manner, giving every particular connected with their arrangement, as well as the names of those scientific gentlemen who assisted me, together with the names of the assistants from my own office, so that the most ample evidence of accuracy and care may be had. For more advantage will be derived by accurate trains of experiments than will follow from the assumptions of a mathematical century. Who could expect less from a paragraph like this, than some indisputably great accession to "nautical science?" Who doubt for a moment that "trains of experiments" so "accurate," so carefully recorded, so honourably witnessed, and so proudly presented to the world, must have led to the establishment of some important law of nature hitherto concealed from human penetration. On examining the tables of these experiments, however, what do we find? Nothing but a mass of contradictions and anomalies, which seem to be governed by no law whatever, and establish nothing but the empty pretensions of their author. We see different rates of going recorded as having been produced by precisely the same power of traction; arising evidently from differences in the capacity of the canal, of which Mr. Macneill, with all his boasted " accuracy and care," has not taken the slightest notice. He has, indeed, given. five transverse sections of the canal, but these afford no other information than that the canal is of so irregular a form, as to vitiate completely the whole train of experiments. We look in vain for such data as would enable us to calculate and compare the area of the surface and volume of the water contained between the posts, marking the spaces for each of the different experiments, and for want of such data are unable to say what the experiments establish. To account for the variation between theory and experiment, Mr. Macneill refers to the rising of the vessel out of the water at high velocities as sufficient. On reference, however, to the experiments in which the rising is noticed, it appears that at a velocity of 2 miles per hour the boat did not rise at all above her quiescent line of floatation; and that at the highest velocity of 11 miles per hour she rose only 2 inches. Mr. Macneill ought to have shown that the rising was in such proportion to the increased velocity, and the diminished rate of tractive power, as to sustain his assertion, that the boat rises "out of the water according to the velocity she moves with." Every one accustomed to observe the motion of a vessel through the water at high velocities must have noticed that it produces a series of waves of greater or less elevation, according to its peculiar form. The greatest depression of the fluid is at about onethird of the vessel's length, at which point one of Mr. Macneill's observers was stationed. The greatest elevation of the fluid is usually seen at about the middle of the length of the vessel, and here no observation was made in Mr. Macneill's experiments. At about two-thirds of the length from forward the fluid is again depressed, and here there was an observer stationed, and the depression of the fluid noted. It appears to us that the points of observation ought to have been more numerous, and that if the mean had then been given, it would have been more decided evidence of the fact of the general rising of the boat out of the water at high velocities than any with which we are here furnished. Mr. Macneill asserts (p.41) "that the improved speed of steamers within twenty years has its foundation in the improved character of the machinery, and in the elongation and sharpening of the bow, but it has not been in any instance by attempting to draw less water in proportion to her increased velocity." Nothing could be more untrue. The improved character of the machinery, and the elongation and sharpening of the bow, have certainly contributed greatly to the increased velocity of modern steamers; but we happen also to know that great attention has been paid to reducing the draft of water to the greatest extent consistent with safety both in this country and in America; and in many instances alterations have been made in existing vessels expressly for the purpose of reducing the draft of water so as to increase their velocity. We must confess, at the same time, that our expectations of attaining a velocity beyond that already acquired are not very sanguine. The American steam-raft, of which a description recently appeared in the Mech. Mag., has, it is true (if the report be correct), been propelled with a velocity far exceeding any thing previously known, but then it has been at an THE CLAIMS OF MATHEMATICAL SCIENCE. expense of power which cannot be incurred in ordinary cases. Before Mr. Macneill writes again so confidently about conferring obligations on nautical science, we