3 =1, it will follow from those theorems that =P, cubic law of reciprocity. If (2), 3 or p2. It is remarkable that these theorems, "formâ genuinâ quâ inventa sunt," may be obtained by applying the criteria for the resolubility or irresolubility of cubic congruences (art. 67) to the congruence r3-3 Ar—λM=0, mod q (art. 43), which, by virtue of M. Kummer's theorem (art. 44), is resoluble or irresoluble according as q is or is not a cubic residue of X. On the Performance of Steam-Vessels, the Functions of the Screw, and the Relations of its Diameter and Pitch to the Form of the Vessel. By Vice-Admiral MOORSOM. (A communication ordered to be printed among the Reports.) In this the fourth paper which I now lay before the British Association, it may be desirable to recapitulate the points I have brought into issue, and for the determination of which, data, only to be obtained by experiments, are still wanting, viz. 1. There is no agreed method by which the resistance of a ship may be calculated under given conditions of wind and sea. 2. The known methods are empirical, approximate only, and imply smooth water and no wind. 3. The relations in which power and speed stand to form and to size are comparatively unknown. 4. The relations in which the direct and resultant thrust stand to each other in any given screw, and how affected by the resistance of the ship, are undetermined. In order to resolve these questions, specific experiments are needed, and none have yet been attempted in such manner as to lead to any satisfactory result. The Steam Ship Performance Committee of the British Association have pressed upon successive First Lords of the Admiralty, the great value to the public service which must ensue if the following measures were taken, viz.— 1. To determine, by specific experiment, the resistance, under given conditions, of certain vessels, as types; and, at the same time, to measure the thrust of the screw. 2. To record the trials of the Queen's ships, so that the performance in smooth water may be compared with the performance at sea, both being recorded in a tabular form, comprising particulars, to indicate the characteristics of the vessel, of the engine, of the screw, and of the boiler. Hitherto nothing has come of these representations. In the paper read last year at Aberdeen, I showed, in the case of Lord Dufferin's yacht 'Erminia,' how the absence of admitted laws of resistance interfered with the adjustment of her screw, and how, therefore, as a matter of precaution, a screw was provided capable of a thrust beyond what the vessel required. I also showed, in the case of the Duke of Sutherland's yacht' Undine,' how her screw, from being too near the surface of the water, lost a large portion of the thrust due to its size and proportions. In other words, a screw capable of giving out a resultant thrust in sea water of 5022 lbs., at a speed of vessel of 9.26 knots an hour, did actually give out only 3805 lbs. That is to say, the effect produced was the same as if that screw had worked in a fluid whose weight was about 48 lbs. per cubic foot instead of 64 lbs. I am now about to exhibit some other examples from among Her Majesty's ships of war. The questions now before us are 1. The resistance of the hull below the water-line in passing through the water, and of the upper works, masts, rigging, &c., passing through the air, the weather being calm, and the water smooth. 2. The relation in which the thrust of the screw stands to this resistance. [The Admiral here gave certain results from the 'Marlborough,' the 'Renown,' and the 'Diadem,' and proposed that a specific issue should be tried by means of the 'Diadem.'] What would I not give, he observed, for some well-conducted experiments to determine this beautiful problem of the laws which govern the action of the screw in sea-water! It is a problem not only interesting to science, but fraught with valuable results in the economical and efficient application of the screw propeller. After commenting on the performances of the U. S. corvette 'Niagara,' the Admiral observed, I have no means of forming a very definite opinion as to how she will stay under low sail in a sea-way, how she will wear, how scud in a following sea, or how stand up under her sails, or whether her statical stability be too much or too little, or how the fore and after bodies are balanced. These are points to be determined, not by the mere opinion of seamen--for a sailor will vaunt the qualities of his ship even as a lover the charms of his mistress-but by careful records of performances in smooth water and at sea, and a comparison of such performances with calculated results from drawings beforehand. Let a return of such things be annually laid before the House of Commons-we shall then know whether we are getting money's worth for our money; and also we should receive all the benefits of public criticism towards improvement. We should not then allow defects to be stereotyped, till chronic blemishes are turned into beauties, or, if not so, then defended as things that cannot be remedied. I have now completed the task which four years ago I imposed on myself. Beginning with simple elementary principles, and ending with minute practical details, I have, as I conceive, shown the process by which the improvement of steam-ships must be carried on. More than one hundred years ago scientific men, able mathematicians, showed the physical laws on which naval architecture must rest. A succession of able men have shown how those laws affect various forms of floating bodies. Experiments have been made with models to determine the value of the resistance practically. With the exception of some experiments of Mr. Scott Russell, I am not aware that any have been made with vessels approaching the size of ships to determine the relations of resistance to power, whether wind or steam. Ships have been improved, and modifications of form have been arrived at by a long painstaking tentative process. The rules so reached for sailing