MR. WHITE'S QUESTION IN SURVEYING. parallel to A B, and a small horizontal wheel, or by having another carriage on the other side the rails attached at the same instant with C. If C were suffered to move freely, it would describe a well known curve called the tractrix. Experience would soon decide whether a slight modification of this curve or the quadrant would answer best in practice. The latter would require the axles of C to converge to O. A spring might be released, which should set them parallel the instant C came upon the straight rails, A B, FE. Cambridge, June 28, 1838. G. R. MR.WHITE'S QUESTION IN SURVEYING. Sir, I return "O.N." my best thanks for the simple directions he has given me for solving the trigonometrical question which I proposed in your highly useful Journal (No. 760): I found it quite an easy task to make out an arithmetical solution from "O. N."'s rules. I was somewhat surprised to find that the said question had attracted the notice of a gentleman at the Cape of Good Hope, who has given a geometrical construction, and an analytical solution of it, in the South African Commercial Advertiser for June 27th.* I have made out an arithmetical solution of it from his investigations, and I find the required answer exactly agrees with that which I obtained from "O. N."'s method. As the gentleman at the Cape of Good Hope considers the question, and all others of a similar nature, of very high importance in trigonometrical surveying : such being the case, Mr. Editor, perhaps you will republish his solution in your scientific Journal. "To the Editor of the South African Advertiser.” "Sir,-In turning over the leaves of a late number of the Mechanics' Magazine, my attention was drawn to the following notice addressed to the editor of that periodical." [Here Mr. White's letter is quoted, which, of course, we need not repeat.] "This is one of a numerous and interesting class of questions connected with the subject of trigonometrical surveying, which are all reducible to the well-known We also have received a copy of this newspaper from a correspondent in Africa.-ED. M. M. 137 problem originally proposed by Townley; by which, from three objects given in position, and the angles which their mutual distances subtend at a station in the same plane, the relative position of the station is determined. They are all of practical importance, both to the military and land surveyor; and in this colony especially, where in the Survey of Grants every point of importance ought to be determined by triangulation, they should find a place in the note-book of every surveyor. With the view of drawing the attention of our colonial surveyors to the subject, I am induced to request the favour of a corner in your next paper, for the following solution of the above question. 'Yours, &c. I. At H, in the known distance WH, lay off the angles WHQ, WHR respectively equal to the given angles WSC, WCS; and in like manner at W, the angles HWQ, HWR equal to the given angles CS H, SCH. Draw Q R. R Through the points W, Q, H, describe a circle intersecting QR in S; and through the points W, R, H, describe another, cutting the same line in C. By this construction, the position of S and C, where the angles were observed, are determined. Join SH, CH, and on SC describe the triangle S PC, having the angles at S and C equal to the given angles CSP, ON THE CONVERSION OF WATER INTO 1. In the triangle WHQ there are WQ WH. = QH WH sin. (WSC+CSH)' sin. (W SC+CSH) 2. From the three points W, Q, H, thus determined, and the angles they subtend at S which are given, the distance SW may be found by means of Townley's Problem, of which the following is an analytical solution * :Let s semiperimeter of triangle WQH h, w sides WQ and QH Q=angle WQH H, Wangles QHS and QWS m, n-angles HSQ and WSQ 3. In the triangle SW C there are now given SW and the angles; hence S C may be found as in (1); so also may SP in the triangle SCP, of which the side SC, and the angles at S and C, are known. 4. Lastly, in the triangle PSW, from the two sides SP, SW being known, and the included angle given, we have for the distance sought PW [SW+SP] cos. Z where Z is an auxiliary angle, such that 4 SP. SW. cos. 2 WSP (SP+SW)2 2 sin. Z "N.B. Had the geographical position of W been given, and the azimuth of H on its horizon, there would have been sufficient data to deduce the latitude and longitude of P. Quere-what is the solution?" I am, Sir, your obedient servant, *This would be the indeterminate case of Townley's Problem but for the point C, which is determined from the intersection of QR by the other circle. It is well known that water can, in all degrees of temperature, be converted into steam; nevertheless the vaporization becomes rather difficult in some cases, particularly when the solid, conductor which is to communicate the caloric to the water, possesses rather a higher degree of temperature than that under which the liquid is to be converted into steam. In support of this statement, we need only refer to a long known experiment, which was first made by Leidenfrost, in 1756, I mean that of letting a drop of water fall into a platina crucible made into a white heat. The water globule spins rapidly round without ebullition, and the evaporation is slow; in proportion as the