[11]: As the calculation of the power of an engine depends on the number of square inches in the section of the piston, it may be useful to give a rule for computing the number of square inches in a circle. The following rule will always give the dimensions with sufficient accuracy:—Multiply the number of inches in the diameter by itself; divide the product by 14, and multiply the quotient thus obtained by 11, and the result will be the number of square inches in the circle. Thus if there be 12 inches in the diameter, this multiplied by itself gives 144, which divided by 14 gives 10-4/14, which multiplied by 11 gives 115, neglecting fractions. There are, therefore, 115 square inches in a circle whose diameter is 12 inches.
[12]: The external cylinder is not represented in the diagram.
[13]: Also called the snifting valve, from the peculiar noise made by the air and steam escaping from it.
[14]: Also called the injection valve.
[15]: It is a remarkable circumstance, that Watt used the same means for keeping the cylinder hot as Newcomen used in his earlier engines to cool it. (38.)
[16]: The extent of the saving in fuel may be judged from this: that for three engines erected at Chacewater mine in Cornwall, it was agreed by the proprietors that they would compound for the patent third at 2400l. per annum; so that the whole saving must have exceeded 7200l. per annum.
[17]: In a strict mathematical sense, the path of the point P is a curve of a high order, but in the play which is given to it in the application used in the steam engine, it describes only a part of its entire locus; and this part extending equally on each side of a point of inflection, its radius of curvature is infinite, so that, in practice, the deviation from a straight line, when proper proportions are observed in the rods, and too great a play not given to them, is insignificant.
[18]: It is, in fact, the principle of the pantograph. The points C, F, and G evidently lie in the same straight line, since C B : C A :: B F : A G, and the latter lines are parallel. Taking C as the common pole of the loci of the points F G, the radius vector of the one will always be twice the corresponding radius vector of the other; and therefore these curves are similar, similarly placed, and parallel. Hence, by the last note, the point G must move in a line differing imperceptibly from a right line.
[19]: It is not necessary that the rods, forming the parallel motion, should have the proportions which we have assigned to them. There are various proportions which answer the purpose, and which will be seen by reference to practical works on the steam engine.
[20]: The centrifugal force.