A. Ritchie-Scott 
403 
and where it is necessary to specify the limits of integration they will be those of 
this quadrant. Its volume will be denoted by m with, where necessary, a dis- 
tinguishing suffix. 
Hence we may wr ite 
711 = N j L z {x , y ) dx'dy' = N j z {x^ , ) dxdy (6). 
The area of the face bounding quadrant a parallel to the y axis is 
*f ' , (A', ,V,' = ^^V^\ ' p^V»''^rf, A (7). 
NH 
Since the whole area of the section is , A is the fraction which the portion 
bounding the quadrant a is of the whole section. It has no dimensions and is inde- 
pendent of and cr,,. 
Similarly the face bounding the a quadrant parallel to the x axis is 
N z{x,k')dx = — — • ' dx= B ...(8). 
-'-00 v27r a,j v27r-' -cc cr.-/ 
A and B may be taken from Sheppard's Tables when /(, k and ?• are known. 
Writing -7=-- I e '-''^ dx = S {x), 
v27r- -cc 
which is the function tabled, we have 
^-"^M and B = s C-^\ (9). 
.(10). 
Lastly we have the ordinate at the intersection of the planes 
Since y = , e 2 { i - r-) 
^ 27r Vl - r-^ 
we may write 
Vl— ?■- V27r V27r 
= -7=i=.'~7=.-^e 2(1-'=) (11), 
where -^'(a?) is the tabled function . Clearly E{h) = H, and E {k) = K. 
V27r 