temperature of the vessel is high. In an experiment made by Klaproth, six drops of water were allowed to fall into a vessel of white hot iron, during the time it was cooling in the air. The first drop required 40 seconds to evaporate; the second, 20; the third, 6; the fourth, 4; the fifth, 2; and the sixth immediately evaporated. Yet, if such a drop, which has remained some seconds in a white hot platina vessel, be turned quickly into the hand, it will be found scarcely warm. The vaporization of the drop of water proceeds quicker in proportion as the temperature of the crucible falls, and in the not yet ascer tained degree of temperature above 212, the drop is rapidly dispersed. In addition to Klaproth, Doebereines, Berzeleus, Muncke, Laurent, and Tomlinson have repeated these experiments, with various alterations, and have given different explanations of it. The reason that the drop of water did not get hotter and evaporate, they ascribed to the circumstance of its being repelled from the hot surface, and for that reason could not remain in contact with the heated body. Notwithstanding this hypothetical repulsion of the drop of water, by which means it was prevented from getting hot, they found it necessary to account for its rotation, by the circumstance of steam being generated where it touched the hot surface, which forced it away again. ON THE CONVERSION OF WATER INTO STEAM. In the following few lines we will endeavour to ascertain the cause of this phenomenon, and bring it in connection with similar ones not yet known or described. Let us try to heat a fluid at a certain part, i. e. to communicate caloric* to one part of its external surface, and to disperse the caloric, from this point, through the entire mass. In doing this we must bear in mind two forces, on whose relative action depends the dissemination of the heat, from the point where it is first applied, to the interior. The first of these is the force of cohesion, with which one molecule attracts another in infinitely small distances. The second is the force of gravitation, by which each molecule is attracted by the earth, in the inverted square of the distance. If a drop of water be allowed to fall on a base which possesses no attraction towards the molecules of which it is composed, that is to say, on a greasy surface, or in the case of a drop of quicksilver on glass, the drop assumes a spherical shape, that is to say, the force of cohesion with which one molecule attracts another is so overpowering, that the force of gravitation, which likewise affects each particle of the molecule, has not the power to spread the drop over the surface, and occasions only a slight depression on the side upon which it falls, all the molecules in the globule being naturally in a perfect equilibrium, occasioned by their own cohesive force. The circumstances are otherwise with a body of water, which, to preserve its equilibrium, must be enclosed in a vessel. If we imagine this body of water to be composed of single drops, as before described, one drop at the bottom of the vessel has to support the weight of all those in a perpendicular line above it, the force of cohesion in this drop is, therefore, very soon overpowered by the force of gravitation of the drops above it, and would immediately expand, were it not prevented by the vessel it is contained in. Now the only part of this body of water, which is in perfect equilibrium * Melloni, in his interesting experiments on the radiation of heat, has shown that the higher the temperature of a radiating body, the less will the rays of heat be absorbed by transparent bodies. 139 without receiving support from a solid body, is the surface. In a drop of water, on the contrary, the whole is in perfect equilibrium without any foreign assistance. To apply heat to one point of a drop of water, it must naturally be applied to the surface of the globule; to apply heat in a similar manner to the body of water contained in the vessel, we must likewise apply the heat to the surface. Let us now, for example, put the bulb of a thermometer to the bottom of the vessel, and pour upon the surface of the water contained in it some ether, then set fire to the ether, and as it is consumed continue to supply fresh. Were this continued for a whole day the water would never boil, and the thermometer scarcely rise, provided the vessel did not get hot, and by this means communicate caloric. In like manner it will be equally impossible to make a drop of water boil in the centre, by applying heat to its external surface. That part of the surface of a drop of water which is touched by an ignited hody, is immediately converted into steam; if we now consider the drop of water in the hot platina crucible where it touches the white hot surface, steam is immediately developed with explosion on the point which touches, the elasticity of which immediately elevates the drop, till by the force of gravitation it again touches the crucible on another part, and is forced upwards by another explosion. At the same time the hot atmosphere in the crucible creates a cloud of steam around the drop. One part of this expands and disperses, but the other part of it is still retained by the molecular attraction of the drop, and prevents the further immediate touch of heated air.