would suggest to him the propriety of first making himself acquainted with, and understanding thoroughly, what others have done for the science before him. He may then, perchance, discover in what he now ignorantly calls "the etourderies of the past," more sound sense and practical skill, than either the present or the future will ever be able greatly to surpass. The shipbuilder may not possibly have carried his art to its highest attainable perfection, but he has carried it at least far enough to entitle him to protection from the sneers of such surface-skimmers as Mr. Macneill. B. THE CLAIMS OF MATHEMATICAL SCIENCE. EXPLANATION. Sir,-If it be in reference to my article on mathematical pretensions, that your correspondent, Mr. Frend, has raised an appeal in behalf of mathematical science, he has undertaken a superfluous task, and given himself very unnecessary trouble; for I have not said, nor is it my wish to say, a single word to the discredit of that science as simply considered, but only as connected with its abuses, its premature, insufficient, or inappropriate applications, and its inordinate claims; indeed, I distinctly protested against being so misunderstood or misrepresented. All, therefore, that your correspondent says about "the useless race of men called mathematicians," and "the sinful practise of acquiring a knowledge of the analysis," with other similar remarks, is mere flourish, and is unworthy of a candid, or even of a staid and sober writer. It may be worth while to repeat, that my object was to show that mathematical knowledge has a high value and intellectual rank, only as associated respectively with habits of philosophic investigation, or of practical application; and that these habits having for their object the world in general, are more extensively involved in the more important interests of mankind, and exist not only in the utmost perfection independent of a knowledge of mathematical science, but in most 373 ases, to far more useful purposes, when untrammelled by its spirit and its forms However much it may be a work of supererogation, your correspondent, it seems, proposed to himself to advance 66 a few words in behalf of mathematical science;" but by a strange omission, or some hallucination of the mind, all that he has actually said, is in behalf of prac tical science, for in the historical sketch with which he has favoured us, of the several attempts to form an achromatic lens, he has satisfactorily substantiated my assertion, that success was attendant only on experimental research, and that Euler failed because, as he says, “pure intellect was the region of all his speculations." Though calling on me for a reply, he has rendered it unnecessary, by thus answering himself, or rather, by answering the appeal which he intended to have written in behalf of his favourite science. Thus again he says, "Mr. John Dollond, after many optical experi nents, discovered that the refraction of two prisms when made of different kinds of glass might be equal, and that the difference of their refrangibility might be considerable; and that there might be equal divergency, with different degrees. of refraction, in short, that refraction might be produced without colours. Acting from these principles, Mr. Dollond was the first artist that produced a correct achromatic refracting telescope." I could not wish to reply to Mr. Frend with more pertinent remarks. Here was a signal triumph, in a pitted contest as it were, of experimental and practical skill, over mathematical and speculative science. Euler in the self-sufficiency of his might, drew his materials for reasoning from himself, from "the region of pure intellect," and barreness was the result. Dollond, on the contrary, notwithstanding his undoubted mathematical acquirements, and without the least disparagement to them, applied to nature, the fountain head of knowledge, and she rewarded him with a splendid discovery. It were idle to ask, which mode of proceeding was the more characterised by wisdom and philosophy. Mr. Frend says, that Newton stands as to this particular, at least, in the same predicament with Euler. That is a debateable point; but I may not enter on it, it being irrelevant to the subject in discussion; for the appeal,' which your 66 correspondent has volunteered, is "in behalf of mathematical science," and not with a view to make the matter worse by implicating others. Besides, he claims to be the defender of "mathematical science," and not of one of its professors at the expense of another. I here beg once for all, respectfully to enter my protest against being dragged into the discussion of any such incidental topics. Let us have no skirmishing on the flanks an opponent must, according to the Indian mode of expression, "stand in my path," who