4. Name them ? Tropics of Cancer and Capricorn ; the arctic and antarctic circles; and the parallels of latitude. 5. How many great circles may be drawn on the earth ? There is no limit to the number. 6. Will these great circles cut each other ? Yes : every great circle will cut every other great circle in two points 180° apart. 7. What is the object of sailing on a great circle ? It is the shortest distance between any two places. 8. What is the peculiarity in sailing on a great circle ? That you have continually to change your course. 9. Could you not steer one course from one place to another ? Yes. 10. What line would your track then represent ? A rhumb line. a 11. What is a rhumb line ? One that cuts all the meridians at the same angle. 12. How could you find the courses and distances on a great circle, from A to B, by means of a terrestrial globe ? Turn the globe about till A and B touch the woodeh horizon ; then, with a pencil resting on this horizon as a ruler, draw a line from A to B; note the latitudes that it cuts the different meridians at; then mark on a Mercator's chart these latitudes and longitudes ; and so the courses and distance can be taken as wanted. 13. Do you know of any method for drawing the great circ.e on a Mercator's chart directly? Yes : Captain Ludvig Geerken's rule, improved by Professor Airey, is “1. Join the two places by a straight line ; find its middle ; draw thence & perpendicular to that line on the side next the equator, and, if necessary, continue it beyond the equator. “ 2. With the middle latitude between the two places enter the following table, and take out the corresponding parallel. “ 3. The centre of the required sweep will be the intersection of this parallel with the perpendicular." 14. By direct spherics. In the following figure explain the meaning of the different parts ; _shew the steps you would take in working a Great Circle Problem, and give the formula. E Q is a piece of the Equator; P is the Pole ; P C and PD two Meridians; A the ship's place; B the place we wish to reach ; hence, A B is the Great Circle track. A C is the latitude, and AP the co-latitude of the place A. B. CD, or the angle A PB, is the difference of longitude between A and B. V is the vertex, or the greatest latitude the track passes through. Therefore, P V is the co-latitude of vertex, and AP V is the longitude from vertex of the ship at starting. р is any point on the circle whose longitude from vertex is known, and P p is the co-latitude of this point. 1st.—To find the angle A, or the 1st course on the great circle. Tan. 1 (A+B)=Cos. } (a−b)x Sec. } (a+b)x Cot. 1 P. Tan. (A-B)=sine (amb) x Cosec. (a+b)x Cot. P. Then, if a is greater than b, add these two results together for the angle A ; but if a is smaller than b, subtract the less result from the greater for A. 2nd.-To find the distance (A B) on the great circle. Sine A B Sine P Sine B P=Sine A or log sine of the dist.= log. sine diff. long. +log. sine co-lat. of B+log. cosec. of A. a 3rd.-To find the latitude of vertex. Sine P V=Sine A Px Sine A or, log. cos. of lat. of V=log. sine co-lat. of A+log. sine of the 1st course 4tb.-To find the longitude of vertex from A. Cos. A PV=Cot. A Px Tan P V. or log. cos. of long. from A= log. cot. of co-lat. of A+log. tan. of co-lat. of vertex. Then apply this long. to the long. of A, and we get the longitude of vertex. 5th.—Next take a series of points (p) say each 5o from vertex, both ways, then the 1st point will be 5o from vertex, the next 10° from vertex, the next 15° from vertex, and so on. Then, if we find the latitudes of these points, we shall have both their latitudes and longitudes, and then we can find the course and distance from A to the next point, and from point to point, by Mercator's sailing. To find the latitude of the point p. Cos. p P V=Cot. p PxTan. P V. P PV or, log. tan. of lat. of point= log. cos. of its long. from vertex +log. cot. of co-lat. of vertex. 15. Name any advantage in sweeping a great circle track on a chart ? I can see if it will take the ship into too high a latitude, or on to land ; and if I have to keep for a long time on one tack, and so lose the track, I can see which way to head her to recover the track. At some Ports the theory of the Sextant and of the Vernier are also required. APPENDIX A. LLOYD'S RULES FOR THE STOWAGE OF MIXED CARGOES, Prepared by HENRY C. CHAPMAN & Co., Agents for Lloyd's, Liverpool. 1.-Owners, Commanders, and Mates of ships, are considered in law in the same situation as common carriers ; it is therefore necessary that all due precautions be taken to receive and stow cargoes in good order, and deliver the same in like good order. The law holds the shipowner liable for the safe custody of the goods when properly and legally received on board in good order, and for the delivery " to parties producing the bill of lading. The Captain's blank bill of lading should be receipted by the warehouse keeper, or person authorised to receive the contents. Goods are not unfrequently sent alongside in a damaged state, and letters of indemnity given to the captain by the shippers for signing in good order and condition; this is neither more nor less than conniving at fraud. Fine goods are also often damaged in the ship's hold by lumpers, if permitted to use cotton hooks in handling bales. All goods must be received on board according to the custom of the port where the cargo is to be taken in ; and the same custom will regulate the commence : ment of the responsibility of the master and owners. 2.--Hemp, flax, wool, and cotton should be dunnaged 9 inches on the floors, and to the upper part of the bilge; the wing bales of the second tier kept 6 inches off the side at the lower corner, and 21 inches at the sides. Sand or damp grayel ballast to be covered with boards. Pumps to be frequently sounded and attended to. Sharp-bottomed ships one-third less dunnage in floor and bilges. Avoid horn shavings as dunnage from Calcutta. 3.-All corn, wheat, rice, peas, beans, &c. when in bulk, to be stowed on a good high platform, or dunnage wood, of uot less than 10 inches ; and in the bilges, 14 inches dunnage. The pumps and masts encased, to have strong bulk heads, good shifting boards, with feeders, and ventilators, and to have no admixture of other goods. Flat-floored wall-sided ships should be fitted with bilge pumps. Un no On |