xiv Tables for Statisticians and Biometricians 



we can readily integrate for the volume of every cell content, and find at once : 



A o = -sh {4842 , o + 22 (2 , i + 2 , _i + 21, o + ^-i, o) 4- z\, \ + Zi, -i + z~\, i + z-i, -1} 



...... (a), 



/i, i = Tjfo {42 o - 502 i - 22 _i - SOsj, - 22_i, o f 625^, i + 252i, _ x + 252_!, x + s_ lf _ 



...... 08), 



/! -1= 5Je {42 o - 22 i- 502 ,-i - 50^ 1>0 - 22_ 1>0 + 252 M + 625^ _ x + -1,1 + 252_i,_ 



...... (7)- 



/-i i = -rrfs {4o 0-50,00 i 2^o, -i 2^i j0 - 502-i,o 



_!, -1=5^ {4^o, o - 2^ 0) i - SO^o, -i - 2^i, o - SO^-i, + *i, i + 252], _ 

 /o I = TTTC {- 44^0, o h 550^ 0) ! + 22^0, _i- 2^ o- 22_i > 

 0> _i = ^ {- 4420,0+22^0,1 + 550^0, -1-2^ -22_ 1) 

 Ao=5f(T {-442 0>0 - 22-0,1 22 0) _i + 5502^ + 222-1, o + 

 _i )0 = ^ |-442 0)0 - 22 0) i- 22 _i+ 222i >0 + 5502_i, + 



The first of these results, i.e. that for / 0>0 , gives the frequency in the central 

 cell of a group of nine ordinates, 3 x 3, in the scheme above. The other expressions 

 may be useful, where it is impossible to use a central cell, for example, towards the 

 boundary in crateroid surfaces. 



If the units of x and y are h and k, or the cell base a rectangle hxk, then the 

 right-hand sides of equations (a) to (i) must be multiplied by hk. 



The following equations give the ordinates in terms of the nine cell frequencies: 

 *o,o = 5*B (676/0,0 - 26 (/ M +/, 



i,i = irk {4/0,0 + 276/1,! + 254/_ 1 ,_ 1 - 23 (f^+f-^) + 46 (/o,i+/i,o) - 2 (/o,-i+/-i,o)} 



...... W, 



-i = ^rr {4/0,0 + 276/i,_i + 254/_i,i- 23 (/!.!+/_!,_,) + 46 (/i, +/o,-i) 



...... (7'), 



{4/0,0 + 276/-1,! + 254/ lf _ 1 - 23 (/_i,_i +/ lfl ) + 46 (/_i, +/o,i) 



2-1, _a = ^ {4/o,o + 276/_i,_i+ 254/!,i - 23 t/U+A.0 + 46 (/ ,_i +/_i, ) - 2 



^2/0,0 + 598/0,1 - 26/ ,_! - 2 



