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projectile force, would carry a projectile upwards from the surface of the sphere. For this is known by observation to be the case in the earth's atmosphere. The height of the lower half is about 3 miles, or more nearly 3.4 miles. The velocity which would carry a projectile to twice this height, in vacuo, from the surface, is 1,510 feet per second. The mean' molecular velocity of the mixed nitrogen and oxygen of the air is 1,510 feet at -22° F.

The mean temperature of the first 6.8 miles of the atmosphere, as a whole, is probably not quite so low as -22°, but it cannot be very much higher. At the same time the molecular velocity of the air is somewhat less than that of its nitrogen and oxygen, from the presence of carbonic acid, which is heavier, and of aqueous vapour, which is an imperfect gas. Allowing for this, the approximation to the velocity of 1,510 feet is so close, that we can hardly doubt their practical identity.

The relation between these heights must also hold good, whatever the gas may be, and in the case of any attracting sphere.

For the height of the half atmosphere, the square of the molecular velocity at the same temperature, and therefore the projectile height, are all of them inversely as the relative weight of the gas composing the atmosphere. And if the force of gravity varies, the height of the half atmosphere is inversely as the pressure, and therefore as the force of gravity; and so is the projectile height near the surface. And if the temperature varies, the height of the half atmosphere and the square of the molecular velocity both vary directly as the absolute temperature.

The height of the upper half of the atmosphere is not subject to the same laws, but practically it must always be nearly the same multiple of the lower half. Whatever the height of the lower half may be, the density is reduced to

about one-billionth at about forty times this height, and an atmosphere of any density consistent with the constitution of a gas is practically at an end when reduced to this extent. The decrease of gravity in ascending need hardly be considered.

It seems possible, therefore, to state concisely a general law of atmospheres, depending on the relative weight of the gas, the force of gravity, and the temperature. The relative weight and the temperature determine the molecular velocity. The velocity and the force of gravity determine the projectile height. Half this height is the depth of the lower half atmosphere, and forty times this depth is the limit beyond which there can be no atmosphere of an appreciable kind.

Some curious results appear to follow. At ordinary temperatures, no atmosphere of oxygen or nitrogen can be so much as one hundred and forty miles high on any planet larger than the earth. On Jupiter, where gravity is 24 times as great, such an atmosphere could not be appreciable at a greater height above the surface than sixty miles.

An atmosphere of hydrogen on Jupiter might be appreciable at a height of nine hundred miles if in sufficient quantity. But if there is any gas whose relative weight is to hydrogen as that of hydrogen to air, Jupiter might have an atmosphere of it thirteen thousand miles deep; and he could hold a gas of this kind, for its mean molecular velocity at the freezing point would be about four miles per second, while thirty-three miles per second would be necessary to carry it away from him. Such a gas could not remain on the earth, and its absence here does not therefore entitle us to say that it has no existence. Many things connected with the physics of the larger bodies point to the probable presence in the universe of some materials far lighter than anything we are acquainted with. If they exist, it is on the larger bodies only that they can be found, since they could not be retained by the smaller ones.

THE TRAINING OF SAILORS AND EXPLORERS. BY CLEMENTS R. MARKHAM, C.B.

THE nations which, during the last four centuries, have taken part in discovery and geographical research, have all been impressed with the necessity for instructing their explorers by land and sea in all such knowledge as would best enable them to perform the service entrusted to them with efficiency. There seems to be no such impression in England at the present day among many of those whom it most concerns. The Spaniards, Portuguese, Dutch, and our own ancestors felt that their ships would not be safe on long voyages, that their travellers and maritime adventurers would make their journeys and voyages without bringing back any useful results, unless instruction was provided in all the knowledge that could be of service to them. It was found that in proportion as attention was given to the training and instructing of sailors and travellers by land, voyages and adventures were more profitable and discoveries were more successful and important.

Moreover, the instructed explorers, in numerous instances, improved upon the education they had received by bringing their acquired experience to bear upon it; while ignorant mariners returned as they went, without in any way increasing the general stock of knowledge. Such was the view taken by our ancestors, and it was this consideration which led to the efforts they made to supply the means of instruction.

I propose, in the remarks I shall submit to the Institute on this subject, to refer to the system of instruction adopted by Spain, and her Council of the Indies, when in the height of her greatness as a discovering nation, and to pass briefly

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in review her writers on navigation and surveying; and I think it will be seen that Spain's maritime greatness could, in the opinion of her rulers, be maintained only by keeping up the standard of knowledge among her sailors and explorers. In Holland, experience taught the same lesson. When our own country began to enter upon her glorious career of discovery and maritime adventure, the absolute. necessity for educating and thoroughly training our explorers was immediately felt. At first we sought for aid from Spain, and strove to take example from her in this respect. But soon our own trained seamen began to improve upon old methods, while our mathematicians provided books and instruction for their guidance. I will dwell upon these early efforts and upon their results; and I will endeavour to establish to your satisfaction the fact that our maritime greatness, in former days, was due to the care taken by our ancestors to supply instruction to our adventurers, and to the way in which the ablest and best among them profited by the advantages thus received. The conclusion will then, I believe, be inevitable that the same causes would now produce the same effects, and that if, in proportion to our increased wealth and population, equally good means of instruction are not provided, and equal importance is not attached to the subject, a mistake is being made. Finally, I will lay before you the existing provision for supplying the required instruction in Great Britain, as compared with the systems adopted in some other countries; and I will ask you to form your own conclusion as to whether some improvement is not very urgently needed here.

In the very dawn of the history of maritime discovery, there is a remarkable example of the value of careful training in enabling an explorer to improve upon the instruction he has received, and to make his theoretical learning bear useful practical fruit. In the fifteenth century there lived at

Nuremburg the most learned mathematician of his age. John Müller, better known as Regiomontanus, published a work on plane and spherical triangles with tables of sines, completed the translation of Ptolemy's "Almagest," invented several astronomical instruments, and published the first almanac. Among the pupils of Regiomontanus was a young Nuremburger, named Martin Behaim, who studied to such good purpose that, when he entered upon the life of a merchant adventurer in 1479, and went to Portugal, he was a skilful mathematician and cosmographer. He was a man of action and a good practical seaman. He accompanied Diogo Cam on his voyage along the coast of Africa to the mouth of the Congo in 1484. On his return he received the order of Christ from the King of Portugal, won the hand of a daughter of Jobst von Hurter-a nobleman of Bruges who had settled in the Azores, and passed the remainder of his life on those islands, making occasional visits to Lisbon. When he died, in 1506, he left behind him a number of charts, and the famous globe, now at Nuremburg, which is the most ancient in existence. Martin Behaim had learnt the use of the astrolabe from Regiomontanus. It was this theoretical training which enabled him, after having acquired practical experience, so to apply his knowledge as to produce a useful invention. Behaim adapted the astrolabe to the uses of navigation in 1480, and thus supplied to mariners that instrument for taking the altitude of the sun which guided Vasco da Gama in rounding the Cape, and Magellan in circumnavigating the globe. This illustrious Nuremburger was one of the first explorers who used his practical experience to improve upon his theoretical education. Both were necessary. Without having been well grounded in all existing knowledge, his experience would have availed him little. Without experience he could not have usefully applied his knowledge. It was the combination of knowledge and

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