spect perfect. After the removal of the pressure of 207 lbs. on the square inch, and comparing these experiments with the appearance of the crown of the ruptured fire-box, I am confirmed in the opinion that steam of high elastic force must have been present to cause the disastrous explosion which eventually occurred.

Again referring to Mr. Ramsbottom's Report, he states'That it has been objected that the steam could not have been raised from 60 lbs. per square inch, the pressure at which the safety-valve was blowing off before being screwed down, to the pressure stated by Mr. Fairbairn in twenty-five minutes; but although I do not go all the way with Mr. Fairbairn as to the strength of the boiler, I find, from experiments made upon a boiler of somewhat similar dimensions, and placed as nearly as possible under the same circumstances, that the steam was raised from 30 lbs. per square inch to 80 lbs., as shown by Bourdon's steam-gauge according to the following scale, namely―

These experiments, although perfectly satisfactory as regards the time required to raise the steam (under ordinary circumstances of the engine, standing with the fire lighted, and the usual quantity of coke in the furnace) from 30 up to 80 lbs. on the square inch-it was nevertheless considered desirable to repeat them through a still higher scale of pressure and temperature, and to ascertain, not only the exact time, but the ratio

of increase, and the corresponding temperature of the steam in the boiler as the pressure progressively increased. For these objects, two delicately constructed thermometers were prepared by Mr. Dalgetti, and having adjusted Bourdon's pressure-gauge by a corresponding column of mercury, and an engine having been placed at my disposal, the following results were obtained :

Experiment made May 7, 1853, to determine the Rate of Increased Pressure, Temperature of Steam, &c., in a Locomotive Engine with the Safety-valve screwed down and the Fire under the Boiler.

Let us now endeavour, from this table, to discover the law expressing the relation between the time and pressure, or between the time and temperature.*

The observations being made at intervals of one minute of time, and the furnace being maintained at the same intensity, it may be presumed that the quantity of heat communicated to the water was uniform, or that there were equal quantities of absolute heat communicated to the boiler in equal times.

The column of pressures gives the successive augmentations of pressure at equal intervals, and the column of temperatures gives the corresponding augmentations of heat as indicated by the thermometer.

The column of pressures shows that the increments of pressure, in equal intervals of time, increase with the temperature; thus at or near 260° the average increment of pressure is at the rate of 3.1 lbs. per minute; at or near 282°, it is 5.4 lbs. per minute; and at or near 326°, it is 7·1 lbs. per minute.

Mr. Ramsbottom's table of experiments indicates a similar result; thus at or near 268° the average increment of pressure is at the rate of 4 lbs., whereas at or near 304° it is at the rate of 5 lbs. per minute.

The law, therefore, expressing the relation of time and pressure does not appear to admit of assuming a simple form. But the case is different with respect to the law expressing the relation of time and temperature. Thus if T=temperature in degrees, and t=the time in minutes at which this temperature is observed, estimated from the commencement of the experiments, then

will give the relation between T and t with great precision where a and b are constants, whose values, derived from these experiments, are a=4·44 and b=—486.

For example, let t=166, then

T=4.44 × 166-486-251°,

which exactly corresponds with the tabular value.

* I am indebted to my friend Mr. Tate for the mathematical analysis of this question.

If t, the number of minutes which elapses between the temperatures T and T, then we find from 29 (I),

which shows that the temperature increases with the time ; and presuming that the heat of the furnace remained constant, this formula also shows that equal increments of absolute heat produced equal increments of sensible temperature as indicated by the thermometer.

To determine the time, estimated from a given pressure, at I which the boiler would burst

1st. Let the given pressure be that of the atmosphere, and let the boiler be able to sustain 240 lbs. pressure per square inch.

From an experimental table of pressures and temperatures we find 240 lbs. pressure to correspond to 403° temperature, and 15 lbs. pressure to 212° temperature; hence we have by formula (3),

403-212
4.44

=43 minutes,

which is the time in which the boiler would burst, estimated from the time at which the water begins to boil.

2nd. Let the given pressure be 60 lbs. per square inch, and the boiler-pressure 240 lbs. per square inch; then

3rd. Let the given pressure be 60 lbs. per square inch, and the boiler pressure 300 lbs., then

which is nearly the time in which the boiler experimented upon would burst.

These facts appear to be sufficiently conclusive to enable us to judge of the dangers to which people expose themselves under circumstances where the necessary precautions are not taken for allowing the steam thus generated with the fire under the boiler to escape. The great majority of accidents of this kind have arisen during the time the engines are standing, probably with the safety-valve fastened and a brisk fire under the boiler. How very often do we find this to be the case in tracing the causes of these melancholy and unfortunate occurrences !

The statements contained in the earlier part of this paper regarding the strength of the stays of the fire-box would have been incomplete if we had not put those parts of a locomotive boiler, comprised in the flat surfaces or sides of a fire-box, to the test of experiment.

This was done with more than ordinary care; and in order to attain conclusive results, two thin boxes, each 22 inches square and 3 inches deep, were constructed; the one corresponding in every respect to the sides of the fire-box, distance of the stays, &c., the same as those which composed the exploded boiler; and the other formed of the same thickness of plates, but different in the mode of staying, which in place of being in squares of 5 inches asunder, as those contained in the boiler which burst, were inserted in squares of 4 inches asunder. In fact, they were formed as per annexed sketch (figs. 4 and 5), the first containing 16 squares of 25 inches area, and representing the exploded boiler, or old construction; and the other, with 25 squares of 16 inches area, representing the new construction.