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?

_A._--To find how far the piston is from the end of its stroke when the
steam that is propelling it by expansion is allowed to escape to the
atmosphere or condenser--to the lap on the steam side add the lead; divide
the sum by half the stroke of the valve, and find the arc whose sine is
equal to the quotient; find the arc whose sine is equal to the lap on the
eduction side, divided by half the stroke of the valve; add these two arcs
together and subtract 90 deg.; find the cosine of the residue, subtract it from
1, and multiply the remainder by half the stroke of the piston; the product
is the distance of the piston from the end of its stroke when the steam
that is propelling it is allowed to escape into the atmosphere or
condenser. In usin