480 On the Problem of Sexing Osteometric Material 
Laboratory, it is still considerably beyond the powers of most of the present 
workers in anthropometry, and probably no anatomist of the present day has the 
mathematical knowledge requisite for the solution of the reducing nonic, or the 
arithmetical patience required for the calculation of its coefficients. It has occurred 
to me, however, that the work might be considerably shortened by the following 
considerations. The bones usually dealt with are those found in ancient cemeteries, 
in plague pits, clearance pits or crypts. It is probable, though by no means 
certain, that adtdt female bones in such cases would be rather more numerous 
than male. On the other hand being somewhat smaller they are asserted by some 
writers as likely to be more frequently broken, and they certainly may more readily 
escape preservation or measurement. If we take these two causes as counter- 
acting each other, we may assume as a first approximation that the numbers of 
male and female bones will be equal. In the next place it is a result of much 
anthropometric experience that male and female variations, i.e. their standard de- 
viations, are closely alike. These again we can take equal to a fi7'st approximation. 
Accordingly, to this first approximation, our osteometric series may be considered 
to consist of two equal normal components with different means. Let the mean 
of the unsexed material be If, and let the actual means of thesexed components be 
mi, rrio, their standard deviations be o-j, o-g, and their total frequencies rii and Hg, 
where the subscript 1 refers, say, to the males, and 2 to the females. Then mj, 
m.,, cTi, 0-2) ih ih ^I'e the quantities we desire to discover. Let the moment- 
coefficients of the total material be, in the usual notation, fx.,, fi^, fj,^, /x,, and let 
N(=ni + n.i) be the total unsexed population. We shall write as customary 
/3i = /i3-//L^2^ /So = /i4//i2^ /Sg = yttgyu-sZ/xg^ Thcu, if our hypothesis be correct and the 
material consist very nearly of two equal normal distributions, /^j and /Sg ought 
to be very small, while ySg will be large in relation to them. 
It is convenient also to write : 
?3=gi92 (iv). 
Then the fundamental nonic may be written : 
q-^ - U.q-I + f - 3 - m - (37^1 ^1 + 1 
+ 8 - 3fi - 3^,^) q.? + 3 (A ^2 - I ^.K.') qi + m'K.q. - = 0. . .(v). 
where the sign of VA is determined by that of ^1*3. 
Again 
7i - 7-.' 
-72 
N, lu = 
7i_ 
-72 
N 
(vii). 
