Now, in this case, as in the preceding, the centre of gravity of the generating plane, A B C, is the same as the centre of magnitude; consequently, K G is the radius of the circle described by the point G, while the circle A B C revolves about E F at the distance A K, and G M N is the path of the point G. But the centre of gravity of the circumference of the generating circle and that of its area, are in the same point; consequently, the convex surface of the ring, and its solidity, are to each other, as the circumference of the generating circle is to its area, (admitting the propriety of comparing these magnitudes,) because, according to our principle, the surface of the ring is equal to the circumference of its transverse section, drawn into the circumference of the circle described by its centre of gravity, and the solidity is expressed by the area of the transverse section, drawn into the same quantity, viz. the circumference of the circle described by the centre of gravity of the generating plane. = Let A K, the nearest distance of the revolving circle from E F, be denoted by d, and AG by r, as before; then we have KG (d+r), the radius of the circle described by the point G; consequently, we have G M N 2π (d+r), the circumference of the circle whose radius is KG. But the circumference of the circle A B C, whose radius A G=r, is 2 π r; hence by our general principle, we get 2π (d+r)×2 π r=4 π2 r (d+r), for 2 m2 2 (d+r) =π2 r2 (2 d+2 an expression for the solidity, and from which we deduce the following practical rule: To the thickness of the ring add its inner diameter; multiply the sum by the square of half the thickness, and again, by the constant co-efficient 9-8696, and the product will be the required solidity. If we compare the analytical expressions for the surface and solidity of the ring, we shall find them to bear to each other, the relation of 2π2r (2 d+2r) to π2 r2 (2 d + 2 r), and if the common quantities be eliminated or expunged from these terms, the relation is simply as 2 to r. Hence it appears, that when half the thickness of the ring is less than 2, the surface is the surface of the cylindrical ring; which expression reduced to its numerical value, becomes 39.4784 × r (d+r), from which we derive the following practical rule:To the inner radius of the ring add half its thickness, multiply the sum by the said half thickness, &c., again by the co-efficient 39-4784, and the product will be the convex surface required. This rule, it will be observed, is not expressed in the same terms as that which is usually given for calculating the convex surface of a cylindrical ring; but the expression 4 2r (d+r) can be so modified as to supply the identical rule; thus we have Now : 4 π2r (d+r)=2 π2 r (2 d + 2 r). 2 d is the inner diameter of the ring, and 2 r is its thickness, and the numerical value of π2, is 9.8696; hence the rule is :To the inner diameter of the ring add its thickness; multiply the sum by the thickness, and again, by the constant co-efficient 9.8696, and the product will be the surface sought. Which is the rule for calculating the convex superficies of a cylindrical ring, as usually given in the common books on mensuration. Again, for the solidity, we have the area of the generating plane A B C, expressed by r2, and it has been shown above, that the circumference of the circle described by the point G, is G M N =2T (d+r); therefore, by multiplication, we have r)=9·8696 x r2 (2 d+2 r,) greater than the solidity; when half the thickness is equal to 2, the surface and solidity are equal between themselves ; that is, the surface in square measure is expressed by the same number or quantity as the solidity in cubic measure; but when half the thickness is greater than 2, the number or quantity representing the solidity is greater than that which expresses or represents the superficies. If the annulus ABC, fig. 18, be made to revolve about the straight line EF, in the same plane with it, and distant by the length of the perpendicular K G, it will generate a hollow ring or cylindrical tube, of which the transverse section across the centre and both its branches, is represented by the two equal dark-shaded annuli; whilst the horizontal section PREVENTION OF INCRUSTATION IN BOILERS. 21: A B C is in the same point with the centre of magnitude of its bounding circles; consequently, K G is the radius of the circle described by the revolution of the point G, and G M N is the corresponding circumference. Put A K=d, A G=r, and let t-the thickness of metal or the width of the revolving annulus; then is KG (d+r) A C=2r, and the inner diameter of the generating annulus, is therefore equal 2 r-2 t; that is, a c=2 (r-t). Now, according to our general principle, the solidity of the figure generated by the revolution of the annulus A B C is equal to the solidity of a prism, whose base is the area of the annulus, and altitude the circumference of the circle described by the centre of gravity; but the area of the generating annulus is t (2r-t), and the circumference G M N, is 2 (d+r); the solidity of the material constituting the cylindrical ring or tube is, therefore, π 2T (d+r) xπt (2r-t)=22 t (2 r-t) (d+r), and the expression which supplies the following practical rule: From the exterior or greater diameter of the revolving annulus, subtract its width or the thickness of metal which it contains; multiply the difference by the said thickness of metal, and again, by the inner diameter of the ring added to the greater diameter of the generating annulus; then multiply this product by the constant co efficient 9'8696, and the result will be the solidity sought. The same thing may be accomplished otherwise, as will readily appear; for if we calculate the solidity of two solid rings whose diameters are A C and a c respectively, and distances A K and a k, the difference will manifestly be the solidity of the cylindrical tube, and the form of