ERROR TO CASES OF NORMAL DISTRIBUTION AND CORRELATION. Ill 
Fig. 6. 
^ 10. Value of C.—Let A and A' be the areas of two sections through OH at right 
angles to one another; and let V be the whole volume of the solid. Then, since 
the solid is a projective solid, OH.V = A . A' = A" (§ 6 (iv.)) ; and, since it is 
a solid of revolution, V=27ra^.OH (§ .5 (i.), and Guldinus’ theorem), But 
OH = CA/a (§ 4). Hence C = 1/^277. 
It is convenient to consider the solid as obtained from a standard form by an 
orthogonal and an axial'"" projection. As the standard solid we shall take the solid 
whose volume is unity and whose vertical sections are normal figures of semi- 
parameter unity. The central ordinate of this solid is 1/277. 
§ 11. Representation of Segment of Normal Solid by an Area. —-Let S be any 
closed curve in the base of a normal solid, whose principal ordinate is OH, and whose 
parameter is ‘la ; and let V be the portion of the solid which lies above S, i.e., which 
is bounded by S, by the surface of the solid, and by a cylinder K of which S is a 
normal section. We require a method of determining the volume V. 
Let be the upper boundary of V, i.e., the area cut out of the surface of the 
normal solid by the cylinder K. Describe a circular cylinder of radius b, and of 
height OH, having OH as axis ; and project on this cylinder by lines perpendicular 
to OH. The projection will be a closed curve a. Now the volume V can be divided 
into elements by a series of planes through OH at indetinitely small angular 
distances from one another. Let IT and TI' be two consecutive planes of the system, 
* By an axial projection of a surface or a solid with regard to a straight line is meant the surface or 
solid obtained by projecting every point orthogonally with regard to this straight line in a definite 
ratio, 
