The average time of vaporisation in oil bath is rather more than eight times that

in the tin.

These experiments, therefore, do not entirely represent the case in practice where heat is communicated by flame, by contact of heated air, and by direct radiation.

The maximum shown by this table lies certainly between 4600 and 500°; the apparent maximum being at 460°, the maximum given, by omitting the observation at 484°, being about 468°; and that by omitting the observation at 460° being about 500°.

The minimum time for the oil bath is obviously not reached; it will be recollected that this is probably as high as 570°, or about fifty degrees higher than the last observation in the table.

The times of vaporisation for the tin bath, are nearly the same as those for the bowl of three-sixteenths of an inch thick. In fact, the heat may be considered as passing through a very thick tin bowl to the iron, and kept up by flame beneath a second iron surface; the modifying effect of an additional thickness of the iron bowl is therefore small.

Vaporisation of increased Quantities of

Water.

17. It was now an object to increase the quantity of water introduced into the thickest of the iron and copper bowls until the limit of their respective capacities was reached, so that each part of the bowl to which the heat was applied should have also the cooling effects of the water upon it; the effects of the contact of a large quantity of water with hot metal would be thus represented. The nature of the results could not be expected to be otherwise than general.

For reasons already stated, the tin bath was used to communicate heat, and the projection of small particles of water from the dish was avoided by a rim of tin, which gave free escape to the steam, while it remedied, in a considerable degree, the difficulty just referred to. The temperature of the whole bath was in no case reduced very materially, a constant source of heat being applied below; but the metal which was near the bowl had its heat carried off faster than it could be supplied, and thus the temperature of the bath could show nothing more than the temperature of the bowl at the instant of projecting the water into it. The following remarks apply to the thickest iron bowl, or No. VIII., 25 of an inch thick.

One half a fluid ounce of water reduced the temperature of the bowl from 417° to a little below 212°, or through 205° Fah.. Three-quarters of an ounce, introduced at

€

504°, cooled the metal of the bowl below the

point of repulsion for drops, or through about 120 degrees, the higher temperature of the metal more than compensating for the increased, quantity of water evaporated. This bowl contained, up to the level of the bath, nearly three and a half fluid ounces. The surface was oxidated.

The following remarks apply to the temperatures of the metal when the water was first introduced.

The temperature of maximum vaporisation for one-fourth of a fluid ounce, was above 480° Fah., but probably not very far. Between 569° and 628°, the time of vaporisation of the same quantity of water increased from 10 to 20 seconds, or was doubled. The time at the point of maximum vaporisation was about 8 seconds. With one-half of an ounce of water the probable temperature of maximum vaporisation was about 504°, and the time of vaporisation 114 seconds.

The different experiments which one fluid ounce of water, by comparison with a series in another bowl, indicated the temperature of maximum vaporisation to be as high as 555°. At 518° and at 616° the times of vaporisation were nearly the same; namely, 16 seconds.

The temperature of maximum vaporisation, for two ounces, was above 600°; at 580° and at 602°, the times of vaporisation were the same; namely, 24 seconds.

This quantity was as great as the experiment could be made with satisfactorily.

From the results we see that the times of vaporisation of quantities of water in the ratio of,,, 1 and 2, or of 1, 2, 4, 8, and 16, at the temperatures corresponding to the least time of vaporisation, were about as 6, 8, 11, 13, and 22, or as 1, 11⁄2, 11⁄2, 25, 33, not far from the ratio of the square roots of the quantities, which would have given 1, 1.4, 2, 2.8, 4.

The temperatures of the metal on which water being thrown will reduce it to such a degree, that the entire vaporisation shall take place in the least time, increased for quantities varying from one-eighth of an ounce up to 2 ounces, or sixteen times, from about 460° up to 600°. The ratio of the temperatures above 212° was as 1 to about 13, indicating the approach to a temperature of the metal at which any large quantity of water introduced into a thick iron vessel would be vaporised most rapidly.