the resulting expression would be precisely the same as that obtained above. PREVENTION OF INCRUSTATION IN BOILERS-DR. RITTERBANDT'S PROCESS-MR. JOHNSTON'S PATENT BOILERS. Sir, From your remarking on Dr. Ritterbandt's patent, "this has every appearance of being an eminently useful invention, we have never before seen the great evil which it is intended to obviate, grappled with in so scientific and effectual a manner," you are evidently predisposed in favour of his invention; yet, from the impartiality you have displayed towards all controversial writings which I have perused in your Magazine for a series of years, I am satisfied that you will find room for the insertion of the following remarks on boiler incrustations. Scientific men have long laboured under the delusion that the deposits in boilers are insoluble, owing to their being chiefly composed of sulphate of lime. I am much gratified to find that Dr. Ritterbandt and others are now convinced that it is "the heat employed to generate steam causing the lime which exists in the water, in the form of soluble bicarbonate of lime, to be converted into an insoluble carbonate of lime; and (that) in marine boilers, incrustation is generally promoted by the carbonate of lime set free by the heat, which, as it floats in the water previous to subsidence, forms nuclei for the accrescence of other matter, and disposes the saline compounds, such as the sulphate of magnesia, chloride of sodium, to crystallize and precipi tate much sooner than they otherwise would." These are Dr. Ritterbandt's own words, and he is perfectly right in the opinion conveyed by them, viz., that it is heat which causes the salts, both in marine and land boilers to pass from the soluble to the insoluble state. The Doctor admits, or rather declares, that the heat is the grand cause of the disease; and, in order to alleviate it, he puts into the boiler a quantity of ammoniacal salt. Now in this treatment of the patient I do not agree. Instead of attempting to alleviate, I have succeeded in removing the cause-the heat. The temperature to which water is raised in the act of being converted into steam in a boiler is not sufficient to cause the salts to pass from the soluble to the insoluble state. This change is produced by the over-heated state of the metal of the common kinds of boilers; an overheating which is not at all a necessary accompaniment of the converting of water into steam by the application of fire to a boiler. The existence of minute globules of steam on the metal of boilers is the cause of its becoming over-heated. By constructing boilers so that currents of water are formed in them, which sweep along the heating surface, and remove from it the globules of steam the instant they are formed, the metal of the boilers never becomes hotter than the water it confines; and consequently, the salts in a boiler thus constructed can nowhere receive that amount of heat which is necessary to make them pass from the soluble to the insoluble state. I have had a seven-horse power boiler constructed according to this plan, working for the last thirteen months; a portion of that time it was worked with seawater, and the remaining time with fresh water, which naturally contains a large quantity of lime; yet no deposit has ever formed within the boiler. The fact, that the red-lead paint with which the interior of the furnace and flues were painted thirteen months ago, is still in good condition, is a most convincing proof that the metal never exceeds in temperature the water which it confines. The subjoined accounts of some experiments on this subject would, I think, be new and interesting to some of your readers, if you can find room for them. I remain, yours truly, JAMES JOHNSTON.. Willow Park, Greenock, July 3, 1845. Experiments. Experiment First. Put fifty cubic inches of sea water into a vessel, and place it in a water bath over a fire; the temperature of the vessel containing the sea water can never exceed 212° Fahr., as the intervening water of the bath prevents it. After the bulk of the water has been diminished by evaporation until there is only ten cubic inches of water remaining, then allow it to cool, and it will be found that no crystals or hard deposit of any kind has been formed: a considerable quantity of a soft flocculent substance will have settled to the bottom of the vessel; but the slightest motion of the vessel causes it to move about, and on again applying heat to the vessel the flocculent matter rises up and is dispersed throughout the water. Let the evaporation now be carried on until there be between seven and eight cubic inches of water remaining, and then allow it to cool; it will now be evident, by the existence of a few small crystals, that the water is a saturated solution. This experiment proves that no hard or injurious deposit will be formed in a vessel in which sea water is evaporated, until the water has become a saturated solution, provided the vessel containing the water be not heated beyond 212° Fahr. Experiment Second. Place other fifty cubic inches of the same sea water in a Florence flask over a gas light for evaporation; after the water has become thoroughly heated it will assume a milky white appearance, and immediately after the flocculent matter will become visible throughout the water, the same as in the first experiment. Continue the boiling of the water until there is about nineteen cubic inches remaining; if the bottom of the flask be now carefully watched, small specks of a hard scaly deposit will be observed forming; count their number, observe their size, and allow the flask with the water to cool; when cold it will be evident that no increase has taken place in the quantity of the hard deposit, but the soft flocculent matter will have settled down on the bottom of the flask. The specific gravity of the water will now be 1070, and it will float one of Twaddell's hydrometers to the 