If the perpendicular, AC, is one fathom, and it is found, by placing the instrument at A, that the angle, AB, is 40o, it will instantly show that the base, CB, or underlay of AB, supposing it a stratum or lode, will be about five feet and nearly half an inch, while the length of the hypothenuse, AB, will be 7 feet 10 in. nearly. But if the instrument cannot be so placed, but that we can either first place it level, at B, and then, by means of the sights, raise it so as to intersect A, the angle will be found to be 50°. So also would it be if the instrument was placed on the surface of the declination at A, and the other half raised to a level, as shown by the dotted line. In either case the complement of this angle must be used, which will be found to be 40°, as before.

I shall now endeavour to exemplify its utility more fully by a few examples.

EXAMPLE I.

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Given, the angle C, from the perpendicular, 250, and hypothenuse AC, six fathom, or 36 feet; the perpendicular, CB, and base, AB, ̄are required.

6

ft. 15 8.52, base A B.

ft. in. Angle 250.. 5 5.25

6

ft. 33 1,50, perpendicular CB.

ship and elegance of design. It consisted of three arches, elegantly light in their construction, and was admired by all who saw it. Unfortunately a great flood which occurred drifted down a quantity of timber against the bridge. In consequence of this obstruction to the flood, a thick and strong dam, as it were, was formed. The aggregate of so many collected streams being unable to get any further, rose here to a prodigious height, and with the force of its pressure carried the bridge entirely away before it. William Edwards had given security for the stability of the bridge for seven years; it had stood only two years and a half. Of course he was obliged to erect another; and he proceeded on his duty with all possible speed. The second bridge was of one arch, for the purpose of admitting freely under it whatever incumbrances the floods might bring down. The span or chord of this arch was 140 feet, its altitude 35 feet, the segment of a circle whose diameter was 170 feet. The arch was finished, but the parapets not yet erected, when, such was the pressure of the unavoidably ponderous work over the haunches, that it sprung in the middle, and the key stones were forced out. This was a severe blow to a man who had hitherto met with nothing but misfortune in an enterprise which was to establish or ruin him in his pro'fession. William Edwards, however, possessed a courage and a confidence in his powers which never forsook him; he engaged in the work a third time, and, by means of cylindrical holes through the haunches, so reduced their weight, that there was no longer any danger from it. The second bridge fell in 1751; the third, which has stood ever since, was completed in 1761. The present arch is 140 feet in span, and 35 feet high, being the segment of a circle of 175 feet in diameter. In each haunch there are three cylindrical openings running through from side to side; the diameter of the lowest is nine feet; of the next, six feet; and of the uppermost, three feet. The width of the bridge is about eleven feet. To strengthen it horizontally,

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it is made widest at the abutments, from which it contracts towards the centre.-Percy Anecdotes of Industry.

STRENGTH OF LEADEN PIPES.

[From the Caledonian Mercury.]

Some curious and interesting experiments on this point have recently been made by Mr. Jardine, engineer, at the Water Company's Yard in Heriot's Green, Edinburgh, with the view of determining accurately the proper strength or thickness of metal to be given to the pipes intended for conveying water through different parts of the city. This is an important subject, and one regarding which practical men have hitherto been much in the dark. The observations, therefore, set on foot by this distinguished engineer cannot fail to be of great utility, and we hope the particulars of

them will be communicated to the public; for it happens in this, as well as in many other branches of mechanics, that a few judicious and careful experiments, in one or two particular instances, are sufficient to comprehend a vast variety of cases which are continually occurring in practice. The strength of pipes, for example, even those of the same thickness of metal, varies greatly with the calibre of each. The pipe, in fact, becomes weaker exactly as its calibre, or internal diameter, is enlarged. Hence it is quite unnecessary to make trials of all the different sizes of pipes, as one good observation of any particular diameter and thickness of metal affords a rule

for computing the comparative strength of pipes of any other dimensions what

ever.

The following are the results of two of the above experiments.

The manner of making the trial is this the pipe to be tried is closed at one extremity, while the other communicates with a forcing pump, by means of which water is thrown into it and forced, until it presses the pipe on all sides with a violent pressure, in the same manner as if the pipe were conveying the water of a lofty spring, the effect of which is to press out the pipe on all sides in proportion to the height of the fountain-head. But the pump is also furnished with a valve or guage which measures exactly the degree of pressure communicated to the pipe, so

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that, in every experiment, we can compute the height of the reservoir which would have caused a similar pressure by the water conveyed from it, and in this manner obtain a rule for adapting the strength of each pipe to the pressure which its situation subjects it to. When the water from the pump first begins to press out the pipe, little or no alteration is observed on it for some time; as the operation of forcing proceeds, however, and the pressure thereby becomes increased, the pipe gradually swells through its whole length, until at last a small protuberance is observed rising in some weak part, which coutinues increasing until the substance of the metal, becoming gradually thinner and thinner, is at last fairly rent asunder, when the pipe bursts with a crash, and the water issues with great violence. In the first experiment the pipe was 1 inch bore, and the metal, which was remarkably soft and ductile, was one-fifth of au inch in thickness. This was forced, as above described, until the pressure became equivalent to that of a spring or column of water 1000 feet high, which is equal to 30 atmospheres, or 420lbs. on every square inch of the pipe. This it sustained without alteration, but with a pressure equal to 1200 feet it began to swell, aud with 1400 feet, or 600lbs. on the inch, it burst. It appears surprising that the soft material of lead should sustain so enormous a pressure, but this arises from its being equally distributed through every part of the

mass. There is no cross strain nor

unequal action in different parts of the pipe, but a fair stretch throughout the whole surface, which it is well-known is by far the most favourable situation for strength. On measuring the above pipe after the experiment, it was found to have swelled out from 1 inch to 14, so that a part of the original pipe, which had not been subjected to any pressure,

could be inserted within the fractured piece. The fracture of this piece presented a a very striking appearance. The edges were no way ragged, but quite smooth and sharp, like a knife, showing how the metal had been gradually distended and thinned out to nothing by the internal pressure, as if the pipe had consisted of soft clay or wax. the second experiment, the pipe was two inches diameter and one-fifth of an inch in thickness of metal: this sustained a pressure of a column 800 feet in height with hardly any swelling, but with 1000 feet it burst. The fracture here was not so fine as in the other,