This point was elucidated directly by heating a cast iron bowl, half an inch thick, in a charcoal fire; this bowl was of the same f gure, nearly, with those already described, it could contain about ten fluid ounces of water. When heated to redness, being still

118. In the copper bowl, No. VII., the thickness being .07 inch, or about 36 of that of the iron, the following results were obtained, the same tin bath being used, and the surface of the copper being smooth.

At a temperature of 4651⁄2o, one-eighth of a fluid ounce of water was repelled, the repulsion being perfect nearly to the close of the experiment. This quantity required 175 seconds to evaporate. At the initial temperature of 501°, the same quantity required 187 seconds to vaporise it. At the higher of these temperatures, in an iron bowl of nearly the same thickness, but in an oil bath, the maximum of vaporisation was not reached.

One-fourth of an ounce required 13 seconds to vaporise it at 469° Fah., and 405 seconds at 529°, at which latter temperature the repulsion was perfect nearly throughout the experiment.

Three-eighths of an ounce vaporised in 12 seconds, at the initial temperature of 471%, and the metal in contact with the dish was solid. At the initial temperature of 486°, the same quantity required 30 seconds, and the repulsion was perfect for 15 seconds.

Five-eighths of an ounce vaporised in 15 seconds, at the initial temperature of 481°, and also at 50910. The minimum time of vaporisation being, probably, between these temperatures.

One ounce vaporised in 22 seconds, at 465, as the initial temperature; in 16 seconds, at 486°, and the tin was found congealed beneath the cup; in 17 seconds, at 511; the minimum time being probably between 486 and 5112.

Two ounces vaporised in 24 seconds, at 511, as the initial temperature; in 21 seconds at 526°, and in 22 seconds at 556°; the minimum time of vaporisation being probably at or near 526° Fah.

From these results we see that between 471 and 486° Fah. 4,,, and 1 oz. vaporised in times differing but little from each other, the range being from 12 to 16 seconds; and that with two ounces, from 5111° to 5563°, the time of vaporisation was about four times the least of those just referred to. With quantities of water, varying from one eighth of what the part of the bowl

3601342N TO THOTIK

which was in contact with the bath could contain, to one-half the capacity, the maxio mum vaporisation was between 471bands 481°, and 481°; and 511°, and the entire capacity of that part being filled, raised this temperature only to 526°, of paiva ¿

This indicates the energy of the repulsions for the evaporating surface being increased but about three times, and the waterbang creased eight times, the initial temperature corresponding to the maximum of vaporisation was raised but 56°. further, that with metal at this ture, eight times the volume of steam was formed in three times the time, when the en tire capacity was filled and compared with one-sixteenth of this capacity filled; the quantity of 6121 cubic inches of steam, or nearly 34 cubic feet having been generated in 42 seconds, at the initial temperature of 526, the steam having atmospheric pressure."'* mont, te

The copper, which was bright when the experiments were commenced, became dated as they progressed, thus tending to raise the temperature of maximum vaporisation.

Conclusions.

19. From the foregoing details may be deduced the following general conclusions, which will be found of practical import

ance.

1st. The vaporising power of copper, when supplied with heat, by a bad conductor or circulator, such as oil, increases with great regularity as the temperature increases, up to a certain point, the water being supposed thrown upon the copper surface in small quantities. Copper flues, heated by air passing through them, would be in this condition if left bare of water, and then suddenly wet. This holds with copper one-sixteenth of an inch thick, without indication that a limit will be attained by a much more considerable thickness. The temperau ture at which the metal will have the greatest vaporising power, is about 5709 Fah., or about 233° below redness, according to Daniell.

The law of vaporisation of small quantities of water, by a given thickness of copper, is represented with singular closeness by an ellipse, of which the temperatures represent the abscisse, and the times of vaporisation the difference between a constant quantity and the ordinates. hins

*wod

2. The same power in thin iron, 04 (42) inch thick, increased regularly, and was at a maximum, probably, at 510 thicker metal the power increase at the reases more lower temperatures, and varies very little,

comparatively, above 380°, with thicknesses exceeding one-eighth, and less than onefourths of an inch; attaining a maximum at about 507° Fah., when the quantities are small; rising to 550°, and much above, as the quantity of water is increased relatively to the surface of the metal which is exposed. Quadrupling the quantity of water, the entire amount being still small, nearly tripled the time of vaporisation at the maximum.

