A.—­It is an elongation of the valve face to a certain extent over the port, whereby the port is closed sooner than would otherwise be the case.  This extension is chiefly effected at that part of the valve where the steam is admitted, or upon the steam side of the valve, as the technical phrase is; and the intent of the extension is to close the steam passage before the end of the stroke, whereby the engine is made to operate to a certain extent expansively.  In some cases, however, there is also a certain amount of lap given to the escape or eduction side, to prevent the eduction from being performed too soon when the lead is great; but in all cases there is far less lap on the eduction than on the steam side, very often there is none, and sometimes less than none, so that the valve is incapable of covering both the ports at once.

189. Q.—­What is the usual proportional length of stroke of the valve?

A.—­The common stroke of the valve in rotative engines is twice the breadth or depth of the port, and the length of the valve face will then be just the breadth of the port when there is lap on neither the steam nor eduction side.  Whatever lap is given, therefore, makes the valve face just so much longer.  In some engines, however, the stroke of the valve is a good deal more than twice the breadth of the port; and it is to the stroke of the valve that the amount of lap should properly be referred.

190. Q.—­Can you tell what amount of lap will accomplish any given amount of expansion?

A.—­Yes, when the stroke of the valve is known.  From the length of the stroke of the piston subtract that part of the stroke which is intended to be accomplished before the steam is cut off; divide the remainder by the length of the stroke of the piston, and extract the square root of the quotient, which multiply by half the stroke of the valve, and from the product take half the lead; the remainder will be the lap required.

191. Q.—­Can you state how we may discover at what point of the stroke the eduction passage will be closed?

A.—­To find how much before the end of the stroke the eduction passage will be closed:—­to the lap on the steam side add the lead, and divide the sum by half the stroke of the valve; find the arc whose sine is equal to the quotient, and add 90 deg. to it.; divide the lap on the eduction side by half the stroke of the valve, and find the arc whose cosine is equal to the quotient; subtract this arc from the one last obtained, and find the cosine of the remainder; subtract this cosine from 2, and multiply the remainder by half the stroke of the piston; the product is the distance of the piston from the end of the stroke when the eduction passage is closed.

192. Q.—­Can you explain how we may determine the distance of the piston from the end of the stroke, before the steam urging it onward is allowed to escape?