where in the northern sky, patches of light would appear, glow for a time and gradually disappear. These appearances continued throughout the night, growing fainter as the dawn approached. 33. Observations at Wheelock, Texas, (lat. 30° 55', long. 87° 29′), by F. KELLOGG.

At 10 P. M. Sept. 1st, I first observed a zone of crimson light 30° in breadth, reaching from 10° above the horizon due east, vertically overhead, and terminating 10° above the horizon due west. From the zenith to the eastern extremity of the zone the light was mild, the color increasing in intensity toward the east, until within 15° of the horizon where it gradually faded. At 11h 20m a beam of whitish light passed due north through the zenith. At 11h 30m another beam diverged from the former to the west, making an angle with it of 40°. These two beams, if continued, would unite about 25° south of the zenith. At midnight the entire space between these beams was filled up with similar but shorter beams of light, converging toward each other. Soon these central rays began to shoot bright scintillating rays of white light from their northern and western ends which travelled with great velocity. The eastern boundary of the zone became gradually paler until 12h 30m A. M. Sept. 2d, when the color in that direction entirely disappeared, and the brightest light was then in the west and northwest. At 1 A. M. the crimson color had entirely disappeared, and nothing remained but the fan-like appearance of the numerous divergent beams of white light. The two rays first formed never changed their form or position until they disappeared about 2 A. M.

34. Observations at Thomasville, Georgia, (lat. 30° 50′, long. 84° 0′), by W. BLAVETT.

Sept. 2d, about 2 A. M. the whole northern half of the heavens was beautifully illuminated. The daily track which the.sun now describes formed the southern boundary of the illuminated portion of the heavens. Upon this southern boundary was a border of deep blood red light, of 2° or 3° in breadth, extending from the eastern to the western horizon. Streams of pale light diverged from the point where this band cut the meridian. These pale streamers, at one moment, were numerous, and the next moment scarce a trace of them could be seen. The great red belt sometimes changed to a beautiful orange color. 35. Observations at Mobile, Alabama, (lat, 30° 41', 88° 1'), from the Daily Mercury.

Sept. 2d, the aurora appeared at midnight and soon after 1 A. M. the eastern sky seemed bathed in a flame of lurid light, while a yet deeper flame streaked with silvery beams the N.W. These two pillars were united in the zenith, by a broad belt of

dimmer fire. The pyramidal foci of red light were situated, one in the east, the other in the N.W. A little later the red field in the N.W. extended southerly so that one half the western sky from the horizon to the zenith seemed a blaze of fire. Meantime brilliant streamers continued to shoot from the N.E. and N.W. towards the zenith, sometimes extending over 50° or 60° of the heavens. These streamers converged towards a point on the meridian about 15° south of the zenith, and from this point shot forth smaller pencils of silvery showers. At 3h 30m the play of the streamers had ceased, while the flash of fiery red had spread over the whole north. The red flush in the northern quarter of the heavens, continued to glow until obscured by the solar dawn.

36. Observations at Washington, Texas, (lat. 30° 26', long. 96° 15'), by Maj. B. F. RUCKer.

Sept. 1st, at 10h 30m P. M. I observed a bright light in the north and N.E. At 11h 30m the light had become much stronger and a good deal more extended in the base; and some beau tiful rays shot far up on the sky in the north. At midnight the base of fiery looking vapor extended from N.E. to N.W. The rays of fiery colored light rose from every direction like an inverted fan and converged towards a point several degrees south of the zenith. Some of these rays appeared like immense columns; others only as a thin streak; some were pale, others fiery. At 1 A. M. the light continued undiminished, although the darting rays were not so numerous. The aurora continued until obscured by the light of the sun.

37. Observations at Jacksonville, Florida, (lat. 30° 15', long. 82°), by Dr. A. J. BALDWIN.

Sept. 2d, the aurora was witnessed from midnight till daylight. At 3 A. M. the entire heavens, even at the extreme south were in a red glow. Streamers ran up from a point in the N.W. and from the S.E. and tortuous waves swelled up from the bottom of these streamers and illuminated the whole heavens. At times these looked like lambent flames, flickering like a blaze of fire. 38. Observations at Union Hill, Texas, (lat. 30° 11', long. 96° 31'), by Dr. WM. H. GANTT.

Sept. 1st, at 11 P. M. a faint glimmering light was visible in the N.E., which gradually grew brighter and extended over a larger space. At midnight it reached from the north 35° eastward, and mounted nearly to the zenith, and soon began to be seen west of north. At 1 A. M. it extended from west to east, and beyond the zenith. Towards the north, extending east and west about 20°, and rising about 10° above the horizon was a dark looking cloud. Above this, the light was of a whitish color, and

The

from it sprang streamers of pink merging into crimson. grandest display was from 1 A. M. to 1 35m. It now began to fade, and at 3 30 was nearly gone. A few flashes of it, however, remained until daylight.

39. Observations at Micanopy, Florida, (lat. 29° 30', long. 82° 18′), by JAMES B. BEAN.

Sept. 2d, at 12h 30m A. M. I first saw a luminous haze in the north, and at 12h 35 streamers shot up in the north. A few minutes before 1 o'clock a luminous arch appeared, but not weli defined. At 1 A. M. it included 160° of the horizon; at 1" 10 there were many distinct streamers; at 1h 15m beautiful quivering streamers, while patches of white light appeared in different parts of the northern hemisphere. At 1h 25m the corona was very bright; at 1h 35m corona very distinct, of vivid white clouds of light. At 1h 40m very brilliant red beams in the west; at 150m the arch extended from E. to W. passing through Aries and Pegasus; at 2h a faint corona; at 2 11 distinct beams near the zenith and on each side E. and W.; at 2h 25m arch brighter red with red patches of light and distinct streamers reaching beyond the zenith; at 2h 35 arch fading, at 2h 40m red light in N.W. but streamers 1ot so distinct; at 2h 50m beautiful beams in N.E.; at 3 arch disappearing, beams indistinet; at 3 10 red haze and no beams; at 3 30 very faint r.d haze, and faint white light near the horizon.