ships have been superseded by steam, and we are still following the same tedious process, in order to establish new rules for the application of steam power. I think the history of naval architecture shows that it is not an abstract science, and that its progress must depend on the close observation and correct record of facts; on the careful collating, and scientific comparing of such facts, with a view to the induction of general laws. Now, is there anywhere such observing, recording, collating, and comparing? and still more, is there such inducting process? I can find no such thing anywhere in such shape that the public can judge it by its fruits. We are now in full career of a competition of expenditure, and England has no reason to flinch from such an encounter, unless her people should tire of paying a premium of insurance upon a contingent event that never may happen; and if it should happen without our being insured, might not cost as much as the aggregate premiums. Tire they will, sooner or later, but they are more likely to continue to pay in faith and hope, if they had some confidence that their money is not being spent unnecessarily. There is now building at Blackwall the 'Warrior,' a ship to be cased with 44-inch plates of iron, whose length at water-line is 380 feet, breadth 58 feet, intended draught of water (mean) 25 feet, area of section 1190 square feet, and displacement about 8992 tons, and she is to have engines of 1250 nominal horse-power. Is there any experience respecting the qualities and performance of such a ship? Anything to guide us in reasoning from the known to the unknown? Do the performances of the Diadem,' 'Mersey,' and 'Orlando,' inspire confidence? Where are the preliminary experiments? Before any contract was entered into for the construction of the Britannia Bridge, a course of experiments was ordered by the Directors, which cost not far short of £7000, and it was well expended. It saved money, and perhaps prevented failure. This ship must cost not less than £400,000, and may cost a good deal more when ready for sea. But there is another of similar, and two others building, of smaller size. What security is there for their success? The conditions which such a ship as the 'Warrior' must fulfil in order to justify her cost are deserving of some examination. The formidable nature of her armament, as well as her supposed impregnability to shot, will naturally lead other vessels to avoid an encounter. She must therefore be of greater speed than other ships of war. To secure this, it is essential that her draught of water should be the smallest that is compatible both with stability and steadiness of motion, and that she should not be deeper than the designer intended. To ensure steadiness it is necessary, among other things, that in rolling, the solids, emerged and immersed, should find their axis in the longitudinal axis of the ship. To admit of accurate aim with the guns, her movement in rolling should be slow and not deep. Every seaman knows how few ships unite these requisites. It is not quite safe to speculate on the Warrior's' speed; nevertheless I will venture on an estimate, such as I have stated in the case of the 'Great Eastern,' whose smooth-water speed I will now assume to be 153 knots, as before estimated, with 7732 horse-power, when her draught of water is 23 feet, her area of section, say 1650 square feet, and her displacement about 18,588 tons. The speed of the 'Warrior' in smooth water ought not to be less than 16 knots, in order that she may force to action unwilling enemies whose speed may be 13 to 14 knots. The question I propose is the power to secure a smooth-water speed of 16 knots. Reducing the Great Eastern' to the size of the Warrior,' and applying the corrections for the difference of speed of knot, and for their respective coefficients of specific resistance 0564 and 07277, the horse-power for 16 knots is 7543. Raising the Niagara' to the size of the 'Warrior,' and applying the corrections for the difference of speed between 10.9 and 16 knots, and for their respective coefficients of specific resistance 0797 and 07277, the horse-power to give the 'Warrior' a smooth-water speed of 16 knots is 7867, being an excess over the estimate from the 'Great Eastern' of 324 horse-power. If the power required for the 'Warrior' be calculated by adaptation from the Mersey' and the Diadem,' it would be 8380 horse-p wer and 8287 respectively; from which this inference flows:-that unless the mistakes made in the fore and after sections of the 'Mersey' and 'Diadem' are rectified in the 'Warrior,' she will require above 8000 horse-power for a speed of 16 knots, notwithstanding her greater size and increased ratio of length to breadth. Before investing more than a million and a half of money in an experiment, commercial men would have probably employed a few thousand pounds in some sort of test as to the conditions of success. Perhaps such test may have been resorted to and kept secret for reasons of public policy. Perhaps it is intended that the 'Warrior's' speed should not be greater than that which is due to five times her nominal horse-power, which could not exceed 154 knots with 6250 horse-power, under the most favourable conditions, and may be much less. The British Association, by becoming the medium of collecting facts and presenting them to the public, has done good service; but that service ought not to rest there. Collectively, the Association may be able to do little more. It can only act by affording public opinion a means of expression. But individual members may do much. Towards such opinion I am doing my part. I ask, in the cause of science, what is the system under which the Queen's ships are designed and their steam power apportioned; the organization by which their construction and fitting for sea are carried on; the supervision exercised over their proceedings at sea, in the examination of returns of performance and of expenditure? During part of 1858 and 1859, two