M. A. Lewenz and K. Pearson 
375 
the line of most probable values. If he must take a line at all then the only 
thing open to him is to use tlie scientific process of correlation and find the best 
fitting line. 
Scale of Product of Arcs. 
(6) We now pass to the arcs which Dr Beddoe has chosen for the basis of his 
formula. We take first his sagittal arc from nasion to inion. Dr Beddoe makes 
no reference whatever to the difficulty of determining the inion even on the skull. 
The inion is defined in the Frankfurter Verstdndigung as the point where the 
linea superior nuchae meets the median plane. But since the date of that 
concordat the further investigation of the matter has shown that this definition is 
extremely vague. Broca originally defined the inion as the median intersection 
point of the two lineae nuchae superiores. Merkel pointed out that the protuherantia 
occipitalis externa corresponded to the meeting point of two lineae nuchae supremae, 
and termed the meeting point of the lineae nuchae superiores the tuberculum 
linearum. Further the inion is often prolonged with a V-shaped projection, and 
in this case we are told that the median point of the base of this projection is to 
be considered as the inion, or that the lineae nuchae are to be continued on the 
same niveau until a median point is reached, which is to be the inion*. Now we 
shall term the median point fixed by the lineae supremae the sup)erior inion, and 
the point fixed by the lineae superiores the inferior inion. If these two points 
coincide, as they may do, then this is the inion proper. Now Schwalbe defines the 
inion as the common inion of the four lineae when they are concurrent, and as the 
superior inion when they are not. This will work fairly well on many skulls, but 
our experience shows that on certain skulls, (i) only the inferior inion can be fixed, 
* See especially G. Schwalbe: " Studieu iiber Pithecanthropus erectus," ift'i<sc/ir;/t //re il/o;-^/io?o(;ie 
und Anthropoloyie, Vol. i. p. 24, 1899. 
