MESSRS. EDITORS.—In the Scientific Ame rican ot Januaiy 29, on page 54, I find in an article upon the caloric engine, the following sentences:— " Thus this engine is constructed upon the principle of heat force; that is, if a certain amount ot heat can be retained, it will pro duce repeated effects upon innumerable quan tities oT water—a thing utterly at variance with mechanical philosophy." "This was certainly a kind of perpetual motion engine, the same heat and the same air being used over and over again." Now I think that here is a theoretic error. Heat can theoretically be used over and over again, and it only remains to reduce this prin ciple to practice to realize the fact that heat is unlike gravitation. To illustrate my mean ing, let us take the case of a common steam engine. No heat is lost by the condensation. And if the apparatus were not too cumber some—that is", if we could prevent all loss by radiation—we should be able to use the 20 pints of water heated from 50 to 110 in condensing an amount of steam equal to one pint of water, by heating air to produce a force 4 times as great as that produced by the steam. The only way to avoid the conclu sion that heat can be used more than once seems to me to be to deny that the water at 110 , from the hot-well of a common steam engine would tend to expand air at 50 , which is utterly at variance with facts.— There is a fundamental differenee between the force of caloric and that of gravitation, that the latter leaves a power exhausted, while in the case of the former an additional force can be obtained by the natural radiation of the heat, after the caloric has once been used to obtain power by expansion, very nearly the same power being capable of be ing obtained for the contraction. P. M H. [If there is a theoretic error in the princi ple we annunciated, our correspondent has tailed to point it out. When he talks about an additional force being obtained from the radiation of heat he must mean that it is a force different from heat itself, or that it is a portion ot the amount ot heat generated. We can form no idea of the effects of heat apart from bodies possessing gravity. We measure the quantity ot heat generated by the tempe rature of bodies possessing gravity. Our cor respondent (and many others) have confu sed ideas about using heat over and over again. For example let us take a cubic foot of air and heat it to 491 , and it will exert a pres sure, of 15 lbs. on the square inch. Cut off the fire influence and the cubic foot of air will expand to two cubic feet, at the atmospheric temperature and exert a pressure of 0. (Air heated to 491 doubles its volume). Now can this expanded 491 of heat be used over again to heat another cubic toot of air to 491 ? No. How then can it produce repeated effects up on innumerable quantities of matter ? You can compress the two cubic feet of air expan ded to atmospheric temperature into one foot, and it will then be brought back to 491 , and exertthe pressure of 151bs. onthe square inch, but then you must just exert as much force to compress it as the force to be obtained after it is compressed. The idea which has been propagated, that heat can act above and be yond the laws of gravity upon bodies pos sessing gravity is preposterous. We thought we had said enough to show how ridiculous the assumption is, that a certain amount of heat can produce repeated effects upon innu merable quantities of matter, but we see that we must strike a harder blow still. It is stated that " the hot air engine uses the same heat over and over aagin, except 30 , which is allowed to escape every stroke. This is done, it is stated, by interposing pack ages of wire gauze between the feed and working cylinders, which takes up the heat from the escaping hot air, and gives it out to the inlet cold air, thus the same quantity of heat produces repeated mechanical effects ex cept the loss of 30 every stroke." We have fairly quoted the allegements of the advocates of using heat over and over again, and will show by plain figures that it is all moonshine and a deception. Air doubles its volume by the application of 491 . "The advocates ot hot air say 480 , and we will grant them the point. Well, the working cy linder of the Ericsson engine has a six foot stroke. Allowing the air to be heated to 480 , it will move the piston 6 feet with a pressure of 15 lbs. on the square inch. If al lowed to expand to double its volume, its pressure will be reduced to 0. The whole ot this stroke would be 12 feet, and the average pressure 7i lbs. on the square inch, for the expenditure ot the fuel that heated the con tents ot the 6 feet deep cylinder, that is the 480 of heat generated by a certain quantity of coal, would move the piston 12 feet with an average pressure ol 7 lbs. on the square inch. It could not do any more, for the heat would be reduced to that of the atmosphere. But according to those who advocate the hot air regenerator, the 480 will make the piston move 52 feet, with a pressure of 15 lbs. on the square inch, by allowing it to come dashing against a resisting medium of wire gauze at every stroke, and then making another quanti ty of cold air dash against the gauze upon the principle, we suppose, of hyperbolic reasoning. This is the way they do it. The first stroke, 6 feet (72 inches) is performed by the air heated to 480 , this air comes rushing out against the wire gauze and gives out all its heat, except 30 . Cold air is then poured through the wire gauze, which gives out all its heat, to expand all the air which goes under the piston, and raises it up a second time, the whole six feet, excepting the amount of heat, (30 ,) lost, which must be deducted. Now let us cut off the heat from the fire, at the end of the first stroke, and see what amount of work will be done by these wild hot jjii the orists. 480 is the amount of heat applied to the air; the loss ol each stroke is 30 , 72 in. being the length of the stroke. Well (480 -f-30 =16) (72-Hl6=*4) The loss of distance each stroke for 30 of heat is 4 inches.— Well, first stroke 72 inches; second stroke 72 —4i=67jJ. Third stroke 67i—4i—63 inches, and so on for fifteen strokes, when the loss of 30 each stroke will have reduced all the heat to 0, and it will be found that instead of the engine (as it only can do by pure scientific de duction) moving 12 feet with 7i pounds pres sure, it will have moved 52 feet, with a pres sure of 15 lbs. on the square inch, or nine times the actual power which upon any con sideration can be derived from 480 of heat. We can tolerate no more nonsense about using heat over and over again to produce repeated mechanical effects upon innumerable quanti ties of matter; more especially with those who can see by some hocus pocus, that if no loss is caused by radiation and exhaustion, 480 can be made to propel a steamship from Sandy Hook to the Cove of Cork. Dr. Swaim, of Philadelphia, says, m rela tion to the " Curious Properties of the Num ber Nine," if any row of two or more figures be reversed and subtracted from itself, the figures composing the remainder, will, when added horizontally, be a multiple of nine :— 42 846 3261 24 648 1623 18=9X2. 198=9X2. 1638=9X2 This is merely a curiosity, from which h e de rives no result ot practical utility.