chances of a collision, which at best is almost inevitable.

We come now to consider the forces acting on the rings.

If f be the force with which a particle at the outer extremity of the major axis of a ring is attracted to its surface by the sum of the attractions of all the rings, f the same force for the inner edge, s the mass of Saturn, and t the time of revolution of any

ring in days, the centrifugal force at the distance r will be =

log. k=9.1207.

kr

ta'

t2

Then, in order that the particle should remain on the surface, we must have