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(Abstract.)
In nature, all forces tend towards certain points, or “centres of force,” these centres being the affected particles themselves. These attractive forces are found to depend principally on the mutual distances apart of the particles; and the nature of this dependence on the distance is denominated the law of force.
The particular “law of force” by which a moving body is actuated may be ascertained from the nature of the curve in which it moves, and this last is a matter to be determined by observation.
When two material particles move in obedience to their mutual attractions, whatever the law of force may be, it may be shown that (1) they move in a plane which is invariable, (2) their common centre of gravity moves with uniform velocity in a straight line (this velocity may be zero), and (3) the lines joining the bodies and their common centre of gravity sweeps out equal areas in equal times. But, in the case of more than two bodies in motion attracting each other, it is generally found that neither moves continually in the same orbit, but is disturbed by the attraction of the others, and compelled to vary its course considerably.
This is the case in the solar system. Neither the earth nor any of the other planets move in fixed orbits, but are continually perturbed in their motions, but certain peculiarities in its present constitution effectually prevent any injury to its stability.
The particular law of force proposed for consideration by the author, is that each particle attracts proportionally to its mass and distance from the attracted particle. It is shown that the members of a system of material particles actuated by this law would move in permanent undisturbed orbits, that is, there would be no perturbation. The orbits would be ellipses, relatively to the principal heavy central body which would be in the common centre of the ellipses, and the mean angular motions would be all equal, that is, all would complete their revolutions in equal times.
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2. “On the Mechanics and Mechanical Economy of Railways,” by G. M. Barr. (See Transactions.)
Mr. Bathgate, in opposition to the views enunciated in this paper, advocated the construction of narrow gauge railways, lightly built, and adapted to the natural features and sufficient for the traffic of this country; not a system of wide gauge railways, with deep cuttings and tunnels, and heavy rolling stock.
Mr. Blair said that the estimates of the Clutha line compared favourably with the light lines which had been constructed in Queens- land. The estimate of the proposed line was £15,000 more than the average cost of the same length of the narrow gauge line in Queensland and the difference was, he considered, so much laid out towards securing the safety of those who would travel by it.
Mr. Watt alluded to the success of the Dun Mountain Railway whilst the ore was required, and said he would advocate light railways and a narrow gauge. There was no use in having heavy engines and heavy trucks pulling a little weight.
Mr. Cargill participated in the feeling of dissatisfaction expressed by Messrs. Bathgate and Watt at the statements set forth in the paper, for, according to it, railways with the traffic here could not be worked except at a loss. The engineers here should study economy, and suit the means to the end.
Mr. Stout was understood to support the arguments set forth in the paper. We might get a cheap railway, but it would not eventually be able to carry the traffic as the trade of the inland districts expanded.
Mr. Wilding thought the only way to economize would be to have the rails and rolling stock no heavier than would suffice to carry the traffic, and as inexpensive as possible. The bridges and stations should be cheap and unornamental, and constructed at the lowest possible expense.
Mr. Hawthorne did not think it fair to take the average cost per mile of the Queensland railways as a standard of comparison, for they were constructed over a country, part of which was remarkably precipitous, and this had tended to raise considerably their average cost. Railways had been constructed in some parts of the country at from £6000 to £7000 per mile, and their cost had been increased by the Government taking the initiative. But now, with the experience gained there, he had heard that railways could be constructed for about £4000 per mile. Mr. Doyne, of Victoria, once the champion of the 4 ft. 8½ in. gauge, had, with others, since his visit to Queensland, expressed himself
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as being strongly in favour of the 3 ft. 6 in. gauge. It was best adapted to the conformation of the country, and more suitable to the traffic there. The single line of railway, which he had not heard referred to, might possibly be found of use in parts of this country. The borrowing of large sums might some day land the country in anything but a solvent position, and he thought it wise that all available information should be collected before the construction of new works was undertaken.
The Rev. Mr. Stuart said that railways were the life of a country, and they had arrived at that stage when something practical should be done, but he did not believe that they could get good railways constructed at a low price.
The Chairman said that the “battle of the gauges” was occupying the attention of the ablest engineers in the home country. Some of the most eminent men were ranged on both sides, and no doubt both parties were acting on opinions drawn from their own experience. But, as colonists, he thought they had to consider what best suited them, independent of England, Norway, or any other country. He thought, considering the conformation of the colony, that there would be considerable diversity of opinion in the different provinces with respect to the advantages of the different gauges. The gauge of the Canterbury Railway was 5 ft. 3 in., that of the Southland Railway 4 ft. 8½ in., and that of Otago, whose conformation was different from that of those provinces, would, he thought, be of another width. Here the country was different from the plains of Canterbury. It was hilly, and they would have to carry their railway into the interior to reach the centres of mining and farming. In the narrow gauge there was a saving in the cutting. The carrages were spread over a greater length than on the wide gauge, and the weight was therefore distributed over a greater area—hence the bridges need not be so strongly constructed. The question was whether the population of New Zealand could bear the cost of the proposed lines. Mr. Barr's common sense views would, he thought, act as correctives to those who were more enthusiastic.
Mr. Barr, in reply, said he would consider an engineer very culpable who stated views which could not be borne out by figures. He certainly could not tell upon what grounds Mr. Bathgate had founded his views, and he adhered to the opinion that the 4 ft. 8½ in. gauge was the best for the country.