416 
The Incomplete Moments of a Normal Solid 
TABLE I {continued). 
4. 
x*z = 
(<i^ + 6d>- + 3) ^ 
a?yz = 
+ 3(^-«/r + Zr^" + 3r) ^ 
x-y'^z = 
+ c^- + ^r^^ -f- + 2r- +1)2 
5. 
x'^z = 
(0-' + 1003 + 150) 2 
x^yz = 
+ 6(i^i|r + 3-»Ir + 12r(i + 4r(f)n z 
af'y'^z = 
((f>'f- + S^yjr- + (jr^-yjr + (jri/r +3(1 + 2r^) + (f>') z 
6. 
af'z = 
(<h''+ 150^ + 4502 + 15)2 
x'yz = 
(0^1/r + 100^'A/r + 150^/^ + 3Or0= + 5r0^ + 15r) z 
X y z — 
( (h^-\li '- 4- f\fh\lr- 4- 'itlr- 4- ^ilrfhtlr 4- Kvfh^-\lr -i- (\ (1 -i- ff>2 i J.4 i Q / 1 i A^2\\ ^ 
ytp \j/ -J- ^jr -j- o ^'T/ -i- o/ <p -tU^^Xt^^/ _^u) T^<p T^o\^l-r 4<r /y 2 
T^y^z = 
(03-^3 + 303-i/r + 9 /■0^-»/rH 9?'02 + 30-^3 + 9(1 + 2r'') 0-i|r + 9r^/r2 + 3r (3 + 2r')) z 
7. 
x'z = 
(0' + 210= + 10505 4. 1050) z 
x^yz = 
(0''-»/r + 150Y + 450'->|r + lof + 9Or0 + 6Or0=' + 6r0'') 2 
x'y"z = 
(cf)'^|r- + lO03i/r- + 150^/r2 + lO?-0^f + GOrcji^f + 30/">/r + 15 (1 + 4r2) 0 
+ 10(l + 2r=) (i>^ + (l)')z 
x^y^z - 
+ 60=i/^5 + 3>/r3 + 12r03-«|r2 + 36r0x/r2 + 3^4^ + 18 (1 + 2r2) 02'«/r 
+ 9(1+ 4r2) ^/r + 12r (3 + 2r2) 0 + 12r05) z 
8. 
a?z = 
(08 + 280" + 2100^ + 4200" + 105) z 
x'yz = 
(0'i/r + 2105-»/r + lO503\|r + 1050%/r + 315r0- + lO5r0^ + 7?-0'' + 105r) z 
x'^y-z — 
((f)''f- + I5(f)'f' + 450^1/^2 + 15i|r2 + 18Or0>/r + 120r(j>'f + 12r0'A/r 
+ 45 (1 + 4r2) 02 +15(1+ 2r') 0^ + 0'* + 15 (1 + 6r')) z 
x'y^z = 
i<j>'yjr' + 30-'->/r + 30 (1 + 2r2) 0^-^ + 45 (1 + 4^^) 0^ + 30?- (3 + 2r^) 0^ 
+ 15r0-' + 1O0Y'' + 90r(j)^f' + I5(f)yjr' + 45r-»/r2 + 15r0Y'^ + 15r (3 + 4r2)) 2 
xi^y^z = 
(0^-v/r^ + 60Y' + 60^1/^" + 36 (1 + 2r2) 0--«|r- + 30^ + Sf' 
+ 4<8r(j)'f + 48r0i|r3 +18(1 + 4r2) 0^ + 18(1 + 4r2) i/r^ 
+ 48r (3 + 2r^) 4>f + 16r0»>/r3 + 3 (3 + 24r2 + 8r^)) 2. 
TABLE II. 
Polychoric functions expanded in terms of x and y. 
1. <j) (z) = xz 
2. 0H^) =(.^■■--l)2 
(pyfr (z) = {xy — r) z 
3. 0^(2) =(«s-3^)2 
0--^ {z) = (x^y — y — 2rx) z 
4. 0^(2) =(^-6*'- + 3)2 
03-»^ (2) = (a;^?/ — 3?'ic'' — ^xy + 3?') 2 
02x^-2 (2) = (a,'2_y2 _ - - 4ra2/ + 1 + 2r2) z 
5. 0'^ (2) = {x'' - 10^5 + 15a;) 2 
0-'i/r {z) = (ic^j/ — 6iz;2^ + — 4r.«' + 12r«) 2 
0^' (z) = (^'y' - Qrxry - 3a;y- - a;^ + 3 (1 + 2r2) x + 6r?/) 2 