3. When copper of one-sixteenth of an inch in thickness was supplied with heat by melted tin, a worse conductor, and having a lower specific heat than copper itself, the time of vaporisation, in a spherical bowl, of quantities varying from one-sixteenth to onehalf of the entire capacity of the bowl, increased but three-fold, and the temperature of greatest evaporation was raised but 56°, or from 470° to 526°. When the bowl had half of the portion which was exposed to heat filled, the weight of the water was about one and one-tenth of that of the metal.

5th. While a red heat, visible in daylight, given to a metal, even when very thick, and supplied by heat from a glowing charcoal fire, does not prevent water, when thrown in considerable quantities, from cooling it down so as to vaporise the water very rapidly, it is much above the temperature at which the water thrown upon the metal will be most rapidly evaporated. Thus one ounce of water was vaporised in 13 seconds, at about 550°, in a wrought-iron bowl one-fourth of an inch thick, and required 115 seconds to vaporise in a cast-iron bowl half an inch thick, at a red heat. Four ounces in the latter bowl vaporised in about 300 seconds, the bowl being red-hot when it was introduced; and two ounces vaporised in 34 seconds at 600° Fah..

being developed at a lower temperature. With equal thicknesses of iron and copper, the vaporising power of the latter metal, at its maximum, was, with the oil bath, onethird greater than that of the former, and with the tin bath the power of copper 07 of an inch thick, was equal nearly to that of iron, one-fourth of an inch thick, each being taken at its maximum of vaporisation for the different quantities of fluid employed. As the maxima for the iron are higher than those for the copper, the advantage will be still greater in favour of copper when the two metals are at equal temperatures.

7. The general effect of roughness of surface is to raise the temperature at which the maximum vaporisation occurs, and to diminish the time of vaporisation of a given quantity of water at an assumed temperature below the maximum.

Stationary Temperature of Alcohol on heated Metals.

20. A curious fact was observed in regard to the temperature to which alcohol of the specific gravity 81, containing, therefore, 93 parts of absolute alcohol and 7 of water, could be raised in a heated dish. It is necessary, as an introductory remark, to recall the fact, that when the temperature of a liquid is gradually raised, by applying heat. to the vessel containing it, a limit is reached when the temperature of the liquid becomes stationary, the vapour given out in boiling carrying off the heat which enters the mass. When alcohol, of the strength above stated, was projected into a bowl heated above the temperature at which repulsion of the fluid takes place, the temperature of the liquid did not rise to its boiling point. In fact, the stationary temperature, instead of corres sponding with that of ebullition, was lower as the temperature of the dish was higher. This experiment was made in the course of attempting to infer the probable temperature at which water might be repelled from the more readily attained temperature of the repulsion of alcohol. Not being of direct application to the subject before us, it was not carried as far as in other hands it would deserve.

174

REMARKS.

།

Quantity thrown in not measured, nearly fills the dish.

75

One ounce of liquid.

Sir,-As the mowing season is at hand, I hasten to lay before you a few hints on the subject of scythes. The common scythes are formed of a plate of steel, increasing in thickness from the edge towards the back, like most other cutting instruments. The consequence of this formation is, that as the blade wears away in breadth, through use and sharpening, its edge becomes thicker and thicker, till the angle is too obtuse for the purpose of cutting. Razors have the same defect; to remedy which, a French cutler, some thirty years ago, made their blades of a thin piece of steel of one uniform thickness, and then backed them with a rib riveted on like a tenanting saw. A patent has lately been taken out in this country for making scythes on a similar plan; I have seen and handled them, and find that they answer very well. But the mowers complain of these patent scythes being dear, as they cost from seven to ten shillings each. Very few mowers, I should think, having a common scythe already of their own, would feel disposed, or, if disposed, be able to throw it aside to buy a patent one, after the fashion of the French razor. By the use, however, of a very simple contrivance, the edge of the common scythe may be kept as thin as desired until it is entirely worn out; and which little expedient I wish to suggest through the medium of your excellent pub

