458 
PEOFESSOR K. PEARSOE OX MATHEMATICAE 
Mean age of incidence, 8’60975 years. 
= 1-369,345 
fx. — 3-233,194 
jx^ — 19-143,575. 
The moments were not modified by Sheppard’s corrections, for these suppose contact 
of a high order at both terminals of the curve, and it was puite a,pparent that the 
curve must rise at a finite angle on the Ijiith side. Tiie follcwmg additional constants 
were then determined : — 
/3^= 4-071,222, JO-209.333, 
= 2-20.5,000, k. = 2-813,783. 
Thus K., is > 1 and <co and the distribution is of TyjDe W . Now let us suppose the 
incidence of scaidet fever to start with birth, although there might, as in the case of 
enteric fever, be really some antenatal cases. 
Turning to Section (5) we have : 
c = distance from birth to mean = 8-60975 years = 1-72195 units. 
Hence we deduce 
yo = -461,819, 
And so from (xsix.) 
— - 10-532,485, 
or, Pi = 12-974,883, 
Then from 
C z=z jx^' ~ a = a (po+l)/(pi - po - 2) 
we find 
o. = 4-268,104, 
and, finally, after d'^termining from (xxi.), 
logyo = 13-652,5078. 
Tlius the values of the frequency are given by 
logp = 13-652,5078 + 2-442,398 log (.t- 4-268,104) - 12-974,883 log.r. 
The origin of the curve is thus 4-268,104 before birth. The mode is given by 
—^ 5 ) = 5-257,842. 
Thus : a’n.o — a —- -989,738 = 4-94869 yrs. 
* See ‘ Phil. Trans.,’ A, a^oI. 186, p. 390. The remarkably sharp rise of the scarlet-fever distribution 
as compared Avith the enteric is, hoAveA^er, much against this. 
yg = "685,596. 
p, + p^ = 15-417,281 ; 
po = 2-442,398. 
