Ii4 
MR. W. F. SHEPPARD ON THE APPLICATION OF THE THEORY OF 
Suppose, for instance, that 2 ^ — 10- If Xj, X 2 , . . . Xg and Yj,. Y 2 , . . . Yg denote 
the “ decile ” values of L and of M respectively, the table of double classification 
will be of this form ;— 
Values of M. 
Values of L. 
1 
] 
— GO 
to Lp 
Li to 
L, 
L 2 to 
La- 
L 3 to 
L,. 
L, to 
L 5 . 
La to 
Le. 
Lg to 
L,. 
L- to 
Ls- 
Ls to 
La- 
Lg to 
+ CC. j 
! 
— 00 to . 
( 00 ) 
( 01 ) 
( 02 ) 
(03) 
(04) 
(05) 
(06) 
(07) 
(08) 
(09) 
Mj to Mj. 
( 10 ) 
( 11 ) 
( 12 ) 
(13) 
(14) 
(15) 
(16) 
(17) 
(18) 
(19) 
IMj to M 3 . 
( 20 ) 
( 21 ) 
( 22 ) 
(23) 
(24) 
(25) 
(26) 
(27) 
(28) 
(29) 1 
to M,. 
(30) 
(31) 
(32) 
(33) 
(34) 
(35) 
(36) 
(37) 
(38) 
(39) 
M, to M 3 . 
(40) 
(41) 
(42) 
(43) 
(44) 
(45) 
r46) 
(47) 
(48) 
(49) 
to Me. 
(50) 
(51) 
(52) 
(53) 
(54) 
(-75) 
(56) 
(57) 
(58) 
(59) 
]\Ie to M 7 . 
(60) 
(61) 
(62) 
(63) 
(64) 
(65) 
( 66 ) 
(67) 
( 68 ) 
^ (69) i 
M; to Mg . 
(70) 
(71) 
(72) 
(73) 
(74) 
(75) 
(76) 
(77) 
(78) 
(79) 
Mjj to M.j. 
(80) 
(81) 
(82) 
(83) 
(84) 
(85) 
( 86 ) 
(87) 
( 88 ) 
: (89) 
M,j to + CC'. 
(90) 
(91) 
(92) 
(93) 
(94) 
(95) 
(96) 
(97) 
(98) 
(99) 
The correspondint 
portions of the standard solid will be bounded by planes whose 
intersections with the base-plane will form a “plan” such as the following (fig. IT^):— 
and the volumes of these portions are equal to the one hundied compartmeuts in 
the diagram formed by shifting fig. 7 (omitting the alternate curves, which correspond 
to the values T, ’3, ‘5, '7, and ‘9 of a) through the required distance. 
* In this figure, as iu fig. 10, the base-])iane is supposed to be seen from above. lu fig. 9 it is seeu 
from below. 