40. Observations at Corpus Christi, Texas, (lat. 27° 45', long. 97° 30'), by A. M. LEA.

Sept. 1st, the aurora began about 11 P. M, and continued until daylight. Two-thirds of the whole visible heavens were lighted up with a rich red glow, whilst the tremulous columns of variega ted light swept over the heavens, from the northern horizon through the zenith to a line within 40° of the horizon on the south. Its greatest intensity was about 14 A. M. Sept. 2d. 41. Observations at Fort Jefferson, Florida, (lat. 24° 37', long. 82° 52'), by Capt. D. P. WOODBURY.

Sept. 2d, at 12h 45m A. M. a continuous arch of red color extended from N. 0° E. to N. 50° W. having an altitude of about 15°, and the thickness of the arch throughout was about 25°. The shade of red was deepest along the central part of the arch, gradually diminishing above and below. Soon rays began to appear in faint white lines; they grew brighter, and extended above and sometimes a little below the arch. Soon the rays became numerous, traversing the red arch in right lines, and converging to a point in the magnetic meridian somewhat south of the zenith. They sometimes extended as high as the zenith, and even beyond. The aurora continued, gradually fading, till day light.

42. Observations at Key West, Florida, (lat. 24° 33', long. 81° 48'), by WILLIAM C. DENNIS.

Sept. 2d, at 24 A. M. there were two patches of brilliant ruddy lights one in the N.E. and the other in the N.W. From the North extending 15° toward the E. there were rays of light shooting toward the zenith, the longest reaching full 60°. At 2h 50m the patch of light in the N.E. broke up into most brilliant rays extending toward the zenith. At 3 A. M. the patch of light in the N.W. also broke up into rays of light in a similar manner. At 3h 15m the rays gradually disappeared, but there still remained brilliant ruddy lights in the N.E. and N.W. At 3 A. M. the aurora was decidedly fainter, and at 4 A. M. nothing but a faint glow remained. This glow did not entirely disappear until overcome by the light of day.

43. Observations at Sea, (lat. 12° 23′ N., long. 88° 28' W.), by Commander W. D. PORTER, U. S. Navy.

Sept. 1st, about 11 P. M. the sky had a lurid appearance in the north, and there were occasional flashes of lightning. The rest of the sky was clear, bright and beautifully blue. The red appearance was very much like the aurora of high latitudes, and now and then it had a wavy appearance. About 1 A. M. a body of heavy clouds passed over with rain.

ART. XXXII.-On the direction of molecular motions in Plane Polarized Light; by Prof. W. H. C. BARTLETT.

Fresnel's Formulas for reflexion and ordinary refraction.

It is proposed, in the following paper, to deduce these formulas from the principle of the conservation of living force and the rules for the resolution and comparison of forces, without any hypothesis in regard to the condition of the ether in the co-terminous bodies. If this were the only object, however, the solution would hardly be worth the space asked for it in the Journal, because all now-a-days believe in the truth of these formulas. But there is a purpose beyond this. The mode of solution may settle the vexed question in regard to the direction of the molecular motions in plane polarized light; and, on this account, it will have an interest for those who are still in doubt upon the subject. There are few opinions among scientific men held more loosely than that which relates to this question. Some contend for vibrations in, and others perpendicular to, the plane of polarization; and a few of the most eminent and thorough investigators have entertained both opinions at different times,

AM. JOUR. SCI.-SECOND SERIES, Vol. XXX, No. 90.-NOV., 1860.

having changed not once but twice or thrice. Although Professor McCullogh has shown, in his elaborate treatise on crystalline reflexion and refraction, as published in the memoirs of the Royal Irish Academy, vol. xviii, that vibrations in the plane of polarization are absolutely essential to the theory, still other results are adduced which lean to the opposite view, and opinions are still divided.

When a wave of a given length is plane polarized, by a single reflexion, the plane which contains the incident and reflected rays, is called the plane of polarization. Are the molecular vibrations, which in this case are rectilinear, performed in this plane or at right angles to it?

Take the well known wave function, say the first of Equations (528), Bartlett's Analytical Mechanics, omitting the subscripts, x,

in which the molecular vibrations are parallel to the axis x, and the wave propagation in the direction of the plane yz, & the actual molecular displacement at the time t, a its maximum value, V, the velocity of wave propagation, & the wave length, and r the distance of the molecules place of rest from the origin.

Living force and quantity of motion in a plane polarized wave. Differentiate eq. (1), with respect to and t, we find :

Denote the density of the medium by ▲, and the area of any portion of the wave-front by a, then will the mass between two consecutive positions of this area be a.A.dr, and the living force within a quarter of a wave-length be:

V

Dividing by the volume a. V, and recalling that ¬ and are

constant, we shall find that the quantity of living force in a unit of volume of the medium will vary directly as the product of the density and square of the greatest displacement; and the relation of these products, in the case of any two waves, will determine the relation of the effects of these waves upon the organs of sense upon which they act.