In

the metal being much less ductile. Such is the extreme pressure which these pipes will bear before bursting, but it would be unsafe in practice to subject them to more than one-third of this. Still, however, it appears that a two-inch pipe,with one-fifth of an inch thickness of metal, will be sufficient for withstanding a pressure of 300 feet. Many other examples might be given of the application of these experiments, did our limits permit. We shall just mention, however, an interesting piece of antiquity, which was lately brought from Italy by Professor Leslie; it is a Roman lead pipe, supposed to have been used in conveying water to the baths of one of the Emperors; it is not truly round, but of an irregular oval or flattened shape, the metal appearing to have been turned over longitudinally, without any roller or mandrel, and then strongly soldered. It is, as near as we recollect, about 23 inches diameter one way, and 2 inches the other, and the metal about threefourths of an inch thick. Now, it is evident from the above experiments, that the strength of this pipe is enormously above what the occasion could require, and this shows the advantage of having accurate experiments to direct the construction of such works.

LIGHTING STEEPLE CLOCKS.

illumined by gas, may be rendered The face of a Steeple Clock, equally readable by the inhabitants in the night as in the day; this has now, for some years, been exemplified at the Tron Church, in the City of Glasgow. A gas-lantern, whose exterior (except on the side tastefully represents the bird called next the steeple, where it is glazed) the phanir, is supported at several feet distant from and level with the upper part of the clock-face, by two supports acting braceways to each other, and steadied, laterally, by two chains proceeding from the corners of the steeple: the main of these supports is the gas-pipe, which supplies the lantern, and the other is also a gas-pipe used for lighting the lantern. It effects this by means of numerous equidistant small holes, or narrow cross slits in its side, and is called the flush-pipe. At sun-set, when the lantern is to be lighted,

the lamplighter, by means of cocks fixed within his reach in the street, turns the gas into both these pipes, and, after waiting a proper time for the gas to ascend to the lantern, he applies his flambeau to the jet of gas issuing from the lowest of the holes in the flash-pipe, the flame from which instantly communicates to the jet next above it, and so on, until in a few moments this chain of flame enters the lantern, and lights the burner of the main pipe, which being perceived by the illumination on the clock-face, the flash-cock is then turned off, and no further attendance is needed until about sun-rise, when the other cock is shut off, and this clock-lantern extinguished, in its turn, with those in the adjacent street. The lantern is curiously glazed, convexly, in five panes; and a number of plane mirrors are, concavely, fixed behind the burner, to act as a reflector in throw ing the light principally on the clock

face.

CALCULATION OF INTEREST.

SIR,-In Number 105 of your valuable Magazine, I observe a communication respecting the Calculation of Interest; and from it, it appears, that what was written by your Correspondent, and published in Number 93, was to refute, and not to support, the opinion, that if the product of pounds, multiplied by days, be divided by 365/., the answer would be given in shillings. The idea, that it was a letter in refutation, never crossed my mind; because I knew that the rule (though by no means a short one) was quite correct; and, by consequence, I was misled. In that part of his letter which is expressed thus :-365 days: 219 days :: 25l.: 15l., I really imagined he was showing, that if 365 days were used for a divisor, the quotient would be the answer in pounds, instead of shillings; and which appeared to me to be, what it really is, nonsense. Instead of his proving the fallacy of the rule, as he has imagined, I will prove, and I hope to his satisfaction, that his letter is fallacious; and that, too, very briefly, viz.-3651. for one

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day one shilling :: 25. for 219 days: 15 shillings.

I observed the trifling omission I had made, in not stating the rate; and in my letter, which I wrote, and sent a few days after, containing the 5 per cent. method (inserted p. 339, vol. iv.), I requested that it might be noticed.

Your Correspondent has been pleased (in Number 105) to bring the fractional parts, named by me, to a common denominator, and call it a solution of the question! and in the beginning of this letter, he makes reducing the answer from shillings an observation upon my remark of and pence, to pounds, shillings, and pence, by dividing by 20, there being a misprint of "or pence for and

pence.

As a preliminary step to iny solution of it, I will inform him, that it is easier to find the interest at 31. 13s. per cent. than at any other rate. Now, I believe it is well known, that if any sum, the interest of which is required at 5 per cent. for one day, be divided by 7300, the quotient will be the answer; and at 4 per cent., if by 9125. And I find, upon the same principles, that interest at 31. 13s. per cent. is procured by dividing by 10,000.

The difference between 51. and 3. 13s. is 27 shillings, and between 4. and 37. 13s., 7 shillings. Let us take the fractional parts of 73 shillings, which, when added, shall be equal to 7 shillings. I shall take for instance (but, of course, many others may be chosen), 1-12th, 1-80th, and 1-17,500dth; and I find that, when these parts are added to 31. 13s. the amount is 47. and a very small fraction. Thus, 73 shillings.

1-12th 1-80th 1-17,500dth

Shillings

6.0833333 .9125 .0041714, &c.

80.0000047

As 17,500 appears to be an awkward sum to divide by, if it be quadrupled, the sum will then be 70,000 (which in dividing, &c. is the same, as to trouble, as by 7); but care must be taken to quadruple its quotient.