lication; it is one that has been in use in Italy, time out of mind. Every mower in that country carries with him, conjointly with the whet stone, a little steel-faced hammer, and a little anvil. The hammer has a longish head, like those used for driving tacks, brads, &c. The anvil consists of a bar of iron, about one foot long. One end presenting a square surface of about an inch, faced with steel, and tapering to a point at the other end. At three or four inches below the

head, an iron disk, or a double looplike scroll, is welded on to the bar. The bar, or anvil, being driven into the ground (the hardest bit at hand) can enter no further than the disk. The scythe being then laid with its edge flat on the anvil head, is beaten with the little hammer, so as to reduce it to that degree of thinness, which the wear and sharpening is continually depriving it of An Italian mower performs this opera tion two or three times a day; and thus the blade is kept thin, and drawn out in breadth, for a long period of time. The anvil would, perhaps, be more conveniently portable, were the disk removable

from the bar. It might be of cast iron, about three inches diameter. A bit of stout sheet iron would be less liable to fracture.

I have the honour to be, Sir,
Your obedient humble servant,
F. MACERONI.

CIRCULATING DECIMALS..

Sir,-Mr. A. Peacock is surprised that none of your mathematical contributors have taken notice of a certain question proposed by him in your 18th volume, respecting circulating decimals, &c. Í am afraid that this neglect has arisen from your mathematical friends not attaching so much importance to the subject as Mr. Peacock imagined it deserved. In No. 661, he proposes the question :"Given ·3488372+ a part of a decimal circulating series; required the whole of the series, and its equivalent vulgar frac

15

-

tion." Mr. Peacock finds that will

43

the question to finding a fraction that has the fewest possible figures, then in some cases the answer might be obtained by the rule he has given, when the decimal required to be produced is a pure circulate. But when the required decimal ("save the mark!") must be a mixed circulate, the method of continued fractions recommended by G. C. L. of Kentishtown, gives a better chance of producing the vulgar fraction from which the deci mal is to be produced; but even in it there is no certainty, for I shall tell both gentlemen that I have two different vulgar fractions in my mind's eye, the first of which produces a pure circulate, and the second a mixed circulate, and that the first seven decimal places of both are 4256781. Could either gentleman tell me what were the fractions I had fixed upon? Certainly not. All that G. C. L. could do," would be to produce a series

of vulgar fractions that are alternately greater and less than the given decimal, and ultimately he would produce a vulgar fraction exactly equal to the given part of the fraction 4256781. The probability of Mr. Peacock's finding the required vulgar fraction, would be in the ratio of infinity to unity. In all the calculations I have ever met with, we must take the decimals as we find them; some are finite, others recur, whilst others go on to infinity, following no regular law. Decimals, however, of this last order, Mr. Peacock does not recognise, or rather he is doubtful of their existence. However, if he will try to extract the square root of 2, or, what is the same thing, to find the diagonal of a square whose side is 1, he will find that although he should pursue the operation to as many places of decimals as there are particles of matter in the planet Jupiter, he would be as far from producing a circulating decimal as when he began. Well, then, if the ratio of the side of a square to its diagonal cannot be expressed in finite arithmetical terms, is there any thing extraordinary that this should also be the case with the diameter and circumference of a circle? Mr. Peacock still, however, fancies that the exact ratio of the diameter to its circumference may be obtained from some of the fanciful properties which he anticipates will be manifest when a better knowledge of circulating decimals is acquired! For his benefit, as well as all others whom it may concern, I shall give the following quotation from the writings of that ensinent philosopher and mathematician, the late Sir John Leslie:

"The squaring of the circle is a problem which has at all times fascinated the attention and bewildered the reason of many superficial or antiquated students in geometry.