355

NICHOLLS'S SEAMANSHIP AND NAUTICAL KNOWLEDGE

Example.—How many square feet of plating are required to make
a rectangular tank 10 feet long, 6 feet broad, 4 feet high? (Add 10
per cent, for overlapping edges )

Area =2 sides+2 ends+top and bottom
„ =(2X10X4)+(2X6X4)+(2X10X6)
„ = 80 + 48 + 120
„ = 248
add 10 per cent. 24-8

Total 272-8 square feet

See Nicholls's Concise Guide, Volume I., Chapter IV., for further
Examples and Exercises in Mensuration.

SIMPSON'S RULES ARE METHODS FOR MEASURING THE AREAS
ENCLOSED BY PARABOLIC CURVES.

As ship-shape curves very closely resemble parabolic curves no
appreciableei'ror is introduced by utilising Simpson's Rules in calculating
areas and volumes of vessel's waterplanes and cubic capacities If
measuring the area of a waterplane it is u^uai to calculate the half arei
first and multiply the result by two. The centre line of the waterplane
is first drawn to any convenient scale and this is divided into an equal
number of parts by an odd number of ordinates.

Simpson's First Rule,—In Fig. 1 A B represents the midship line of
the waterplane; lines denoted by the letters a, b, c, d, etc., are the dis-
tances from the midship line to the edge of the waterplane AC B and
termed ordinates. The spaces between these ordinates are all

axe

equal and are termed the "common interval/' To find the area of
A B C we multiply the first ordinate by 1, and the last ordinate by 1
and the intermediate oxdinates by 4 and 2 successively; thus, if we had