106 
STATISTICS: J. R. MINER 
Proc. N. a. S. 
forces do not give rise to any moment. Resolving parallel and perpendic- 
ular to the chassis, 
F' + F coso: = Ccosck" + R since", 
Fsina = Csina" — Rcosa", 
and taking moments about the center of mass, 
F'd' - Fdcosa = 5, 
or making'use of the relation between a and a'\ 
F' - Fsin(Q;-a'0/sin a" = S/d'. 
Solving these equations we obtain 
R - S/d'sma'\ 
F = sinaVsina: (C + Scosa'/d'), 
F' = sin (a — a")/sma C + S/d' (sin(Q: — a'Ocosoi'VsinQ: —1). 
Now since C = mv'^/p" and 5 = mkWxP/dt^ = mk''{d^d/dt^ + dV/dt^) 
and in the method of steering assumed this is nik'^d^O" /dt^ = mkhVd/ds'^, 
if V is constant, both terms are proportional to v"^. Consequently the con- 
clusions above stated are justified. (It is to be remarked that if v is con- 
stant, the kinetic reaction above is to be replaced by the force of traction 
necessary to maintain the velocity constant.) The term in C is propor- 
tional to the curvature, and the term in 5 to the rate of increase of cur- 
vature, the latter is greatest at the beginning and end of the curve, the 
former at the middle. 
Finally I have made some experiments to determine the coefficient of 
friction ju of rubber on slimy stone, with the conclusion that it is about one- 
fourth. Using the criterion v"^ < iigp we arrive at the conclusion that the 
safe speed for curves as above is somewhat less than ten miles per hour, 
which may account for the common traffic rule of "eight miles around the 
corner." 
THE PROBABLE ERROR OF THE VITAL INDEX OF A POPU- 
LATION 
By John Rice Miner 
Department of Biometry and Vital Statistics, Johns Hopkins University 
Communicated February 14, 1922 
In comparing the birth-death ratios of different communities we need 
their probable errors to determine the significance of observed differences. 
Let N = the population of a community, 
B = number of births in a year, 
D — number of deaths in a year. ^ 
Then the birth-death ratio or vital index is defined as ^ . 
