On page 186 are two letters discussing the merits of water and hot air, as applicable to propel machines with the greatest economy by expanding them through the agency oi heat produced by combustion. The question discussedstrictly speakingis not one we have raised, and we might truly say, " there is no controversy between us " in respect to what we have hitherto said. The arguments presented, however, are the only scientific ones that we have seen in favor of hot air as a superior substitute for steam. Mr. Mathiot expresses himself in favor of steam, while Mr. Bass seems to be halting between two opinions. We are well aware that the capacity of water for heat is 3'74 times greater than air weight for weight ; but at the same time air is 815 times lighter than water; it takes 815 cubic feet of air to weigh as much as 1 cubic foot of water. Knowing as we do, that we would have a poor set of flying artillery if every pound shot required a cubic foot of powder to discharge it, we have in all our articles on this subject spoken of the comparative values of air and water, bulk for bulk, as motive agents, especially as air cannot be used at a high heat. Instead of adopting a positive theory, that " substances have a capacity for heat inversely as their atomic weights ;" we would rather say, " substances have a capacity for heat, according to their nature and conditions," for ice, water, and steam (the same substances under different conditions) have different capacities for heat ; water has a capacity of 0000, ice, '5130, steam, '8470. The manner in which Mr. Bass has treated the question, shows him to be exceedingly dexterous in exterminating non-existing im- la probabilities. He compares water and air Ils. julk for bulk, and raises the temperature of volume of the latter to 3.682,210, a heat especting which no one can form any pos-ible conception who has not visited the warmest corner of Hades. Let us treat the [uestion as it stands plain and open. As the capacity of water for heat is to lir as 1000(-2669=374, so will the same mount of heat which will raise a certain veight of water to 1180, raise 3'74 jtimes the veight of air to the same temperature. In mparing the two bodies we must take the eal temperature of them both as it is. Air is il5 times lighter than water; it doubles its 'olume by the application of 491 of heat, ind with the doubling of its volume, its capa-:ity for heat is increased 50this we must ilso take into consideration. One pound of vater multiplied by 1180 expands to 1728 imes its volume. But air is 815 times lighter han water, and it takes 791 volumes of it one of water multiplied by 1180 to equal he expansion of the water into steam. It is rue, there is much less fuel used, but look at he volume of air tobe operated on, and any jerson can see that when we take the ele-nentoftime into consideration, the balance s in favor of steam, yes in favor of the steam ingme without a condenser. But as in the Ericsson engine, the air is heated only to i84, therefore we have (with the saving of uel to be sure, for how can it be otherwise) :8(-384=307 ; 791 X3'07=2428\37 that is f the Ericsson engine could use its air at a ;emperature of 1180, it would only have to ise 791 cubic feet to produce the same effect )y the same fuel, which it now requires to ieat 2428 37 cubic feet of air. Mr. Mathiot tdews the question aright respecting the value )f highly heated air. The man who eon-:umes five times more food than another, and pet does the same amount of work five times 'aster, is the more profitable laborer ; so it is with the steam and hot air engines ; the form-)r consumes more fuel, but yet does more work in less time. And what is meant by opacity far heat, just this, that if a body requires more heat to raise it to tEe tempera-;ure of another body, it takes a longer time in Proportion to part with it. In the steam boil-ar we have a magazine of heat of 1180a,yet it raises the iron to only 212, the strength of which is but insensibly diminished at such a temperature. The heat of a common fire is only 1141 ; heat up the crown plates of the Ericsson's furnaces to this heat, and put on a pressure of 30 lbs. to the square inch, and what would become of them ? they would be flattened out like pan cakes. They are limited to both a low heat and pressure, and to produce as rapid and as good effects in the same time as water to which heat is applied, they would have to carry hot air reservoirs as large as the temple of Babylon. The cold water fed into the boiler to supply that taken off in steam from it, is diffused among the hot water in the boiler, which may be compared to a mass of liquid fire as great in quantity as the hot water in the boiler is to the feed water. On the otherhand,the cold air fed into the hot air chamber of the caloric engine, fills up the whole boiler, as it were, every stroke, and the heat of the furnace acts upon such a quantity of so bad a conductor as air, and the fire-surface is so small in comparison with the quantity of matter to be heated every stroke, that steam, when the element of time is taken into consideration, is far above air as a cheap agent in moving machinery. The pressure of steam (force increased for the engine) can be highly augmented in any steam boiler, without absorbing extra power of the engine, but this cannot be accomplished in the hot air engine, its pressure is limited and circumscribed by a low figure. In calculating the economy of any motive jgent, we must never leave out the element af time. Water being 815 times less bulky than air, weight for weight, has thereby the idvantage of being more quickly acted upon because of its density. The feedpump of a steam engine is required to restore one volume yf water for every 1728 volumes of steam used ; the feed pumps ef the Ericsson engine bave to feed in 491 volumes of cold air for every 875 volumes of hot air used ; and thus the difference of capacity in the two elements air and waterfor heat is beautifully compensated in the steam engine, by using the less bulky agent, to supply the magazine of force. We would like, had we room, to say something to corroborate Mr. Mathiot's views ofMr. Frost's experiments. The time has already arrived when the honor which is justly due to his memory, is sought to be purloined by others. We will speak of this at some future time. We perceive that some ignoramus in the " Akron (Ohio) Standard," has been endeavoring to astonish mankind by his knowledge, asserting that if, as we stated, the Ericsson required 8 times its power (250 horsepower) to double its speed, it would have engines twice the power of the Arctic's. Why, the engines of the Arctic work up to 2,290 horse-power. The saving of heat to use it over and over again, is an idea imbibed by the false teachings of Prof. Harvefelt, of Sweden, who, perhaps, after reading the boast of Archimedes about his lever, stated in a public lecture, " that there is nothing in the theory of heat which proves that a common spirit lamp may not be sufficient to drive an engine of 100 horse power." Ericsson embraced this view, and " he has been in the habit of regarding heat as an agent, which, while it exerts mechanical force, undergoes no change ;" so said John O. Sargent. This is a converse theory to that of Mr. Paine, with respect to the decomposition of water by mechanical action.