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FOURTH MEETING.

ROYAL INSTITUTION, November 28, 1853.

J. B. YATES, Esq., F.S.A., VICE-PRESIDENT, in the chair Mr. THOMAS CROXON ARCHER was ballotted for, and duly electe Ordinary Member.

Mr. J. B. YATES read extracts from a paper, on the "Palatin Jurisdiction of the City of Chester," with a Memorial of the Life Character of Edward, third Earl of Derby.

Mr. J. T. TowSON read the first part of a paper on "Great Circ Sailing."

FIFTH MEETING.

ROYAL INSTITUTION.-December 12, 1853.

J. B. YATES, Esq., F.S.A., VICE-PRESIDENT, in the Chair.

The Rev. JAMES PORTER, B.A., Mr. THOMAS MCNICHOLL, Mr. JOSEPH GODDEN, and Mr. JOHN KEATES, were ballotted for, and duly elected Ordinary Members.

Mr. J. T. Towson concluded his paper on

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GREAT CIRCLE SAILING.

GREAT CIRCLE SAILING is the art of navigating a ship by the shortest possible route. A straight line is absolutely the shortest track between any two points; but a straight line cannot be projected on the surface of a globe. It must either touch it at one point, passing off from the surface as a tangent; or, if two points on such a surface be united by a straight line, it must be effected by tunnelling below the surface; the straight line in this last case being the chord of the arc between the two points. Since then we cannot sail over the surface of the ocean in a straight line, let us inquire what route is practicable, which differs less than any other from a straight line. This we shall find to be what we denominate the arc of a great circle. If we slightly bend a straight rod

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into a circular form, we shall find it to be the arc of a large circle. If we bend it more into the form of an arc, we find that it becomes the part of a smaller circle, and the more we bend it into a circular form, the smaller will be the radius of the circle with which it will correspond. Thus we find that the larger circle deviates less from a straight line than the arc of any of smaller radius; so that, if the mariner sails over the ocean by the route of an arc of the largest circle that can be drawn on the surface of the globe, he may be said to sail directly to this port. We may draw an unlimited number of circles on the surface of a globe, each varying in its diameter; but we cannot draw a circle on such a surface, the radius of which is greater than that of the globe; the arc of a circle, the radius of which is equal to that of the globe, is what we call the arc of a great circle. The arc of any larger circle than that of a great circle, will, as is the case with a straight line, be a tangent to the globe, touching at one point only. A great circle may also be distinguished from any other circle drawn on the surface of a globe by its dividing the surface into two equal parts; thus, the equator is a great circle, dividing the surface of the earth into two equal areas, called the northern and southern hemispheres. But the tropics are not great circles, and we consequently find that each divides the earth into unequal parts. Thus, north of the Tropic of Cancer we have 66° of latitude, whilst south there are 11310. On the north of the Tropic of Cancer we have a temperate and a frigid zone; on the south we have three zones—a temperate, a frigid, and a torrid zone. There is also a practical method of determining whether any arc on the surface of a globe be the arc of a great circle. If we hold a piece of string tightly by its ends, and press it down on the surface of the globe, it will describe the arc of a great circle; and this method of projecting the arc of a great circle at once, is also a proof that a great circle is the shortest possible track over the surface of a globe. The carpenter draws his straight line on a plane by a chalk-line. The principle is this-he employs a tension which draws the line as short as the points to which the ends are fastened will allow. Now, since a straight line is the shortest track on a plane, he produces a straight line by this means; but, when we stretch the line over the surface of a sphere, the rotundity of the surface bends the line from a straight into a circular form; but, since it deviates as little as possible from the straight line, it forms the arc of a great circle, such being the shortest track across the surface of a globe. There are, however, other circles connected with the science of navigation, besides great circles. The parallels of latitude are circles lessening in their diameters as we approach either

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