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the wind, revolve with it, and thus be carried round all the points of the compass, still keeping the centre of the storm in the same relative position. But just as the sun seems to move round the earth, or the telegraph posts appear to fit by a railway carriage,

to any one on board the ship the wind would seem not, as it really is, to be blowing in a circular course, but rather in a straight line, and to be gradually but perpetually shifting through all the points of the compass from West to North, from North to East, and so on. Hence the change of direction which is in reality due to the motion of the ship through an arc of the circle is measured by the angle through which the wind has shifted (chap. xvi.,) and is called the “Shift of the Wind.” And it may be observed from diagram (3), that if a ship were to approach the centre, the wind would gradually shift aft, that is, she would “break off;" but if she were moving from the centre, the wind would shift forward, that is, she would “ come up." And this, of course, is as true when the centre approaches or recedes from the ship, as in the case of the ship's motion. Hence when it becomes advisable to heave-to in a cyclone, it is usual, in order to avoid the centre, to do so on the “coming up tack."

II. Next let us conceive the Axis of the storm to move along a curve, approximately, parabolic. Since this would appear to be the case from the generally ascertained tracks in the Indian Ocean, and other seas where they chiefly occur.

Now, of course, all that we have said with regard to the rotatory movement holds good still, when the axis moves also. There is, then, no difficulty whatever in ascertaining the position of the ship in regard to the cyclone; but there is, unfortunately, very considerable difficulty in ascertaining the position of the centre, or vortex, of the storm in regard to its own orbit. (3.) And this is the main point for anxiety. For upon this depends the momentous question whether the storm is approaching or moving away from the ship. For it will be observed that, since the velocity of the wind decreases as the distance from the centre increases, if she can be brought near the edge of the storm, the hurricane will have dwindled to a fresh breeze, of which she may reap the advantage, and thus literally ride upon

the wings of the whirlwind.” But if, on the contrary, the centre bear down upon her, the wind becomes more and more furious, and at the same time more fitful, until at last on reaching the centre itself it ceases altogether for a time, a dead calm succeeds, when the vessel rolls and plunges wildly in the sea with no wind to steady her, and then the storm catches her again with terrible violence from the diametrically opposite quarter, taking her dead aback, carrying away yards and masts, if they have escaped the fury of the wind and the rolling in the calm, and, perhaps, forcing her stern foremost beneath the waves.

For a description of the means by which endeavours are made to ascertain this momentous point I must refer the student to Piddington's work, and especially to his “ cards;" having, I fear, ventured somewhat out of my own depth already. Ne sutor ultra crepidam.

III. We proceed to the Cyclonoid, f and we repeat its definition.

A Cyclonoid is the locus of a point revolving around an axis which itself moves along a parabolic orbit. To find its equation, let us take the first point of the cyclonoid as the origin; and let OM = x, MP y be the co-ordinates of any point P in the cyclonoid (5.) Let OQ & QAY

be the co-ordinates of the moving centre, corresponding to the position of P.

Let OA = c be the length of the revolving radius.

Then A'P A'L = OA = C Let PA'L φ

(f)-In finding the equation to this curve, Ihave certainly outstepped the proper limits of the treatise, and it will not be intelligible to those who are not already acquainted with Analytical Geometry. But my excuse is that I hope it may prove interesting to those who are so.

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S

And &
= OQ

= OM + HA' = x + c cos. = x + c cos.

(v)

C

8

= MP

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2

n =
QA'

- PH

y c sin. $ = y c sin. (8) And since A'is a point on a parabola n2 4m (Ę — c)

(e) where m is a constant which determines the size of the parabola, and in the calculation of which lies the chief difficulty of which we spoke above. Hence, substituting from Equations (,) and (8) in (e) we have (y - c sin. :)* = 4m (+ c cos. -c) '

.

(5) And this is the transcendental equation to the cyclonoid. If the sine and cosine be expressed exponentially it will be found

of that (3) becomes a biquadratic equation, in terms of e(-)**;

) e which if p be a root,

s=(-)+c log. P
ds' =(-) odpa

(.)
But dx2 + dyr=.ds?

(x) .. p*dx + p*dy+ cdp = 0

(a)

=

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This last equation involves only functions of x and y, and is therefore the differential equation to the cyclonoid, from which the generating equation may be obtained by means of Integration.

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The curve itself

may be traced by means of equations (y) and (8.) For since & = 2 + c cos. and,

c sin. φ
c cos. and,

y = n + c sin.
Hence as & and n increase to infinity,

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8

=

if o

T

ks

(a.)

k Now s is the course, which may be calculated by observation, or by dead reckoning: and o or is the "shift" of the windconsequently it would appear that the distance of the ship from the centre or vortex (viz., the length c,) may be calculated in terms of the course and the shift.

k

The Charles Heddle appears to have traced out no less than five loops of a cyclonoid, modified, of course, by the resistance of the water. “This brig,” says the little Treatise on Circular Storms, to which reference has been made, “sailed from Mauritius in February, 1845, and falliag in with a revolving gale, she at once put her head up, in order, as it is commonly said, to “run out of it,' or to let it “ exhaust itself;' but the wind drew round and round according to the now known laws of these circular storms, and she, with a perseverance that might have been more wisely employed, continued to scud “right before it' for four successive nights and days, by which time she had actually circumnavigated the storm field five times.” In this case, o 107 = 10 X 22, and the distance run was found to be 1,300 miles.

Hence from equation (2)

1

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That is, the vortex was a little more than forty miles distant from the vessel. And thus the account goes on: “In performing this singular exploit, the ship had kept at the end of a radius of about forty miles, and had run through the water upwards of 1300 miles, though her real change of place, the joint result of the onward movement of the vortex and of the current (of wind, did not much exceed 500 miles.”

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