would prefer a claim to my attention. I wish, in conclusion, to correct a mistake into which Mr. Frend has fallen, as to my meaning in one particular. How is it possible that he could have imagined, I referred to Dollond and his achromatic telescope, when I said, that "the most valuable method of determining the longitude, was at last accomplished by practical means, and by practical men?" I of course alluded principally to Harrison and his time-keeper. Yours, &c. BENJ. CHEVERTON. Sir, In travelling through Sutherlandshire I was ferried across one of its rapid streams by means of a chain ferryboat, lately placed there by the Duke of Sutherland, which, though on a principle common enough, seemed to me completer in its arrangements than any thing of the kind I ever before met with. The following descriptive details will probably be acceptable to your readers. Fig. 1 is an external view of the boat as seen in operation; fig. 2 is a side view of the framing; fig. 3 a plan of the bottom framing; and fig. 4 an end view of the framing. The greatest draught of the boat (at the centre) is not more than 14 inches; at the ends it is next to nothing. The chain wheel a is 3 feet in diameter, with a shaft 2 feet long, and 1 inch in diameter: t is a pinion on FIRST TRIP OF BURDEN'S STEAM-BOAT. the same shaft, 7 inches in diameter. The fly wheel b is 4 feet in diameter, and has a shaft of the same length and diameter as the chain wheel: s is a The spur wheel on the same shaft. crank handle is so adjusted as to take off and on the spur wheel. A series of pulleys and frames (c c), 10 inches in diameter, serve to keep the chain in the groove or rim of the wheel; d d are guiding rollers, 12 inches in length and 6 in diameter, with lifting rollers and frames 6 inches by 6; ee are rollers 6 inches long by 5 inches in diameter, for raising and letting down the gangways with a rope running on a pulley fastened to the top of the post; ff the gangways; gg iron rods 1 inch in diameter, which run through the gangway hinges; k is the capstan set in stone. The whole expense of the boat, with' its apparatus, did not, I am informed, exceed 130. The designs for it were furnished by Mr. Alexander Coupar, civil engineer. I am, Inverness, June 23, 1834. FIRST TRIP OF BURDEN'S STEAM-BOAT HELEN FROM NEW YORK TO ALBANY, (From the New York Gazette.) On Monday (the 7th July), Mr. Burden accompanied by only five or six friends, whom he had invited, and of whom we were one among the number, left the Dry Dock in his new steam-boat Helen, at six minutes before seven A. M., reached the North River, opposite the foot of Barclay-street, at twenty-six minutes past seven. The Erie, said to be the fastest boat on the river, had left this dock twenty minutes before, and was then in sight six miles a head. The two boats proceeded on in gallant style, attracting numerous persons along the wharves to witness the race. One remarkable feature in the movement of Burden's boat, which struck every one on board as an improvement of a most important and highly novel character, was the smoothness with which her sharp pointed cylinders glided over or rather through the water, like the sliding motion of a locomotive on a rail-road, causing not the slightest disturbance, and only a mere ripple. There was nothing whatever of that piling up of the water on the bows, and corresponding gush on the stern; none of that fluctuation or swelling on the river 375 which all other steam-boats cause, and which is perceptibly seen as well as felt by the craft in their vicinity, and even by those along the docks and banks, though they may be a mile distant. We passed the handsome and swift little steam-boat Champion, after a tough contest, near Dobb's Ferry, at fortysix minutes past seven. We had not then attained more than sixteen or eighteen revo lutions of our wheel per minute; nor was the steam fairly on, or twenty-two revolutions procured, till we neared Poughkeepsie, which we reached at twenty-two minutes past twelve. This is eighty miles, or half the distance from New York to Albany. We were now going at the rate of a mile in three minutes, or twenty miles an hour, and had come within three miles of the Erie. When we had every certainty of thus passing her in a very short time, the gear of the cut-off valve suddenly gave way at half-past one P. M., between Poughkeepsie and Lower Red Hook Landing, which immediately reduced our revolutions to sixteen, fourteen, and twelve. At ten minutes before three P, M., finding our speed thus unhappily retarded by an unforeseen accident, we lay too and repaired, and got under weigh again at thirtytwo minutes past three. But in ten minutes it broke again, and thus with every effort, and one of the boilers leaking as it had done the whole distance from New York, we found