280 SHIP CALCULATIONS; 
2. Transversely.—To find the moment of inertia of an area generated 
by the elementary strips ydx about the x axis we have, since 
and 
I= ({=y' dx (5) 
3° 5 
Dividing the figure into sections by the common interval, s, we have 
the working formula 
[== y" (6) 
3 
It is necessary to remember that 
Diy SS Sap GAGE PEGE oso 3 BOR 
The error is frequently made of cubing one-half the end ordinates thus, 
3 
Sf 3 Yn 3 
2 pe aed eg 
but this error should be borne in mind and guarded against. 
VALUE OF BM. 
We know this value, as ordinarily derived, to be 
J 
For a figure, about its x axis as a base, we have found J =4( ydx; 
in the case of a water-line having symmetrical areas on both sides of the 
x axis, I = 2{y*dx. Hence 
2 3 
BM = uy de (2) 
Putting this into working form, we have 
2 3 
_ 3szy 
Ie = (3) 
