188 RULES FOR CALCULATING THE LENGTHS OF PENDULUMS. resistance to the outward expansion on its borders. When an egg is frozen, it bursts from the same cause, with a wide fissure. The same is true of trees, which in very severe weather sometimes burst with a loud report. Again, I have observed, that in large ponds and lakes, where thick ice has been formed, a disruption, just at the edge, between the main body of the ice and the shore, has taken place, and that the ice has projected upon the shore a considerable distance over the line of disruption. In case this ice bad formed upon a rock near the shore, the rock must have been carried with it in its expansion towards the shore, and must have been left in that situation at the melting of the ice. When the ice formed again, it would be carried further forward, and since in New England the ice forms and melts often several times in succession during a single winter, it is easy to see that in several years a rock might make very perceptible progress. I have also noticed, that, in New England, fences which originally stood erect, near the edge of the grounds, covered by water during the winter, have considerably inclined towards the shore as soon as the ice was formed, and fences in this situation always require to be placed upright in the spring. It is well known among the farmers of New England, that, if a stone fence is erected in a similar situation, it will, after some time, be overturned. These instances show both the reality and great force of expanding ice. It is no objection to this explanation, that the principal rock which Dr. Dwight saw, was originally, jection must have often been seen, by every one accustomed to cold climates, when thick ice is melting, as it fre quently lies several feet beyond the edge of the water; and if the fracture of this ice be examined, the appearance indicates that the lower part of the formation has been forced outwards. "Whenever the shore is perpendicular to the water, or approaching to it, this projection cannot take place in any considerable degree, and in such circumstances I have seen the ice cracked in many places, and numerous planes joined at the crack, elevated so as to be gently inclined to each other, like a very flat roof. This was the natural effect on the mechanical principles which must govern the results. My views on this part of the subject are very much confirmed by the circumstances of the Deerfield disruption.' In this instance, the earth, to the depth it had frozen the past winter, 14 inches, was broken in a straight line above six rods, and the south edge of the fissure having been forced up, overlapped the other three feet."" according to the testimony, two feet at least under the surface of the water, because in New England the ice sometimes forms three feet in thickness, which would be sufficient to form about this rock, and also, for aught that appears to the contrary, about those mentioned in the Massachusetts Transactions. The firmness with which ice attaches itself to rocks, may be estimated from the circumstance, that those of many tons weight are sometimes raised from the beds of rivers, where the ice reaches to the bottom, and carried imbedded in the ice to a great distance. that the principal rock now moves much "It appears also by the testimony, this is what might have been expected, more rapidly than many years siuce, and according to the explanation I have suggested. When the top was' two feet at least' below the surface, only the thickest formations would reach it, and of course its progress would be very slow. When the top reached the surface, the thin formations would effect it, and when it rose above the surface, it would be grasped in the middle by every successive formation, and would be carried forward by the whole amount of the expansion. "The circumstances of the channels behind the rocks, and the earth heaped up before them, render two things evident:-First, that each rock was always without ever being turned over; for if moved in a position similar to itself, the motion had been produced by repeatedly overturning the rocks, they would not have left channels behind them. And again, an immense force must have been exerted to remove these rocks, especially when we consider that one of them weighed, by estimation, 40 or 50 tons, and when we add to the resistance arising from its weight, that which must have been caused by the formation of a deep channel after it. The expansive power of ice is a force abundantly sufficient." PRACTICAL RULES FOR CALCU- SIR,-If you think the following practical rules for calculating the lengths of pendulums, &c. would be useful to any of your readers, I shall be obliged by your giving them a place in your very valuable Magazine. 