The Locomotive - Lighthouse Survival Blog

54 THE LOCOMOTIVE. [APHIL r
Finding" of the Areas of Irregular Figures.
We have received the following communication from Mr. Thomas L. Hadley of
Woonsocket, concerning the determination of the areas of irregular figures :
" I notice that
you say in The Locomotive for January, 1890, that ' the most satisfactory way to calculate
the area of a segment is that given in The Locomotive for December, 1886. This,
method is exact, but it requires the engineer or inspector to have the table with him
whenever he wishes to calculate a segment/
Here is another method for finding the area
Fig. 1. — Area op a Segment.
of a segment. It is not original with me,
however. I believe that the idea came from
France, where it was used to find the average-
pressure of an indicator card. I have ap-
plied it also to the determination of the
areas of segments and of irregular figures.
Suppose, for example, Ave consider a boiler
6G inches in diameter, in which the upper
row of tubes is 26 inches from the top of the
shell. Suppose we allow 3 inches out for
the flange to support, and 2 inches out for
the tubes to support.. This leaves a segment
21 inches high, of a circle 60 inches in di-
ameter. To determine the area of this segment,
first draw a diagram of the boiler on
a scale of one inch to the foot, as shown in
Fig. 1. Then find the area of the whole head of the 66-inch boiler. Divide this by 2 T
which gives the area of half the head. Bisect Fig. 1, as shown by the horizontal
diameter, as only half of the diagram is needed to do the problem. Now cut out the
upper half of the diagram carefully, and weigh it. This piece in the diagram I send
Figs. 2 and 3.— Area of a Segment.
you, weighed 12.3 grains. Then cut out the
segment from this piece, and weigh that
also. You will find that the segment
weighs 6.35 grains. Then make a propor-
tion as follows:
12.3:6.35 :: 1710.6 (area of half the
head): 883.1
From which we conclude that the area of the segment is 883. 1 square inches.
"The area and average pressure of an indicator diagram may be found in the same