500 Dr. D. J. Cunningham. 



than is usually the case. Perhaps the average which is given in the 

 table for the four Irish spines more nearly expresses the relative share 

 taken by vertebral bodies and intervertebral disks in the production 

 of the curve. In these the average lumbo-vertebral index is 96'3 

 and the average intervertebral index 65'6. 



In analysing the composition of the axial curve in the lumbar 

 region of the Australian spine,. J have had the advantage of the advice 

 and assistance of my friend and colleague Professor Alexander, of the 

 Engineering School in Trinity College, Dublin. The drawings which 

 illustrate this point were executed by him. The axial lumbar curve 

 was found to be composed of the segments of three circles. Thus the 

 portion of the curve which traverses the central points of the fifth 

 lumbar vertebra and of the disk immediately above and below it, con- 

 stitutes one arc ; the central points of the third and fourth lumbar 

 vertebra?, and of the third and fourth intervertebral disks, are traversed 

 by the arc of a second and larger circle ; whilst the line passing- 

 through the central points of the dorso-lumbar disk and of the first, 

 second, and third lumbar vertebrae with the intervening disks, forms 

 the segment of a third and still larger circle. Segments of three 

 circles can also be detected in the axial lumbar curve of the European, 

 -but the parts entering into the formation of these are different. The 

 fourth and fifth lumbar vertebrae with the fourth and fifth disks are 

 ranged in the arc of the lowest and smallest circle ; the second, third, 

 and fourth lumbar vertebrae with the two intervening disks, constitute 

 the segment of another circle ; whilst the twelfth dorsal vertebra and 

 the first and second lumbar vertebrae, with the interposed disks, form 

 the segment of a third circle. 



As I have explained in my " Cunningham Memoir," where I have 

 entered somewhat fully into this point, the composition of the differ- 

 ent arcs of the axial curve is one into which .many fallacies may 

 creep. Slight inaccuracies in the tracing or a deviation from the 

 mesial plane in sawing the spine will tend to vitiate the results. 



The radii of the three arcs which build up the axial lumbar curve 

 present very different lengths. In the lower part of the lumbar 

 column of the Australian the bend is much sharper and more sudden 

 than in the European. This is rendered evident when the radii of 

 the two lowest arcs are compared with each other. Again, the 

 highest segment in the European shows very little deviation from a 

 straight line. It presents a radius more than twice the length of the 

 highest segment in the Australian spine. In the European the 

 lumbar curve is more uniform and gradual throughout. The lengths 

 of the radii of the different arcs of the two spines were ascertained to 

 be as follows : 