it utterly impossible to obtain more than sixteen and sometime eighteen revolutions. Nevertheless we resolutely pushed on in spite of every difficulty. We passed over the shallow water from Hudson upwards, and the overslaugh, with the same ease and facility we had the deepest channels. This we were enabled to do from the few inches of water we draw, a fact which of itself speaks volumes, and is unprecedented in the history of other steam-boats on this river. And thus, notwithstanding the most uncontend favourable auspices we had to against, and it may be said two and a half hours detention, taking the retarded operations of the engine into the account, we reached Albany at six P. M., about three quarters of an hour after the Erie. This boat was prepared beforehand for the anticipated race, and had the advantage of her highly polished machinery by long use, and in the most perfect order; and she burned, we understand, large quantities of turpentine and tar to accelerate the generation of flame-heat. Our machinery had never been fairly put to trial before, and, therefore, the reflecting part of the community may judge of the immense friction which a new engine must create, to say nothing of the leakage and the accident. The Helen, therefore, performed her first trip to Albany THE MATHEMATICAL CALCULATOR BRIDGEWATER TREATISES. 376 in nine hours! Will she not, when in ample order, and when these difficulties are removed and, subdued, make the passage in eight hours, if not less? We believe she will. This experiment, therefore, cannot be deemed conclusive. All along the river crowds manifested the deep interest they felt in our behalf, by cheering, waving flags, &c.; and at Catskill, Cocymans, and New London, cannon were fired from the docks in honour of our vessel. There is not to be deducted more than ten or fifteen minutes from the Erie's time for the few stops she made. We witnessed ourselves, that at two or three places she was not detained two minutes at each. (From the New York Mechanics' Magazine.) Mr. Burden has since made another excursion from Troy to Hudson, and accomplished eighteen miles in sixty-five minutes. He is about building another boat, 100 feet longer than the present one, the parabolic spindles of which are to be of iron. THE MATHEMATICAL CALCULATOR; OR TABLES OF LOGARITHMS OF NUMBERS, AND OF LOGARITHMIC SINES AND TANGENTS: WITH OTHER USEFUL TABLES; AND AN INTRODUCTION, THEoRETICAL AND PRACTICAL. By ROBERT WALLACE. Glasgow, 1834. 24mo. In this little work we have an addition to the list of portable Mathematical Tables, of which an account was given in our vol. xiv. p. 135. There is great resemblance between the present publication, and that of Barker, which it would have been fair in Mr. Wallace to have acknowledged; and although upon the whole the additional Tables contained in the present work entitle it to preference, yet there are some points to be set off on the opposite side, for instance, the want of the proportionate parts to the Log. of Nos., and the differences for each second to the Sines and Tangents. Nor are we by any means satisfied that the change which Mr. Wallace has made in the form of the last mentioned Tables is a judicious one. Those who adopt Mr. Wallace's volume as a pocket companion, using the larger Tables in their libraries, will certainly wish that the old established form had been preserved. The smaller Tables appended to the work are very convenient, but some of them might The last Earl of Bridgewater, a most eccentric nobleman, who died in 1829, left the magnificent sum of 8,0001. for the composition and publication of a grand work, "On the power, wisdom, and goodness, manifested in the creation." The testator's intention appears to have been to attract the first literary talent in the kingdom to the task, by the great amount of the premium offered, and thus to be instrumental in the production of a standard classic, on a subject of the very highest importance. He left the sum, however, at the disposal of the president of the Royal Society for the time being; and that gentleman (Mr. Davies Gilbert), it appears, thought the end in view would be accomplished by dividing the whole amount into eight portions, and paying over one thousand pounds to each of eight gentlemen who should be appointed by himself, to produce a cut-and-dry essay on some given fraction of the whole "high argument." So that now, instead of being called upon to hail one most important and valuable standard addition to British literature, as might have been the case had the 8,000l. been offered as a reward for the best treatise which should be produced from "all England, in a specified time, -the public is presented with some nine or ten volumes of "shreds and patches," duly furnished to order, by their respec |