218 MATHEMATICAL MODES OF 



be remembered that the breadth of the pelvis was less, and the 

 outlines of the thigh-bones were situated closer together, in the 

 male than in the female ; that also in the female the knees were 

 brought together. Besides these distinctive marks, Mr. Hay 

 had, moreover, of himself, brought in the female elbow and 

 bent out the wrist ; although he was not aware, till he (Pro- 

 fessor Goodsir) had told him, of the difference in this respect 

 between the sexes for in a well-made man the arm was 

 always perfectly straight. This showed that, however artifi- 

 cial the system, the artist might depend upon it for giving to 

 the figure the correct anatomy in its great leading features. 

 The breadth of the thorax from side to side had been ascer- 

 tained by the general angle, which gave the breadth of the 

 male thorax (33 45'), and so increased in like proportion. 

 In regard to the depth, by assuming the angle 30 again, and 

 taking the average depth of both male and female ; on the 

 harmonic hypothesis the angle for production of the equi- 

 lateral triangle, half of which gave the depth of it in the 

 female, would be 27. Now 33 45' to 30 is as 9 to 8 ; 

 whereas in the female, 30 is to 2*7 as 10 to 9 these being 

 the ratios of the major and minor tones in the science of 

 musical harmony. 



This very ingenious, piece of research was an approach to 

 those principles indicated in the previous day's and this day's 

 lectures. With regard to Mr. Hay's views, if they followed 

 the directions in the diagram, they would be mechanically 

 correct in filling up, which a little practice would enable them 

 to do, for the male as well as for the female, the outline of a 

 figure anatomically correct. 



This was an extremely useful result. If they were to view 

 it in no other light, artists were greatly indebted to Mr. Hay. 

 This could not be denied. And, without involving himself 

 or them in the hypothesis on which it depended in the ratio 

 of angles, or the number of times which they were repeated 