committees appointed by the Admiralty collected evidence and made reports on the Dock Yards and on steam machinery. I have read both reports with some attention. They are not conclusive, but they are entitled to respect. I have also read the replies and objections of the Government officers. There is a clear issue between them on some of the most essential principles of effective economical management, and on the application of science. A Royal Commission has been appointed to inquire into the system of control and management in the Dock Yards. This is so far good, but it does not go far enough. It does not comprise the steam machinery reported on by Admiral Ramsay's Committee, and it cannot enter upon the questions I have just enumerated. Yet the efficiency of the fleet depends quite as much upon the adaptation of the machinery to the ship, and of the ship to the use she is to be put to, as it does upon the manner in which she is built. The Commission ought to be enlarged both in objects and in number of members. It consists of five members only. Report on the Effects of long-continued Heat, illustrative of Geological Phenomena. By the Rev. W. VERNON HARCOURT, F.R.S., F.G.S. THE chief occupation of those who during the present century have employed themselves in investigating the history of the earth, has been to develope the succession of its strata. In following this pursuit, they have found their best guide in the study of its organic antiquities, and have not been led, for the most part, to very precise views of the physical and chemical changes which it has undergone. Yet there are questions in Geology to which no answer can be given without an accurate examination into these. In regard, for example, to the chronology of the earth, the observation of organic remains alone can never supply reliable data for reasoning. If we should attempt to draw inferences from biological analogies, and measure the duration of beds by the growth of imbedded skeletons, we should be stopped by the probability that the first species of every series were successively created in a state of full-grown maturity*, and by the intrinsic weakness of all comparisons instituted non pari materiá. Neither can any precarious mechanical analogies render the inquiry more definite, or give a logical value to our conclusions. We are not entitled to presume that the forces which have operated on the earth's crust have always been the same. Were we to compare the beds of modern seas and lakes with the ancient strata, and assume proportionable periods for their accumulation, we must assume also that chemical and mechanical forces were never in a state of higher intensity, that water was never more rapidly evaporated, that greater torrents, fluid or gaseous, never flushed the lakes and seas, and that more frequent elevations and depressions never gave scope for quicker successions of animal life. To gain any real insight into these obscure pages of ancient history, we must have recourse to a strict induction of physical and chemical facts, and thence learn the probable course, and causes, of the wonderful series of changes which geology unfolds. I am not aware that any full and connected statement has been published of the facts which have been contributed by physical observations, and chemical experiment, towards elucidating the conditions of those changes, and propose therefore to preface the account which I have to give of experiments designed to throw light upon them, with a sketch of the progress of science in that department. Forty years have elapsed since the author of the Mécanique Céleste' drew attention to the fact that multiplied observations in deep mines, wells, and springs, had proved the existence of a temperature in the interior of the earth increasing with the depth. He remarked that, by comparing exact observations of the increase with the theory of heat, the epoch might be determined at which the gradually cooling globe had been first transported into space; he stated the mean increase, collected from actual data, to be a centesimal degree for every 32+ metres, and added that this is an element of high importance to geology. "Not only," he said, "does it indicate a very great heat at the earth's surface in remote times, but if we compare it with the theory of heat, we see that at the present moment the temperature of the earth is excessive at the depth of a million of metres, and above all at the centre; so that all that part of the globe is probably in a state of fusion, and would be reduced into vapour, but for the superincumbent beds, the *To suppose otherwise with regard to animals which take care of their young would be absurd; and hence it is probable also that this is the general system of creation. The most remarkable fact which modern geology has disclosed is the continual succession of newlycreated species. It has been attempted to account for these according to known laws of progeniture, by supposing numerous non-apparent links of transitional existence to fill up the gaps in the chain of derivation by which one species is presumed to have descended from another. But this is only twisting a rope of sand; conjectural interpolations cannot give coherence to a set of chains which are destitute of all evidence of continuity one with another, and between which, as far as our experience goes, Nature has interposed a principle of disconnexion. In using the word creation, we acknowledge an agent, and own our ignorance of the agency, with regard to which, in this case, we only know that it is systematic; for we see successive species accommodated to successive conditions of existence. + M. Babinet (Tremblements de Terre, 1856), taking M. Walferdin's measurement from artesian borings, which gave 31 metres for 1° C. as the most exact, remarks, that the temperature at the depth of 3 kilometres must be above the heat of boiling water, and at that of 60 kilometres, about 2000° C., sufficing for the fusion of lava, basalt, trachyte, and porphyry. |
