-90' sin 48 Arc Kq = --------------- = -1 6' 46?.

R

Arc AR = 28 57' 3?

RK = - 0 39' 13?

Kq = - 1 6' 46?

Sum = 26 51' 4? = corrected arc AQ.

We have now the necessary elements in the Nautical Almanac, which we must reduce for the instant of the vortex pa.s.sing the meridian in Greenwich time.

July 2d.

Meridian pa.s.sage, local time, at 9h. 5m. A.M.

" in Greenwich time 2d. 3h. 1m.

Right ascension same time 56 42' 45?

Declination north " 18 00 1 Obliquity of the vortex " 26 2 32 Polar angle " 18 5 7 Arc AQ " 26 51 4

[Ill.u.s.tration: Fig. 14]

PA = 17 59' 59? } P = 128 37' 38?

PV = 26 2 32 } VA = 89 3 0 V = 47 59 44 VQ = 62 11 56 A = 20 3 42 PQ = 47 14 22 Q = 26 22 55 Lat.i.tude of Q on the sphere = 42 45' 38?

CORRECTION FOR PROTUBERANCE.

We have hitherto considered the earth a perfect sphere with a diameter of 7,900 miles. It is convenient to regard it thus, and afterwards make the correction for protuberance. We will now indicate the process for obtaining this correction by the aid of the following diagram.

[Ill.u.s.tration: Fig. 15]

Let B bisect the chord ZZ'. Then, by geometry, the angle FQY is equal to the angle BTF, and the protuberance FY is equal the sine of that angle, making QF radius. This angle, made by the axis of the vortex and the surface of the sphere, is commonly between 30 and 40, according as the moon is near her apogee or perigee; and the correction will be greatest when the angle is least, as at the apogee. At the equator, the whole protuberance of the earth is about 13 miles. Multiply this by the cosine of the angle and divide by the sine, and we shall get the value of the arc QY for the equator. For the smallest angle, when the correction is a maximum, this correction will be about 20' of lat.i.tude at the equator; for other lat.i.tudes it is diminished as the squares of the cosines of the lat.i.tude. Then add this amount to the lat.i.tude EQ, equal the lat.i.tude EY. This, however, is only correct when the axis of the vortex is in the same plane as the axis of the earth; it is, therefore, subject to a minus correction, which can be found by saying, as radius to cosine of obliquity so is the correction to a fourth--the difference of these corrections is the maximum minus correction, and needs reducing in the ratio of radius to the cosine of the angle of the moon's distance from the node; but as it can only amount to about 2' at a maximum under the most favorable circ.u.mstances, it is not necessary to notice it. The correction previously noticed is on the supposition that the earth is like a sphere having TF for radius; as it is a spheroid, we must correct again. From the evolute, draw the line SF, and parallel to it, draw TW; then EW is the lat.i.tude of the point F on the surface of the spheroid.

This second correction is also a plus correction, subject to the same error as the first on account of the obliquity, its maximum value for an angle of 30 is about 6', and is greatest in lat.i.tude 45; for other lat.i.tudes, it is equal {6' sin(double the lat.)}/R.

The three princ.i.p.al corrections for protuberance may be _estimated_ from the following table, calculated for every 15 of lat.i.tude for an angle of 30, or when the correction is greatest.

Lat.i.tude. 1st Corr. 2d Corr. 3d Corr.

0 + 20' + 0 - 2 15 + 19 + 3 - 1.5 30 + 15 + 5 - 1.5 45 + 10 + 6 - 1.

60 + 5 + 5 - 1 70 + 1 + 3 - 0.5

We can now apply this correction to the lat.i.tude of the vortex just found:

Lat.i.tude on the sphere 42 45' 38? n.

Correction for protuberance + 14 22 ---------- Correct lat.i.tude 43 00 00

MILWAUKIE STORM, JULY 2.

As this example was calculated about ten days before the actual date, we have appended an extract from the Milwaukie papers, which is in the same longitude as Ottawa, in which place the calculation was made. It is needless to remark that the lat.i.tude of Milwaukie corresponds to the calculated lat.i.tude of the centre of the vortex. It is not intended, however, to convey the idea that the central line is always the most subject to the greatest violence--a storm may have several centres or nuclei of disturbance, which are frequently waning and reviving as the storm progresses. Generally speaking, however, the greatest action is developed along the line previously pa.s.sed over by the axis of the vortex.

