RADIATION OF HEAT.

A subject which is at this moment exciting considerable interest among the philosophers of Europe is, to ascertain the difference of temperature in the shade and in the sun, both with the bulb of the thermometer naked, and with one covered with black silk. Mr. Daniell thinks there is a much greater difference in high latitudes than in low. In Philadelphia I have frequently found the naked thermometer rise 40 degrees, and once 56, above the temperature of the air, while the one covered with black was generally 12 degrees higher. Mr. Daniell also thinks that in high latitudes radiation after sun-set cools the surface of the ground much more than in low latitudes. In this latitude I have seldom found the temperament of the grass more than eight degrees below the temperature of the air; whereas, Mr. Wells, who wrote the beautiful little Essay on Dew, says he has seen it as low as 16 degrees below the temperature of the air. This would allow frost to occur in low situations when the temperature of the air during the night would not be below 47 degrees; whereas, here frost can hardly occur unless the temperature of the air falls below 40. Capt. Scoresby mentions, as a strange and unaccountable phenomenon, that he has frequently observed, when sailing in high latitudes, the surface of the sea begin to be covered with thin ice, immediately after sun-set, while the temperature of the air was still several degrees above the freezing point. When he called it unaccountable, he probably did not think of the principle of radiation. In Peru, where they have such heavy dews every night, the power of radiation must be very great, or, if not, the dew point must be but little below the temperature of the air during the day. Some traveller, (I do not recollect his name,) says he has seen frost in Africa in the torrid zone. Now I do not think this at all incredible; for the temperature in those regions must fall as far below the mean in the night, as it rises above the mean in the day. The mean temperature of the torrid zone is about 84 degrees, and as loose dry sand is a very bad conductor, and a very good absorber and radiator of caloric, the surface of those wide ex

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tended deserts of sand in calm weather may easily be conceived to become 50 or 60 degrees above the mean during the day, and fall as far below it during the night, which would bring it down to the freezing point.-Mr. James P. Espy, Journal of the Franklin Institute.

DEMONSTRATION OF THE FALLACY OF A PROPOSITION IN PLAYFAIR'S " NATURAL PHILOSOPHY."

Sir,-Kinclaven's doubts respecting the accuracy of the construction of the proposition in mechanics, as given by the late Professor Playfair, in p. 63, vol. i. of his "Outlines of Natural Philosophy," and by O. C. F. in the Mechanics' Magazine, No. 291, are certainly not without foundation. How so cautious and profound a mathematician, as Playfair unquestionably was, could have fallen into such a mistake, I am at a loss to imagine. He has given no demonstration for the construction; but had he attempted to do so he would have doubtless discovered his error. Who O. C. F. is, I know not; but that he is an able mathematician no one can doubt who has read with attention the various articles he has contributed to the Mechanics' Magazine. He may very_likely have trusted to the accuracy of Playfair's construction, and been hence led, without further inquiry, to give the solution as we have it in No. 291, vol. x.

The proposition is this, that "if from the centres of gravity of any number of bodies given in position, lines be drawn to their common centre of gravity, the sum of the products formed by multiplying each of these lines by the weight of the body from which it is drawn, is a minimum, or is less than if the lines were drawn to any other point." Now, that this is not universally true, the following solution for one of the simplest cases of the problem, will perhaps suffice to shew.

Let there be three bodies whose centres of gravity are A, B, C; and suppose the body Be, also the distance ABAC. It is required to determine the position of a point P, so that a. AP+B. BP +c, CP may be a minimum.

D

Supposing AP to be constant, the lo cus of the point P will be in the circumference of a circle described from the centre A and distance AP. Draw EF parallel to BC, touching the circle in P; join BP, CP; and draw APD; then AD is perpendicular to BC, BDDC, and the angle BPE angle CPF. Hence BP+ CP is a minimum (Prop. 27. Book III. Leslie's Geometrical Analysis). And since b c, hence b. BP + c. CP or 2 b' BP will also be a minimum. Again, assume BDDC=d, AD=P, DP = x .. AP = P−x; hence 2b d2+x+ a(P—x) = minimum. Or, in fluxions, --ax = o. From which x=

2 bx x

√ d2 + x) √d2 ad

553846)+25746152, hence a.AP+26 BP =363 999; which exceeds the sum of the first products by 3.888.

