sum by half the stroke of the valve; find the arc whose sine is equal to
the quotient, and add 90° 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°; 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 using these rules, all the dimensions are to be taken in
inches, and the answers will be found in inches also.

193. _Q._--Is it a benefit or a detriment to open the eduction passage
before the end of the stroke?

_A._--In engines working at a high rate of speed, such as locomotive
engines, it is very important to open the exhaust passage for the escape of