"SUMMIT, Waukesha Co., Wis., July 4, 1853.

"Our town, on Sat.u.r.day, the 2d, was visited by a terrible storm, which will long be remembered by those who witnessed its effects and suffered from its fury. It arose in the south-west, and came scowling in blackness, sufficient to indicate its anger, for the s.p.a.ce of eighty or a hundred rods in _width_, covering our usually quiet village; and for nearly half an hour's duration, the rain fell in torrents, the heavens blazed with the lightning's flashes, trees fell and were uprooted by the fury of the blast, fragments of gates and of buildings, shingles, roof-boards, rafters, circled through the air, the playthings of the wind--and buildings themselves were moved entire from their foundations, and deposited at different distances from their original positions. A barn, fifty-five feet square on the ground, owned by Mr. B. R. Hinckley, is moved from its position some ten feet to the eastward; and a house, some fifteen by eighteen feet on the ground, owned by the same person, fronting the east, was driven by the wind to the opposite side of the street, and now fronts nearly west; and what is most strange, is that the gra.s.s, in the route the house must have pa.s.sed over, stands straight as usual, and gives no evidence that the building was pushed along on the ground. A lady running from a house unroofed by the storm, took an aerial flight over two fences, and finally caught against a tree, which arrested her pa.s.sage for a moment only, when, giving way, she renewed her journey for a few rods, and was set down unhurt in Mr. O. Reed's wheat field, where, clinging to the growing grain, she remained till the gale went by."[11]

The weather at this place is briefly recorded in the accompanying abstract from the journal, as well as in an extract from a note to Professor Henry, of the Smithsonian Inst.i.tution, from a friend of the authors, who has long occupied a high official station in Illinois. But such coincidences are of no value in deciding on the merits of such a theory, it must be tried before the tribunal of the world, and applied to phenomena in other countries with success, before its merits can be fully appreciated. The accompanying record, therefore, is only given to show how these vortices render themselves apparent, and what ought to be observed, and also to exhibit the order of their recurrence and their positions at a given time.

_Extract of a note addressed to the Secretary of the Smithsonian Inst.i.tution, by Hon. John Dean Caton, on this subject._

"As a striking instance of the remarkable coincidences confirmatory of these calculations, I will state, that on Friday, the first of July last, this gentleman[12] stated that on the next day a storm would pa.s.s north of us, being central a little south of Milwaukie, and that he thought, from the state of the atmosphere, the storm would be severe, and that its greatest violence would be felt on the afternoon or night of the next day. At this time the weather was fine, without any indications of a storm, so far as I could judge.

At noon on the following day he pointed out the indications of a storm at the north and north-west, consisting of a dark, hazy belt in that direction, extending up a few degrees above the horizon, although so indistinct as to have escaped my observation. At five o'clock a violent storm visited us, which lasted half an hour, although a clear sky was visible at the south the whole time. On Monday morning I learned, from the telegraph office at Chicago, that early on Sat.u.r.day afternoon communication with Milwaukie had been interrupted by atmospheric electricity, and that the line had been broken by a storm."

NEW YORK STORM.

After this was written, the author discovered that the vortex was equally violent the day before at New York, July 1st, 1853. An account of this storm follows. The calculation has not been made, but it is easy to perceive that the lat.i.tude of the vortex, on July 1st, must be very nearly that of New York--being in lat.i.tude 43 next day and ascending.

"At a meeting of the American a.s.sociation, convened at Cleveland, Professor Loomis presented a long notice of the terrible hail storm in New York on the 1st of July. He traced its course, and minutely examined all the phenomena relating to it, from a mile and a half south-east of Paterson, N.J., to the east side of Long Island, where it appeared nearly to have spent its force. It pa.s.sed over the village of Aqueenac, striking the Island of New York in the vicinity of the Crystal Palace.

It was not much more than half a mile wide. The size of the hail-stones was almost incredibly large, many of them being as large as a hen's egg, and the Professor saw several which he thought as large as his fist.

Some of them weighed nearly half a pound. The princ.i.p.al facts in relation to this storm were published at the time, and need not be repeated. The discussions arising among the members as to the origin and the size of these hail-stones, and the phenomena of the storm, were exceedingly interesting. They were partic.i.p.ated in by Professors Heustus and Hosford, of Cambridge University, Professor Loomis, and Professors Bache and Redfield. The latter two gentlemen differ somewhat, we should suppose radically, in their meteorological theories, and had some very sharp but very pleasant "shooting" between them."[13]

CENTRAL VORTEX DESCENDING.

