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 latitude at the equator; for other latitudes it is diminished as the squares of the cosines of the latitude. Then add this amount to the latitude EQ, equal the latitude 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 circumstances, 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 latitude 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 latitude 45°; for other latitudes, it is equal
The three principal corrections for protuberance may be estimated from the following table, calculated for every 15° of latitude for an angle of 30°, or when the correction is greatest.
| Latitude. | 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 latitude of the vortex just found:
| Latitude on the sphere | 42° | 45′ | 38″ | n. |
| Correction for protuberance | + | 14′ | 22″ | |
| Correct latitude | 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 latitude of Milwaukie corresponds to the calculated latitude 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 passed over by the axis of the vortex.
“Summit, Waukesha Co., Wis., July 4, 1853.
“Our town, on Saturday, 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 space 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 grass, in the route the house must have passed 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 aërial flight over two fences, and finally caught against a tree, which arrested her passage 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]