How to Measure Your Own Garden Area 
A SIMPLE DEVICE WHEREBY ONE CAN COMPUTE THE SURFACE OF IRREGULARLY BOUNDED 
AREAS-THE PLANIMETER, A USEFUL INSTRUMENT IN ESTIMATING THE HOME GROUNDS 
by Arthur W. Dean 
T 
^HE prospective builder is often desirous of* knowing the 
acreage of his real estate and is in considerable difficulty in 
finding this out, especially where his land is of irregular bound¬ 
ary. Perhaps a garden surrounded by a wavy path is to be filled 
with loam, or a large space of lawn sodded. Such a proposi¬ 
tion is either regarded as extremely difficult for the laymen to 
solve, or is given up as utterly hopeless. Among the curious in¬ 
struments of the architects’ craft, however, there is one which 
renders such problems comparatively simple, and of accurate solu¬ 
tion. This is the planimeter. If one is not readily available it is 
an easy matter to make one from the following illustrations. 
All that is necessary to make a planimeter is a decimal rule 
and stiff, thin cardboard—squared surveyors’ paper makes the 
work still simpler. Take a piece of this cardboard or the sur¬ 
veyors’ paper ten inches by five and use it for the calculations. 
If we could discover some way of making a measure of vary¬ 
ing form so that it might be applied an equal number of times to 
the area in question, our difficulty would be at an end. But it is 
possible to construct a figure having such a constant measure of 
area. In this case it is a rectangle which is capable of infinite 
variation of base and altitude. This is the planimeter. 
The first step in its construction is to lay off a constant rect¬ 
angle of convenient size. In this example 5" by 1" are the dimen¬ 
sions. Divide this in two by a perpendicular line (the long dotted 
line of Figure 1), for the two rectangles, 2.5" by 1" (A and B) 
thus made, are necessary when using the planimeter from a cen¬ 
tral point. Each of these rectangles then contains 2.5" square 
inches of area. With the decimal rule mark off tenths of an inch 
upon the perpendicular and run lines paral¬ 
lel to the base through these points. Take 
the point 12/10" above the zero point N 
(Fig. 1), then plot the width or base of 
a new rectangle of equivalent area and 
12/10" altitude. By simple division we 
find this to be 2.08" and we let a dot on 
the first line, 2.08" from the perpendicular, 
represent the terminus of this new base. 
Succeeding points will be 1.78", 1.51", 
I - 39 ”> etc., respectively. Proceeding sim¬ 
ilarly along the perpendicular at every 
1/5" we plot bases of rectangles equiva¬ 
lent to our constant. After 40/10" have 
From the Builders Journal and Architectural Engineer” 
Fig. 2. When the planimeter is used from 
the central point mark the divisions made 
where it cuts the boundary 
been marked off in this manner the variation in width is found to 
be so slight that it is only necessary to add 5/10" to the successive 
altitudes. When the 100/10" point is reached, carefully connect 
the dots by a curved line. This curve is the hyperbola, and geom¬ 
etry can prove the products of each of these bases and altitudes to 
be equal. 
Simply reduplicate the area bounded by the curve, on the other 
side of the perpendicular and the whole figure is complete. Since 
the card is to be used from a centre point some notch is necessary 
to hold it against the pin, so a little superfluous edge is left and a 
cut made up to the base line as at N (Fig. 1). Cut out along the 
lines and the planimeter is ready for use. 
Find the approximate centre of the area to be measured and 
place a pin in the plan at this point. With the base resting on 
this pin apply the planimeter as shown in Fig. 2, marking a dot 
where either edge cuts the boundary of the surface to be meas¬ 
ured. Slide forward until the back edge touches the last mark 
and make another dot until the perimeter is divided all around 
in this manner. If lines were drawn from these marks to the 
center the plan would contain a number of triangles equal in 
area—in this case 2.5 square inches. Where the figure has a 
straight base line the planimeter is moved along it, base to base, 
and the resultant divisions will be rectangles, therefore, of twice 
the size of the triangles. In this instance the whole constant area of 
5 square inches is used. Simply multiply the number of triangles 
by 2.5" or the number of rectangles by 5" and you have the desired 
area. 
For illustration let it be supposed that the planimeter has laid 
off thirty-four divisions on the perimeter 
with a remainder approximated to be .4" 
of the average of the divisions on each 
side of it. The area of the figure would 
then be 34.4 x 2.5" — 86 square inches. As¬ 
suming that the plan to be plotted is 4 in. to 
the foot, we must multiply by the scale 
area or 16, which equals 1326 square feet. 
In computing Fig. 3 the principle is ex¬ 
actly similar, except constant 5 square 
inches is used instead of 2.5 square inches. 
Llsed in this manner the planimeter enables 
one to figure out irregularly bounded areas 
very easily and with sufficient accuracy. 
length of the successive bases of trial rec¬ 
tangles, those on the left, the altitudes 
division is equivalent to the whole area of 
the constant, or A plus B 
(225) 