We will now make the calculation for the central vortex _descending_, for longitude 88 50' west, August 7, 1853,--putting down the necessary elements for the time of the meridian pa.s.sage in order:

Meridian pa.s.sage in local time at 2h. 25m. P.M.

" " in Greenwich time 7d. 8h. 18m.

Ma.s.s of the moon 1/12.3 M. R. V. minor 3,256 miles.

Obliquity of the vortex, same time 26 5' 0?

Polar angle of " " 17 41 47 True longitude of moon's node " 78 42 0 " inclination of orbit " 5 5 0 " longitude of the sun " 135 20 0 Moon's longitude " 169 44 0 " distance from node " 91 2 0 " distance from quadrature " 55 36 0 " true semi-diameter " 943 " right ascension " 172 30 0 " declination north " 8 42 20 Constant logarithm 2.889214 Arith. comp. of log. of 943 7.025488 Log. cos. arc. AR 9.914702 = 34 44' 48?

1st. correction, + 2 45 0 2d. correction, - 1 14 15 -------------- Corrected arc AQ = 36 15 33 PA = 81 17' 40?

PV = 26 5 0 P = 115 11 47 V = 63 34 26 A = 23 28 24 AV = 92 48 39 Q = 31 32 18 Complement of lat. = PQ = 48 49' 41?

The lat.i.tude is therefore for the earth, as a sphere 41 10 18 Correction for protuberance + 0 16 0 ------------ True lat.i.tude of centre 41 26 18 north.

------------ Lat.i.tude of Ottowa 41 20 0 "

------------ Vortex pa.s.sed 6 18 north of Ottowa.

[Ill.u.s.tration: Fig. 16]

As this was nearly a central pa.s.sage, and as the influence was less extensive than usual, on account of great atmospheric pressure with a low dew point, the central disturbance could the more readily be located, and was certainly to the north, and but a few miles. The following is from the record of the weather:

_August_ 6th. Very fine and clear all day; wind from S.-W.; a light breeze; 8 P.M. frequent flashes of lightning in the northern sky; 10 P.M. a _low bank of dense clouds in north_, fringed with cirri, visible during the flash of the lightning; 12 P.M. same continues.

7th. Very line and clear morning; wind S.-W. moderate; noon, clouds acc.u.mulating in the northern half of the sky; wind fresher S.-W.; 3 P.M.

a clap of thunder overhead, and black c.u.muli in west, north, and east; 4 P.M. much thunder, and scattered showers; six miles west rained very heavily; 6 P.M. the heavy clouds pa.s.sing over to the south; 10 P.M.

clear again in north.

_August_ 8th. Clear all day; wind the same (S.-W.); a hazy bank visible all along on _southern horizon_.

This was not a storm, in the ordinary acceptation of the term; but the same cause, under other circ.u.mstances, would have produced one; and let it be borne in mind, that although the moon is the chief disturbing cause, and the pa.s.sages of the vortices are the periods of greatest commotion in both settled and unsettled weather, still the sun is powerful in predisposing the circ.u.mstances, whether favorable or unfavorable; and as there is no periodic connection between the pa.s.sage of a vortex and the concurrence of the great atmospheric waves, it will, of course, happen only occasionally that all the circ.u.mstances will conspire to make a storm. There are also other modifying causes, to which we have not yet alluded, which influence the storms at different seasons of the year,--exaggerating their activity in some lat.i.tudes, and diminishing it in other lat.i.tudes. In this lat.i.tude, the months of May, June, and July are marked by more energetic action than August, September, and October. The activity of one vortex also, in one place, seems to modify the activity of another vortex in another place. But the great question to decide is: Do these vortices really exist? Do they follow each other in the _order_ indicated by the theory? Do they pa.s.s from south to north, and from north to south, at the _times_ indicated by the theory? Do they obey, in their monthly revolutions, a mathematical law connecting them with the motions of the moon? We answer emphatically, Yes! And the non-discovery of these facts, is one of the most humiliating features of the present age.

OTTOWA STORM, DECEMBER 22, 1852.