* As it was therefore found impossible to conduct heat from the free surface of a liquid to the interior, it being, as it is well known, proved by Count Rumford, that the radiation of heat from one mole By this I am reminded of a similar oft-repeatexperiment of a man sitting on a heated oven with out receiving any injury, although a fowl was at the same time cooking in it, but the heat was only rendered supportable to the man, so long as he continued to drink pretty freely. The reason of this is obvious. The first attack of heat caused a profuse perspiration, which surrounded the human body with an atmosphere of steam, which being a bad conducting power for caloric, prevented the body from absorbing the heat, which soon decomposed the fowl in which animal life was extinct. cule to another in liquids was = 0; in order to heat a fluid, it is necessary that each single molecule of the fluid should come in absolute contact with the source of heat. It is scarcely necessary to say that this is effected with a quantity of liquid contained in a vessel in which the force of gravitation is unchecked by the force of cohesion; by applying heat to that part which bears the most pressure, which is naturally the bottom. That part of the water which comes in contact with the heated bottom expands, becomes lighter,and is immediately forced up to the surface by the unheated parts of the water, which are naturally heavier, which process continues until each part of the fluid has come in contact with the heating body. If you apply heat to the drop of water, the outside layers first get warm, and are then of less specific gravity than cold water, and will, therefore naturally always remain on the outside of the water sphere, as was recently shown in an experiment made by Tomlinson, who placed, on some oil heated to 450 or 500 degrees of Fahrenheit, a drop of water coloured with ink, and a drop of ether, whose density in compa rison with water =0.7155. Both drops were immediately amalgamated, the water being of the greater density occupied the centre, the ether forming the exterior of the globule. That the attraction of the vessel towards the water ceases to be perceptible in a degree of temperature in which the water cannot longer exist in its liquid state, is self evident; and we have no reason to have recourse to repulsion, where the evolution of vapour is sufficient to explain all the phenomena of which we have just spoken. If, therefore, it thus appears impossible, under the above-mentioned circumstances, to convert a drop of water, even by an immense quantity of accumulated heat, into steam, it nevertheless is easily accomplished by the following methods: We have seen that each time the drop of water came in contact with the hot surface, a certain portion of the water has always been immediately converted into steam; that is, the portion of the surface which came into immediate contact with the vessel. Now, to convert the whole drop at once into steam, it is necessary to divide it into so many small parts that each particle may simultaneously touch the vessel. In a somewhat similar manner a ball of gunpowder when ignited requires a long time to be consumed, and would not be capable of forcing a bullet out of a gun-barrel; yet if we divide this ball of gunpowder into small grains, of which the common gunpowder is composed, the whole mass when ignited immediately explodes, and propels the bullet with great force to a long dis tance. The division of the drop of water above alluded to, is to be effected-first, by mechanical means-viz., by violently propelling it against an incandescent vessel. The drop is thus, by the concussion, scattered into very small particles, which are simultaneously converted into steam. On this principle I constructed a steam-engine, which worked effectually with a cylinder of the diameter of 6-8th parts of an inch to a halfhorse power. The second method is accomplished by chemical means, by balancing the cohesive forces, on which depends the globular form of the drop by the capillary action of a body which has just been ignited. To elucidate this point, let us heat the bottom of a sand-bath to a dark red heat, and cover it about two lines deep with fine well-washed sand. This mass of sand forms an aggregate of small speridical bodies, which, with the interstices between them, act with great capillary force on liquids. As soon as we let a drop of water fall on the heated sand, each grain of the surface of the sand which comes in contact with the water globule, imparts its heat to an equal particle of the surface of the water' globule, and thereby each of the grains is perfectly cooled, as the particles of water are converted into steam. cooled layer of sand imbibes immediately the remaining portion of the water globule, and a further repulsion of it is therefore quite impossible. This The greater height from which the drop of water falls, that is to say, the greater force with which the water is driven into the sand, the more water of the drop is converted into steam, and therefore the greater is the explosion produced. Let us now fill the sand-bath about two inches deep with the same description of sand, and take an evaporating dish with a semi-circular or spheridical bottom, and press it carefully about an |