166 ANNUAL OF SCIENTIFIC DISCOVERY. 



eye is capable of appreciating the exact subdivision of spaces, just as 

 the ear is capable of appreciating the exact subdivisions of intervals 

 of time ; so that the division of space into an exact number of equal 

 parts will affect the eye agreeably, in the same way that the division 

 of the time of vibration in music into an exact number of equal parts 

 agreeably affects the ear. IJut what spaces does the eye most readily 

 divide ? Mr. Hay supposes those spaces to be angles, not lines, be- 

 lieving that the eye is more affected by direction than by distance. 

 According to his theory, bodies are agreeable to the eye, so far as 

 symmetry is concerned, whenever the practical angles are exact sub- 

 multiples of some common fundamental angle. We should, therefore, 

 expect to find that spaces in which the prominent lines are horizontal 

 and vertical will ba agreeable to the eye when all the principal par- 

 allelograms fulfil the condition that the diagonals make with the side 

 angles which are exact submultiples of one or of a few right angles. 

 In applying this theory to the construction of the human figure, in 

 which we should expect a priori the most perfect development of 

 symmetric beauty, we find that not a single linear measure is em- 

 ployed in its construction. The line which shall represent the height 

 of the figure being once assumed, every other line is determined by 

 means of angles alone. For the female figure these angles are one 

 half, one third, one fourth, one fifth, one sixth, one seventh, and one 

 eighth of a right angle, and no others. It must be evident, therefore, 

 that, admitting the supposition that the eye appreciates and approves 

 of the equal division of space about a point, this figure is the most per- 

 fect which can be conceived. Every line makes with every other line 

 a good angle. The male figure is constructed upon the female figure 

 by altering most of the angles in the proportion of 9 to 8 ; the propor- 

 tion which the ordinary flat seven bears to the tonic. 



Mr. Russel said, that he was afraid that artists would not admit of 

 such a mathematical definition of beauty as Mr. Hay was attempting 

 to establish, yet all analogy proved that there was truth in the theory. 

 A few centuries ago the philosopher would have laughed at the man 

 who should have announced that the great irregular rocks of the earth, 

 and the stones on the road, were all formed on mathematical princi- 

 ples, and yet every one now knew that such was the fact, and the 

 science of mineralogy used these mathematical forms as the basis of 

 classification ; so in the plant and in the animal are frequently found 

 such regular repetition of the same form, and such perfect obedience 

 to mathematical principles, that it could not but be felt that one day 

 we should be able to reduce all typical beauty to mathematical forms. 

 London Athenceum, Aug. 



