284 SHIP CALCULATIONS; 
DISCUSSION. 
THE PRESIDENT:—The paper by Naval Constructor T. G. Roberts on “Ship 
Calculations; Derivation and Analysis of Methods,” is now upon for discussion. 
Pror. WiLL1am HovcaarpD, Member:—The author of this paper has given to 
the student an exceptionally clear exposition of the formulas underlying ship cal- 
culations and of the principal methods in carrying them out. The comparison 
between the pure French method of applying the trapezoidal rule and that used in 
the United States Navy is interesting, and one cannot but admit that the French 
‘subtraction’? method appears shorter and simpler than the “addition’’ method. 
There isone point onwhich I do not quite agree with the author, viz., his remarks 
on page 277 that ‘“‘It is much more accurate to calculate the longitudinal center of 
gravity of the shell plating from the simple uncorrected halfgirths.’’ The longi- 
tudinal obliquity of the surface and the structural features of the shell are, in 
fact, rarely symmetrical and may often influence the position of the center of gravity 
in a longitudinal direction. Since a correction of the girth for obliquity should in 
any case be made in the weight calculation of the shell, no additional work is in- 
volved in using the augmented girth in the calculation for longitudinal center of 
gravity. 
This calculation is best carried out by first constructing a curve for the aug- 
mented girths allowing not only for obliquity, but also for overlaps at the seams 
and for deviations from the standard thickness of the plating, including doubling at 
the ends. By means of the integraph or an integrator, the weight and longitudinal 
center of gravity can then be easily determined, irrespective of the irregularities of 
the resulting diagram. The accompanying Fig. 1 shows the general character of 
such a diagram. 
CURVE OF WEIGHT OF SHELL PLATING. 
FIG.S 
The obliquity is most readily determined by measuring with a planimeter the 
area on the body plan between every second station. Dividing each area so ob- 
tained by the girth of the intermediate station, we obtain an approximate value of 
the mean distance between the two stations, enclosing the area in their transverse 
projection. This mean distance, divided by twice the longitudinal spacing of con- 
secutive stations gives the mean value of the tangent of the angle of obliquity of the 
