Miscellanea 
469 
But C^ = \/(^^l{\+(l>^), and thus in the last case we ought to have f\ = '7517, and not •6275, 
which is due to an oversight in the arithmetic. 
Thus we see that the coefficient of contingency whether found from a sample of 775 or one of 
1550 from the Dictiomiry has sensibly the same value, and this value is identical with one found 
with the same classification and the same number of cases from such an entirely difi'erent source 
as the annual Who's Who. It seems clear that whether we take the present, or the long period 
of the past embraced by the Dictionary, the environmental influences which induce a man in 
this country to follow his father's occupation must have remained very steady. The coefficient 
of contingency for parental inheritance will be like the coefficient of correlation about '5. I 
think, therefore, we may say that in the choice of a profession inherited taste counts for about -| 
and environmental conditions for about g. These numbers of 2 to 1 are somewhat less than 
the 3 to 1 given by Professor Pearson on the basis of the erroneous value '6275 cited above. It 
would be extremely interesting to compare these results for an old country like Gi'eat Britain 
with those for a new country like America. A priori we should expect to find a greater freedom 
from environmental influences, a greater choice in the son, and so a nearer approach to a pure 
inheritance of taste. 
IV. On a Convenient Means of Drawing Curves to Various Scales. 
By G. UDNY yule, Newmarch Lecturer in Statistics, University College, London. 
Let an ordinary scale of equal parts, say inches, be engraved on the moving blade of a 
" clinograph," or adjustable set stpiai-e, the zero point of the scale being at the lower cud. If the 
blade be set at an angle 6 to the horizontal, the vertical distances of the points 1, 2, 3... of the 
scale above a horizontal line XX drawn through the zero point, are evidently sin 6, 2 sin 6, 
3 sin 6, etc. Hence if a curve be jjlotted to the base A' A', with the scale maintained at this incli- 
nation, it will be drawn with a scale of which the unit is sin 6, where 6 may take any value we 
please from 0° to 90°. The plotting proceeds in the ordinary straightforward way. Supposing 
two ordinates to be plotted are 8-95, 7-63, the clinograph is slipped along the T-square until 
the 8-95 of the scale falls over the i)roper vertical, when the point is pricked off ; the clinograph 
is again shifted till the 7-63 of the scale comes over the second vertical and its value is similarly 
marked, and so on. A scale of variable inclination thus becomes, for plotting purposes, a 
scale with a continuously variable unit. 
Such a scale is particularly convenient for plotting certain curves of given equation, e.g. the 
normal curves of errors, 
_ — 
y=y^Q '^"'^ 
?/q being the ordinate at the mean, and a the standard deviation. In the ordinary way, the curve 
is plotted by the aid of tables giving the value of e~^"^", the most complete tables being those 
of Mr W. F. Sheppard {Biometrika, Vol. ii. pp. 174 — 190). Intervals of, say, Ith of the standard 
deviation are marked off along the base in either direction from the mean, ordinates erected 
at these points, and their magnitudes plotted from the tabular values multiplied by y^. With 
the inclined scale this process may be considerably abbreviated. 
To divide the base, the T-square or straight-edge is turned round at right angles* to the base, 
a length, say MS, equal to the standard deviation is plotted from the mean along XX, and the 
* If the adjustment be made as described below, any inclination will do. Hence it is of no 
consequence if the two edges of the drawing board are not at right-angles. 
