I am not wholly prepared to say what portion of the oil it might be best to re-elevate by the pressure of the aforesaid weight f g; but, if it were a considerable part of that contained in the central compartment c c, that column would be shortened in proportion; and the reservoir at i would, doubtless, feel the want of it to preserve it’s level. I think, therefore, it might be well to use, below, a cup or two more than sufficient, so as to raise the main column higher than actually wanted; and to coerce this rising tendency, by a small stop-cock in the rising branch, to be gently opened at the will of the person using the lamp. I cannot say I have exhausted this subject; either in these respects, or as to it’s technical capabilities. But I have fully tried this method of raising oil above it’s level; and used, for some time, a lamp made on this principle, and which is still in my possession: and, at some future time, I intend to bring forward an Hydraulic Machine, founded on the same principles.
OF
A MECHANICAL ESSAY,
To derive Power from expanding Metals.
It is not supposed that this Essay can lead, immediately, to any result of magnitude; but it is thought to be a subject capable of further extension, and thus, finally, of future usefulness. Were this process only sufficient to supply a single house with water, at a small expence, the labour bestowed on it would not be altogether in vain.
By General Roy’s experiments, cast iron (and steel) expanded by 180° of heat (or, by passing from the freezing to the boiling point of Fahrenheit) 0.013 of an inch per foot.
Supposing, then ([Plate 34], [fig. 1]), the tubes A B C to be 20 feet long, their whole expansion will be 0.26 hundredths of an inch. But, as the tubes are placed in the figure, the half tubes A D B D act together on the sphere D, and, both together, drive it in the direction E D, more than as the above expansion, in the proportion of the line E D to that A D. Taking, then, one half only of the above expansion = 0.13 hundredths of an inch, that must be augmented in the ratio of the sine of 60 degrees to radius, or in that of A D to E D. I, therefore, multiply this decimal 0.13 by the fraction 1000⁄866, which gives 1300 to be divided by 866, or very nearly 0.15 for the expansion, in the direction E D, occasioned by the two half bars A D B D: and the same is true at the other angles F and G.
Again, to find the expansion (and contraction) of the bars a b c, we must compute their length as compared with the half tubes above-mentioned; and that length is to 10 feet (the half tube A D or B D) as 866 is to 1000 = 11.54 nearly: the expansion of which is thus found:—if 10 feet expand 0.13, what will 11.54?—Answer, 0.15. Now, as the machine acts by the heating of the pipes A B C simultaneously with the cooling of the bars a b c, we must add the former expansion to this contraction, which gives us 0.30, or three tenths of an inch for this combined effect at the three angles of the Machine. And, supposing, now, any pair of bars to act directly against each other, as at H I K; and that, further, the bars be stretched until the angle with the horizon be only 2 degrees, then the vertical motion at I will be to the horizontal (arising from the expansion aforesaid) as 1000 to 35, the sine of 2; that will be, in round numbers, 28 times as great, or 28 times three tenths of an inch = 8.4 inches, which is the stroke of this Machine in these dimensions.