Again, suppose bc=13, a, d, and P

as before, then x =

this case the point P falls into the point A, and the sum of the products will be 312; and by considering P as the common centre of gravity, the sum of the products will be 348-074, exceeding the first product by 36 074.

Lastly, let a =24,b=c=

13, d=5,

and P =12, and the distance of the common centre of 24 X 25 gravity from D will be DP =

50

12. In this case the required point and the common centre of gravity coincide.

Yours, &e. G. S.

Sir,-At page 455 of your last volume, I stated my opinion, that the 5th, 8th, and 9th of Saxula's fundamental principles of Locomotion, were erroneous; and that I would hereafter endeavour to

prove them so. In the present communication, I propose to offer some remarks on the fifth; in which it is stated, "that an engine or mechanical power, suppose equal to 100 pounds, carried by a wheel, and trying to start that wheel forward (as in locomotive machinery) is only

equal to 100 pounds weight, hung by a line on a horizontal spoke of the wheel, at the place where the engine-power is applied to that wheel."

Now the terms of this proposition suppose, that in the action of a loco motive engine, there is but one force generated, and that in a downward direction. The incorrectness of this supposition has already been pointed out, by Mr. Chapman, in your 411th number. Saxula, in commenting upon this paper,

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denies the existence of any second force, or upward pressure ;" and introduces cases in which the steam cylinder is placed diagonally, and horizontally, and significantly asks, "Where then is the upward pressure?" I admit, that in these cases, the direction of the forces is changed, and that they cease to be upward and downward pressures; nevertheless, I maintain that in these-and in every other case of locomotion which the ingenuity of Saxula can devisetwo forces are called into action. And, by the way, I would observe, that a locomotive engine with diagonal or hori zontal cylinders, forms but a sorry illustration of Saxula's fifth fundamental principle !

It is an established law in dynamics, that action and reaction are equal, and in opposite directions; and many beautiful applications of this law may be every day witnessed in the mechanical world.

Saxula has more than once talked about re-action, but he does not appear to see the tricks it is playing with several of his "fundamental principles."

In locomotive engines, as usually constructed," action and reaction continually ensue, between the top and bottom of the cylinder and piston alternately. For the sake of perspicuity, we will take an imaginary case, and suppose the pressure of steam, and area of the piston such as to generate an act ing force of 100 lbs. The pressure upon every portion of the surface, exposed to the action of the steam, must be equal; the boiler, tubes, and sides of the cylinder, will be pressed with an uniform force, and that, in every direction; action and re-action here precisely counterbalance each other. The piston, in the descending stroke, will be pressed down with a force of 100 lbs. as before stated; the top of the cylinder inside, of the same area, and exposed to the same pressure as the piston, must inevitably be forced upwards with a similar force, i. e. 100 lbs. Action and re-action are here equal and uniform, and in opposite directions, and the circumstances being such as to admit of the production of motion, two forces are the result.

With the aid of the accompanying diagrams, I proceed to apply this doctrine

of two forces, to the action of locomotive machinery:

Let A, Fig. 1, represent the body of a locomotive engine, with the piston vertical over the wheel; b the axle, c the crank. D is the downward pressure of the steam upon the piston, tending to force the crank round with a force of 100 lbs. E is the upward p essure of the steam on the top of the cylinder, tending to lift the cylinder, and consequently the axle of the carriage, in the direction of the arrow, with a force of 100 lbs. The first of these forces cD, operates to turn the wheel round its axis b, in the direction Deb. The second force has a tendency to turn the axle of the wheel round the crank c as a centre, in the direction b D c.

Fig. 2 exhibits what takes place in the ascending stroke of the engine. A, as before, is the engine, b the axle, and c the crank. D is the piston-rod, pulling the crank upwards with a force of 100lbs., and turning the wheel in the direction c Db. E represents the downward pressure of the steam upon the bottom of the cylinder, pushing the axle down with a force of 100 lbs.

Fig. 3 represents the downward; and Fig. 4, the upward stroke of a locomotive engine with diagonal cylinders; and Figs. 5 and 6, respectively, those of an engine with horizontal cylinders.