1st. To find the length of a pendulum that shall make any number of vibrations in a given time, as one minute. Now, it is demonstrated by writers on mechanics, that no: 602: : 39.14: L; RULES FOR CALCULATING THE LENGTHS OF PENDULUMS. therefore, by multiplying means and = L 189 of gravity in the time of one vibration of a pendulum, is to half the length of a pendulum as the square of a circumference of a circle is to the square of its diameter, that is (denoting the space fallen through in a second at the given place by S, and the length of the pendulum by L). S: L: 3.141592: 1; therefore S LX3.141592. EXAMPLE III. = EXAMPLES I. AND II. D 35 {number of vibrations per minute which, in words, is this:-Set the number of vibrations given on the line marked D to 39.14 on C, and against 60 on D you have the length of the 115 inches. $60. pendulum on C; or set the length of the pendulum given on C to 60 on D, and opposite to 39.14 on C you have the number of vibrations per minute on D. C 19.57 DI EXAMPLE III. 193.14 inches, space fallen through in one second. 14159. COMPRESSIBILITY OF WATER. This experiment has been tried by the distinguished Danish philosopher Ersted, by an ingenious apparatus of his own invention. The result is thus stated: "Agreeably to the mean of a great number of experiments, a pressure equal to that of the atmosphere produces in water a diminution of volume of 0.000045. In all the trials with my apparatus, from the pressure of onethird to that of six atmospheres, I have the compression of water to be in the ratio of the compressing force. Canton had obtained, in the greater number of his experiments, 0.000044 for a pressure equal to that of the atmosphere, which differs only one millionth from my result. The ingenious experiments of Mr. Perkins, made with several hundred atmospheres, give 0.000048 for each atmosphere! am induced to attribute this difference, in itself very small, to a compression which the sides of his vessel (being of metal) may have sustained. Another circumstance ought, perhaps, also to be taken into consideration, viz. that water seems to lose a little of its compressibility after several compressions. I dare not, however, aver this to be the fact, not having subjected it to a rigorous trial." ART OF BAKING. A machine for accelerating the fermentation of flour has been invented at Lausanne, in Switzerland. It consists, simply, of a round box of pinewood, a foot in diameter, and two feet long, placed upon gudgeons, and put into motion by a handle or winch, resembling exactly the cylinder used for burning coffee. An opening is made on one side for receiving the dough. The time necessary for fermentation depends on the temperature, the rapi dity of its motion, and many other circumstances; but, when the paste is properly raised, the operator discovers it by the hissing sound of the fixed air, as it rushes out of the machine. It never fails to work well, and requires, at most, half an hour's attention. The labour is nothing, as a child can turn the machine. If made longer, and divided into compartments, it would serve for the preparation of several kinds of paste at the same time. This machine offers the double advantage. of raising paste expeditiously and to the exact degree required. An improvement on this instrumeut has been made in Paris by M. Buntem, instrument-maker, 26, Quai Pelletier, so as to save the necessity of suction. Near the top of the outer and Jonger branch, just below the bend of the syphon, a ball is blown, forming part of the stem itself, and of a suitable size. On filling this branch (together with the ball) with a fluid, stopping. the end of the tube with the fingery and then immersing the short leguin the liquor to be drawn off, the operation will go on at pleasure. SIR,-In Number 69 of the Mechanics' Magazine, a Water-wheel is mentioned to be required for a weak stream, the whole fall being 13 feet. Now, I shall be glad if any of your readers will recommend, through the medium of your Magazine, a Water-wheel for a weak stream, the fall not being capable of being made above 11 feet. Mr. Lambert has laid it down, that a breastwheel should be used when the fall of water is above four feet in height, and below ten.