divided by the number of confluxes and refluxes in an intire ofcillation, or 18. 642

2

172 years, the time nearly at the equator, but decreases towards the poles. But the radius of curvature will be principally affected by the obliquity of the nodes, with the obliquity of the obliquity of the ecliptic. The greater limit of the moon's nodes, when in the fyzigias is 5° 17′ 20", and the Jeffer, when in the quadratures is 4° 59′ 35′′ difference 17′ 45′′, which muft be added to the obliquity of the ecliptic 23° 30' 23° 47′ 45′′ for the angle of direction of the conflux and reflux of the pyrogeneric principle on the earth's axis. But its power to alter the curve will be as the motion on the equator to that in the orbit, about 1 to 25. Whence to find the greater and lefs limit in any latitude, firft find the angle of the axes as before, then let P. (fig. 82) be the earth's axis, Co the axis of direction of the pyrogeneric principle from the motion of the earth in its orbit 23° 47′ 45′′ the angle POA the pyrotic angle, which in lat. 50° is 24° 24′ as before found. From O to b fet 1, and from 0 to 25, complete the parallelogram in a and draw E O, then will the angle IOP 22° 30' be the leaft limit. From b to e fet 25, and from e to d parallel to bo fet 1, then will L Po F 28° be the greater limit from whence the time must be taken. The ofcillation will fometimes be made in the leffer, but more commonly in the greater, which expreffes the confluxing curve as the leffer does the refluxing one.

To reprefent the pyrotic curve on a plane, let A Bo R (fig. 83) be the equator, P the pole, A B the direction of the pyrotic fluid, the LBA 0= 23° 47′ make o R to PO as the centrifugal to the centripetal force at the equator, then will the arches 1, 2, 3, 4, &c. reprefent the centrifugal force in the feveral parallels of latitude through the points a, b, c, d, &c. in each of the parallels, draw lines parallel to A B, and make at each the angle aeb to the angle bec as 25 to 58, then will the curve P, a, b, c, d, e, g, h, i, l, represent the courfe of the pyrotic current from the pole to the equator, during the revolution of the earth on its axis and motion during that time in its orbit. Here it must be observed, that this curve cannot be well expreffed in plano, as it inclines from the centre of each parallel to the equator. When arrived at the vertex the agitation decreafes, and the curve reflects back in the direction / QP and the curves P10, P 20, &c reprefent under the fame angles to ever 40 of the equator; and are continued equally to the fouth pole, but what is the direction weftward in one will be eastward in the other, and vice verfa. Allo the conflux

will decrease the angle of inclination and the reflux increase it.

It has been obferved, that the direction of the pyrotic curve is not parallel to the plane of the equator, much lefs fo to that of the horizon, but which will be ufeful to know on feveral occafions. In refpect to the horizon, it is always equal to an angle formed by a line drawn from the pole through the vertex of the place and plane of the horizon.

In order to find this angle, let EQ reprefent the equatorial diameter of the earth, and PC (fig. 84) the femi-polar axis, the arch Pm E, the direction of the curve drn direct from the equator to the pole, which fection in this cafe will refemble the elliptic curve, Z the zenith of any place of given latitude, HO the horizon, the fine, and x C the co fine of the latitude; then will m be the` -latitude on the earths' furface, from Z draw the circular tangent z T and parallel to HOC, and alfo to m draw the tangent Tm. Perpendicular to Tm draw mp, and perpendicular thereto mp, the radius of curvature in the point m. Then will the L & T m be equal to the Lpm C, the angle which the curve makes in that place with the plane of the horizon. Draw nr a parallel C and equal

equal to C. Put CE=a, CP=b, zx=x, x Cy. Then per nature

ay + xb: ax - x

b ::

• xb: 2 a2 y x + a by x — a b x2 + x2 b2

2 a2+zabx

Whence when x is equal to a, y =

wherefore by fim. A's as x: a ::

mC and x: y ::

in the triangle pm C

by trig. as mĈr

zay x + 2 bxy

2ay

we fhall have

2 ay x + 2 bx y

za2y x + 2 by xa

2axy

= % 11.

a2

a

b = PS.

a

2bay-bax

=zm..

2 ay-bx

bx2

are given the fides m C and p C to find the L m. pbx Lpm C the angle of the declination required. But b, nm or p C whence at the poles and equator the declination is nothing, the direction of the curve in thefe points being parallel to the horizon when the nodes are in the quadratures and fyzigias.

when xa or y=

The abore theory, if the earth was homogeneous in every part and affected by no other bodies than the fun and moon, would be nearly correct; but from the different densities and fpecies of matter which the earth is compofed of, and the state of the pyrogeneric principle in the feveral parts, no theoretical calculation can exactly agree with obfervation, and both the angle of pofition and time, will be beft afcertained from obfervation. For befides the actions of the nodes of the earth and moon, those of the other planets will have fome effect, as alfo the elliptic figure of the earth, and the state of the atmosphere and nature of the soil, at the place of observation.

Notwithstanding, however, thefe irregularities, the general tencr of the curve will follow the theory, and is the cause, either immediate or remote, of a number of curious phenomena and operations in nature. By the agitation of the pyrogeneric principle, the production of the animal and vegetable creation is brought forth. By its motion and direction, hail, rain, winds, ftorms and most other operations of nature in the atmosphere are effected. By it the effects of electricity are produced. By the conflux and reflux of this principle the aurora borealis and a number of other meteors are formed. But what ftill more renders it worthy the attention of mankind is, that the conflux, reflux and direction of the pyrotic curve, is the immediate caufe of the power of magnetism and the variation of the magnetic needle. To the investigation of which curious and ufeful fubject of natural philosophy, we shall proceed in our next.

MENTOR.

A PHYSICO-MATHEMATICAL PROBLEM.

S

By DR. MICHAEL O'RIORDAN, MATHEMATICIAN,

CARLOW.

UPPOSE the centripetal force was changed from the fquare to the cube of the distance inverfly, let the earth's radius be 3985 miles, and 16 feet the defcent of heavy bodies on its furface in one fecond of time; if now a body, whose distance from the earth's centre (which I fuppofe at reft) is equal to four times its radius, be projected in the direction of a right line making an angle of 60° with a line drawn from the centre of the earth with a velocity fufficient to cause it to move uniformly through 80 miles in one minute; 'tis required to find in what time the body will perform one gyration, and what will then be its dif

tance from the center?

ANOTHER CURIOUS PHYSICAL PROBLEM.

BY THE SAME.

SUPPOSE the velocity of the tide to be as the time of its flowing for the first four hours; and that it fets a body over the space of fixteen miles in that time. Now admit a fhip fets out just as the tide begins to flow, and fails perpendicular to the direction thereof uniformly at the rate of fix miles an hour by the log; one hour after a fecond fhip fets out from the fame place, keeps continually bearing on the firft, and comes up with her in three hours chace. Required the length of both fhips curves, with the rate of the fecond fhip's failing by the log, fuppofing it also uniform, and that the tide begins to flow every where at the fame time, fo far as it affects the ships.

POETRY.

IF you think, on perufal, the following lines worthy a place in your Magazine, by inferting them you'll oblige a conftant reader.