60 NATURAL INHERITANCE. [CHAP. 



radius, or with an entire Ellipse in terms of its major 

 and minor axes. We can also apply the various beau- 

 tiful properties of the Law of Frequency of Error to 

 the observed values of Q. In doing so, we act like 

 woodsmen who roughly calculate the cubic contents of 

 the trunk of a tree, by measuring its length, and its girth 

 at either end, and submitting their measures to formulae 

 that have been deduced from the properties of ideally 

 perfect straight lines and circles. Their results prove 

 serviceable, although the trunk is only rudely straight 

 and circular. I trust that my results will be yet closer 

 approximations to the truth than those usually arrived 

 at by the woodsmen. 



The value of a single Deviation at a known Grade 

 determines a Normal Scheme of Deviations. When 

 Normal Curves of Distribution are drawn within the 

 same limits, they differ from each other only in their 

 general slope ; and the slope is determined if the value 

 of the Deviation is given at any one specified Grade. 

 It must be borne in mind that the width of the limits 

 between which the Scheme is drawn, has no influence on 

 the values of the Deviations at the various Grades, 

 because the latter are proportionate parts of the base. 

 As the limits vary in width, so do the intervals between 

 the Grades. When measuring the Deviation at a speci- 

 fied Grade for the purpose of determining the whole 

 Curve, it is of course convenient to adhere to the same 

 Grade in all cases. It will be recollected that when 

 dealing with the observed curves a few pages back, I 