I have spoken of the two forces, as tending to produce-first, rotation of the crank round the axle; and, secondly, of the axle round the crank; and this effect would ensue if the resistance to motion was in each case equal. The practical application of this doctrine, however, is very simple; it is well known that locomotive engines possess great weight; we will in the present case suppose each axle to support its proportion of the weightsay 1,000 lbs. In the downward stroke of the engine (fig. 1) we have seen that the axle of the carriage is pulled upwards. with a force of 100 lbs.; its weight or pressure on the surface of the road must therefore be lessened that quantity; in other words, it will be reduced to 900 lbs. In the descending stroke (fig. 2) the reverse occurs, and the weight of the carriage upon the axle becomes increased by the 100 lbs. steam-pressure, to 1,100 lbs. From this view of the case, it appears, that in a locomotive engine with vertical

cylinders, the amount of friction or hold which the wheels have upon the ground, and consequently its power of locomotion, increases and decreases with the alternate strokes of the piston. In a locomotive engine with horizontal cylinders, the axle is alternately pushed in the direction of, and pulled in opposition to, its line of motion; and, although in this, as well as in the former case, in the long run, an average quantity of motion is produced, yet, at the moment of starting, or in surmounting an obstacle, considerable difference may arise from the particular direction of the piston at the time. So far as my investigations have yet gone, cylinders placed diagonally appear to have a practical advantage over every other position; and there are circumstances connected with diagonal cylinders which Saxula has not yet discovered, and which go to prove the justice of the choice which Messrs. Stephenson and others have made of this position.

After a careful and dispassionate reading of the foregoing, I flatter myself no one will attempt to deny the existence of Two forces in the action of a locomotive engine, independent of that which takes place between the wheels and the ground; and I need hardly add, that these forces cannot be represented by the terms of Saxula's fifth proposition.

Although not altogether free from objection, yet I would submit that the action of a locomotive engine is represented much more correctly by fig. 7 than by the terms of Saxula's fifth fundamental principle. A is the body of the engine, b the axle, c the crank. D is a spring, endeavouring to unbend itself with a force of 100 lbs. ; one end is attached to a bolt e, the other to the crank c, so that while it presses down the crank with a force of 100 lbs., it exerts an equal force in an upward direction upon the bolt e.

One of the principal points at issue between Saxula and his opponents is contained in his fifth fundamental principle; myself and others contend

that at

whatever part of the wheel the power is applied, it is transferred to the rim, and there acts in proportion to its intensity." Saxula says no; it acts directly from the point at which it is applied to the wheel. If Saxula is right, how are we to account for the performances of the Novelty, and other engines, in which the power is applied to the axle of the wheel, and which,

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according to Saxula's theory, with a lever so extremely short should not be able to surmount any obstacle larger than a straw! And yet, the power of such engines is not so very much behind that of others, differently constructed. Again, if Saxula's theory be good for any thing how is it that Mr. Gurney has not succeeded better? I had the pleasure of riding with that gentleman some time since on his steam-carriage, which was said to weigh 22 cwt., of which 16 cwt. was carried by the hind wheels, and the steam poer was applied by two radii to the rims of these wheels!* And yet this engine is not entitled to be called the Triumph.

As I have already exceeded my usual limits, I must reserve my further remarks until I come to discuss another of Saxula's singular propositions, which I do at my earliest leisure.

propose to Yours, &c. W. BADDELEY. London, Nov. 8, 1831.

THE ALMANACS FOR 1832.-Just Published.

Moore's. As usual, this is the best of all the popular Almanacs in point of astronomical information. Besides a very circumstantial and accurate account of the eclipses and lunar occultations that are to take place next year, we have two excellent articles on the very rare phenomena by which 1832 will be distinguished-namely, the visible transit of Mercury on the 5th of May, and the entire disappearance of Saturn's ring from the 2d of October to the 8th of December. It is now nearly thirty years since a transit of Mercury was visible in this country, and the disappearance of the ring occurs but once in fifteen years.→ A very convenient mode is pointed out of shewing the transit to a company of persons. The sun's image is to be transmitted by a telescope to a sheet of writing paper, held a few inches from the eye-end of the instrument; and by regulating the focal distance accordingly, the planet may be seen very distinctly. This is preferable to looking through the telescope; for one person only can use the instrument at a time, and a change of