By reference to our list of patent claims, on the succeeding page, our readers will perceive that a patent has been granted for some new improvements on hot air engines. In a number of our exchanges we have also noticed that improvements in this class of engines have likewise been made by mechanics in Boston, Cincinnati, and New York. What those improvements are, except in one case, we know not, but their authors would have shown more prudence had they investigated the matter more profoundl y before they added superfluities to existing defects. In its very nature, hot air can never supersede steam as the moving power of machinery. Why it should, not one of its advocates have given nor can give a reason. The advocates of the Ericsson call it the " caloric engine;" this is for effect; the steam engine has a better title to this name, as there is more caloric in steam than in the hot air of the Ericsson. They say it economizes fuel by using a definite pro-portion of heat over and over and over again, to produce repeated effects upon new quantities of matter. This is a fallacy, a piece of nonsense; if it were true we could say the same of the heat in steam, it surely could1 be used the same way. We have said much on this subject, and have more arguments left, but those we have produced have not yet been answered. On page 317, we quoted a letter from Capt. Ericsson, which was an answer to one by Brevet Major J. G. Barnard, Engineer U. S. A., who assailed the fallacies of the caloric engine. Major Barnard has answered Capt. Ericsson, and on every point that could be raised, has shown that he was wrong in his information, and consequently wrong in all his conclusions: it is a complete settler. All those who have advocated the use of hot air as a superior motive agent to ster.m, have blindJx seen some grand multiplier oi fSwlf Ifl the iTrlcssorr fegelieftitor—a Tew packages of wire gauze—whereby 491 degs ot heat, in' a cylinder full of hot air, could be'made to drive a vessel from Cape Cod to Cape Horn and back again in amazing quick time. They have talked the greatest! nonsense about " the transfer of heat," its condensation in the pores ot metal," and such stufF, as it such arguments could not all be used in lavor of the steam as well as the hot air engine. Capt. Ericsson and all those who have talked about using the same heat over and over again, do not seem to have ever asked the question, " what is heat and what is its nature as applied to water or hot air, &c." They have in every instance spoken of it as a ponderable body, the least minutia of which could produce (by transfer) infinite mechanical effects. Heat as applied to hot air or steam, is merely according to its quantity, a force—a repellant force the opposite of gravity, consequently its effects are only in proportion to its quantity. One quantity cannot produce two effects, no more than the one effort of a man who gives one revolution to large main wheel could multiply its effects, by transferring it to the resisting point through a multitude of other wheels ; the power is transferred through the gearing of wheels, but not multiplied. Had the advocates ol the hot air transfer legerdemain been more deeply versed in mechanical philosophy, they never would have committed such blunders ; as it is, they have reasoned as profoundly as the old schoolmen on the question ot two spirits occupying the same space at the same time. In all its essential and important principles, it is easy to show that the steam engine is as superior to the caloric engine, as a locomotive is to a donkey. The Ericsson has at last been moved from her dock at WiDiamsburgh, and is now, we believe, getting in her new machinery; we hope it may yet be the means of earning as much as will save the proprietors from losing the large amounts they have invested in her. If her owners have confidence in her abilities, we would suggest to them a fair trial of speed with some of our steamships during the period the Crystal Palace is open; this would be a proper way of testing its qualities.