* What kind of wheel will be best suited to a weak stream where the fall may be made 11 feet? Can any of your readers recommend any thing preferable to a breast-wheel, of the above form and the following dimensions:Radius of the wheel from the extremity of the float-boards, 7.52 feet. Breadth of the float-boards, 1.71 feet. The float-boards to be confined, both at their sides and extremities, so that the water may accompany them to the lowest part of the wheel; the float-boards to incline to the radius of the wheel, so that each float-board, when lowest, shall not be vertical, but have its edge turned up the stream about 20 degrees. G. B. K. NO. 133. CONSTRUCTION OF BEE-HIVES. SIR-Through the medium of your valuable Magazine, allow me to inquire During the last three years, I have with glass fronts, in the window of kept bees, with varied success, in boxes a south room of my house; but as all within doors is occupied, I placed one the space proper for their establishment swarm, of prodigious size, in flut hives in my garden, on the 21st ult., in preference to the dome-topped hive, so well known to most of your readers; and my principal motive in doing it is, that shall be enabled (as I am informed) to that contained in the upper hive, if not take away a portion of their honey (say that in the next also), without destroying its industrious inhabitants. conical hats or hackles, usually placed on hives for the purpose of sheltering them from the weather, are commonly, in this neighbourhood, made of reed or straw, of a length insufficient to cover more about six inches deep, and twelve inches than two or three of such hives, each in diameter. How is this defect best re medied? The Possibly, some of your numerous Correspondents may also be enabled to afford information relative to the construction, cost, situation, productiveness, &c. of the Leaf or Book Hive, invented by the indefatigable Huber. It is to be regretted, that the culture See Nouv. Mem, de l'Académie de of so prolific and industrious an insect Berlin, 1775, p. 71, as the bee, is not more attended to in a 192 ANSWER TO INQUIRY-CORRESPONDENCE. country so highly cultivated as England, where the greatest variety of flowers presents themselves to its taste, when collecting those sweets which produce honey equal to that of any part of the world, more particularly when we take into consideration the great amount paid every year to foreigners for this article of commerce. Straw hives, of either make, are within the reach of every frugal cottager, whether artisan or husbandman, who, whilst pursuing his daily labour, has (generally speaking) a wife or children at home, capable of securing the swarm or swarms which every stock of bees may be expected to throw off. 'Thus their more extended cultivation might be made a source of individual profit, and, at the same time, by employing the resources with which an allbountiful Being has blessed us, contribute, collectively, to an increase of the happiness and prosperity of Burton. "THE LAND WE LIVE IN." ANSWER TO INQUIRY. No. 119, VOL. IV. p. 64. SIR,-On looking over some Numbers of your Publication, I found it asked, why the force communicated by the rod from the beam was greater when the rod was eight feet long, than when only five feet long? If we resolve the force which is communicated in the direction of the rod into two parts, one in the direction of the crank, the other perpendicular to that direction, the part which is perpendicular to the crank is alone productive of rotation. Now I think that the mean inclination of the rod to the crank is more nearly equal to a right angle when the rod is eight feet, than when only five feet. Hence the part of force which is productive of rota tion is greater in the former case, greater effect will be produced. and a I am, Sir, yours, &c. M. O. E. CORRESPONDENCE. F. O. Z. will perceive, that he was anticipated by the article in our last Number on the line of draught in carriages. His conclusion is precisely similar :→ "Hence it is plain,” he says, "that great part of the leaders' force is actually employed in breaking the wheelers' back." R. H.'s Plan for Measuring Heights was, from the first, intended for insertion, but the diagram accompanying it has been mislaid. If he will oblige us with another copy, the article shall appear forthwith. T. M. B. will please send to our Publishers for a letter addressed to him. We shall be glad to receive the farther communications of Mr. G. M. (Dublin), and Philo-Naut. Communications received from—W. C--y.-A Mechanic-A BookbinderMr. Lake-G. M. A.-J. Jay-S. W. T.E. A.-J. T.-A Constant Reader-W.F.R. A.-D. Thomas-S. G. R.-R. Crusoe-Telloc Trigger-A Visitor to our Atmosphere-A Reader, but no Philoso pher J. S.-D. C.-R. J.-Z.-A Promoter of Improvements-Aurum—Jo. Senhouse-Au Old Mouse-A Manufacturer-A Mechanist-T. C.-Mr. Hayter •Mr. Dowden. Advertisements for the Covers of our Monthly Parts must be sent in to our = = ERRATA. Page 150, col. 2, line 15, for ",14 1421. 17s. 1d." read, ",875 = 1371. 2s. 104d."-Line 16, for “ 1427. 17s. 1‡d.” read, “1371. 2s. 104d.”. Communications (post paid) to be addressed to the Editor, at the Publishers', KNIGHT and LACEY, 55, Paternoster-row, London. 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