elliptical tube with the result of the experiments on the cylindrical tubes, we find that the general formula (6) will apply approximately to elliptical tubes, by substituting for D in that formula the diameter of the circle of curvature touching the extremity of the minor axis. Thus we have.

Diameter of the circle of curvature=

nearly.

2u2 2 × 72

=

b

5

=20

Now the pressure on this elliptical tube was 6.5 lbs., which reduced to unity of length and diameter, gives 650 lbs., which result nearly agrees with 688 lbs., the mean pressure of the 12-inch tubes also reduced to unity of length and diameter.

Although this deduction is based on merely one experimental result, yet it appears to be confirmed by the following proposition derived from mathematical analysis.

The pressure P per square inch, requisite to flatten equal angular portions of a tube of variable curvature, varies inversely as the diameters of curvature.

Hence it will be observed how very much the strength of a tube subjected to external pressure is deteriorated by a deviation from the cylindrical form.

Strength of Cylindrical Tubes subjected to Internal

Pressure.

Taking the mean of the results of Experiments 36 and 39 on iron tubes, we have from formula

which gives the formula of strength of thin sheet-iron tubes subjected to internal pressure.

Now the tenacity of boiler plates has been found to be 23 tons, or 51,520 lbs. per square inch; hence it appears that a considerable reduction of tenacity must be made for the riveting of the plates. The ratio of reduction is in this case.

One remarkable fact distinctly established by these experiments, is the comparative weakness of tubes subjected to external pressure. If p be put for the internal pressure per square inch at which a tube is ruptured, then for tubes of the same thickness and diameter, we find from (6) and (7) the following relation of strength:

in this case the tube subjected to internal pressure will have about 7 times the strength of a similar tube subjected to external pressure. When

If k=25, then we find L=33 feet nearly; that is, a tube of this length and thickness will be equally strong whether subjected to external or internal pressure.

Taking the mean of Experiments 41 and 42 on the lead pipes, we have from formula (1),—

which gives us the tenacity of lead per square inch.

4440k

P=

(8)

which gives the formula of strength of lead tubes subjected to an internal pressure.

Practical Application to Construction of the Results of the Experiments.

Throughout the whole of the experiments enumerated the preceding pages, it has been proved that the resistce to collapse from a uniform external pressure, in lindrical tubes, varies in the inverse ratio of the lengths. his law has been tested to lengths not exceeding fifteen ameters of the tube; but the point at which it ceases hold true is as yet undetermined, and could only be certained by a new and laborious series of experiments à tubes of considerably greater length, in which the rength of the material modifies the above law of resistce to collapse. Such experiments are, doubtless, very sirable; but the vessels necessary for the purpose would most expensive, and the results already obtained apar to supply all the data necessary for calculating the engths and proportioning the material in all ordinary

ses.

If we take a boiler of the ordinary construction, 30 et long and 7 feet in diameter, with one or more flues 3 et or 3 feet 6 inches in diameter, we find that the cylincal external shell is from three to four times stronger its powers of resistance to the force tending to burst than the flues are to resist the same force tending to lapse them. This being the case in boilers of ordinary nstruction, it is not surprising that so many fatal accints should have occurred from the collapse of the ernal flues, followed immediately by the explosion and pture of the outer shell. To remedy these evils, and to uce the security of vessels so important to the commuy upon a more certain basis, it is essential that every rt should be of uniform strength to resist the forces ought to bear upon it. The equalisation of the powers resistance is the more important, as the incres

strength of the outer shell is absolutely of no value, so long as the internal flues remain, as at present, liable to be destroyed by collapse, at a pressure of only one-third of that required to burst the envelope which surrounds them.

The following Table, deduced from my own experiments, exhibits the safe working pressure, and the bursting pressure of boilers of different diameters, calculated for an external shell of a thickness of 3ths of an inch.

Taking from the above Table the strength of a boiler 7 feet in diameter, we find its bursting pressure to be 303 lbs. per square inch. For such a boiler the flues would be ordinarily 3 feet in diameter, and of the same thickness of plates as the shell; and by the formula, log P=1.5265 +2.19 log 100k-log (L.D.), we obtain for their collapsing pressure, 87 lbs. per square inch. As, however, the formula does not apply with strictness to tubes of such length, the actual collapsing pressure will be somewhat greater than this. The immense excess of strength in the outer shell is, however, sufficiently apparent; the extra thickness of boiler plate which causes it being so much material

rown away, adding nothing to the strength whilst the es remain in so dangerously weak a condition.

To meet this disparity of strength, the experiments licate the necessity of shorter flues, and one of them ows how this may be obtained, practically and efficiently, thout interfering with the present construction of boilers. Experiment 6, Table I., the tube F was divided into ee parts by two rigid rings soldered upon its exterior, its powers of resistance were thus increased in the io of three to one; virtually, the length was reduced in s ratio, and the strength was actually increased from to 140 lbs. per square inch.

It is proposed to apply a similar construction to the flues boilers, to equalise their powers of resistance with those the outer shell, on the supposition that the law of dease of strength holds true, within no great limits of or, for tubes of much greater length than in the preing experiments. That this conclusion is not empirical, 1 be seen by the following experiments upon boilers of I size, where it will be observed that the flues were Eorted with one-third the pressure required to rupture external shell.

These boilers were made for the North-Eastern Diviof the London and North-Western Railway Company, Fig. 2.

) (

were respectively of 35 and 25 feet in length. They e 7 feet in diameter, and composed of plates ths of an thick. Each boiler had two cylindrical flues 3 feet ches in diameter, and of the same thickness of pla