14°. Apply the flame of the gas again to the bottom of the flask; all the flocculent matter will immediately rise up from the bottom and be dispersed throughout the water, without any PREVENTION OF INCRUSTATION IN BOILERS. increase being made to the scaly deposit previous to the water having commenced to boil; but as soon as ebullition has fairly commenced, then the scaly deposit will begin to increase and go on as it did at first. Now this experiment shows that scaly deposit is only formed during the time the water is boiling, and where the ebullition is greatest. There is another fact connected with this experiment which I must make known. If the hard deposit was formed in consequence of the water being saturated with matter, it is reasonable to suppose that the deposit would fall to the bottom in a circular or round shape, as the bottom of the flask is spherical, but this is not the shape that it assumes. The gas flame which I used was what is called a swallow-tailed burner; the top surface of the flame next the flask is a flat narrow strip, and, what is very remarkable, this hard deposit inside the flask is formed in the shape of a narrow strip crossing the bottom of it, and exactly coinciding with the flame outside. From this it is evident that the hard scale is formed in consequence of the overheating of the part of the flask acted on by the flame. * * * * * * When the salt water comes in contact with the over-heated plates, they produce or cause a premature crystallization. The process is a production of salt from water which is not saturated. Can any other circumstance connected with the working of boilers but the overheating of the plates be assigned as the reason why the water in marine boilers deposits salt, although it is not a saturated solution? After a little reflection on these observations, the following question is likely to be suggested, and I shall therefore answer it. As the salt is produced from water that is not saturated, by the over-heating of the plates; why does the salt not re-dissolve after the producing cause has been removed, by the boiler being allowed to cool? Now the fact is, that salt thus produced does re-dissolve into the water from which it was taken, provided another change be not allowed to take place; for after that change it is insoluble even in fresh water. I frequently repeated the second experiment, and in all my trials of it but one, I found that the scale of salt formed, gradually dissolved in the course of twelve hours after the boiling ceased. The trial in which the scale did not re-dissolve at first excited my curiosity, but I soon found out the cause. The person that I sent for the sea-water on this occasion brought it in a rusty iron vessel, and the water had absorbed a consider 23 able quantity of the oxide of iron from it. When the water was boiled, the oxide of iron united with the scale, and formed an insoluble compound. In the other trials pure sea-water was used, and it could receive no oxide of iron from the vessel in which it was boiled, as it was a glass flask; therefore in those repetitions of the experiment the scale dissolved when the water cooled. Marine boilers are themselves the source whence the scale receives the metallic oxide, and becomes an insoluble compound. In making the above experiments, I observed that the coating of deposit, after being formed, did not continue to increase in thickness so rapidly as I supposed it would, judging by the rapid manner in which the first coating was formed, and the reason why it did not do so, is owing to the first coating being attached to a firm substance (the glass); whereas the succeeding coatings required to attach themselves to the first coating, a substance which was, comparatively speaking, soft, and from which it was easy for the bursting bubbles of steam to detach portions of the newlyformed scale. On carrying on the experiments for a length of time, I found that there was a considerable quantity of those detached portions of scale moving about in the water. Now I think it will be admitted, that the same circumstances will occur in marine boilers: viz. that when scale has been and is continuing to be formed in a marine boiler, there will always be suspended in the water minute portions of detached newly-formed scale, and as you are aware that this scale has an affinity for iron, the only conclusion that can be drawn is, that those portions of scale are carried by the ebullition of the water to the comparatively speaking quiescent side parts of the boiler, where they have undisturbed freedom to satiate themselves with their favourite, the iron composing the shell, with which they soon become united in the form of a hard crust. From a careful inspection of the two kinds of scale, it is evident that scale from the flues of a marine boiler is of a hard crystalline nature, whereas that from the shell is of a soft, chalky structure,-facts which corroborate my experiments and theory. ers, I now consider it an established fact, that the premature crystallization in marine boilfrom water which is not saturated with salt, is caused by the local action of the overheated plates on the water which comes in contact with the plates immediately after each bubble of steam has detached itself from the plates. COUPLAND'S PATENT BOILER FURNACE FOR THE PREVENTION OF SMOKE AND SAVING OF FUEL. there, till the fuel is consumed and a fresh supply required, and all this without interfering with the draught necessary for the combustion of the fuel while being so consumed. The means by which this is effected will be readily understood from an inspection of the accompanying figure. The bars g, are lowered to a level with the grating f, when a supply of fuel is required. When the fuel is supplied, the whole is raised by the handle a; whereupon the grating fis lowered, and the bars g are retained in their original position. If, on lowering the bars g the |