960 Transactions of the American Institute. 



one of its sides. This is the crowning beauty of the regular hexagon, 

 and it is this peculiarity which renders it so admiraMy adapted to 

 the architectural instinct of the bee, and other insects, which con- 

 struct hexagonal cells. In common with the equilateral triangle 

 and the square, the regular hexagon can also be united, side to side, 

 to others similar and equal — a property not possessed by any other 

 regular polygon of a greater number of sides. It is well known 

 to mathematicians that the regular hexagon affords greater capacity 

 and strength, in proportion to the quantity of material, than either 

 the triangle or the square. 



In mineralogy we find cubical and spherical crystals, prisms, and 

 rhombs; such as ai'e seen on Iceland spar. On examining snow- 

 flakes beneath a miscroscope, they are found to consist of regular and 

 symmetrical crystals, having a great diversity of form. Here again 

 the hexagonal figure is the most prominent, as the majority of a 

 number of flakes show six points or sides 



The lecturer next proceeded to consider the geometrical principles 

 of architecture. The various styles of architecture which have 

 prevailed in different countries, are really exponents of the social 

 development of the people where those styles have prevailed. In 

 Egypt, where the people were serfs, and the religious ideas pre- 

 dominated over all others, the style of architecture was devised to 

 embody the idea of the vast, the infinite, the enduring. And to 

 embody these ideas, no style of architecture has j^et been devised 

 which equals the Egyptian. Its striking peculiarity is the oblique 

 line — neither vertical nor horizontal — but oblique to the vertical. 

 And this, though a simple element, when Combined with massive 

 parts and sacred symbols, gives an idea of almost eternal endurance 

 and power. The style of architecture which has been principally 

 studied for sacred edifices, is the Gothic. Here the leading ideas 

 are to embody in symbols the doctrines of Christianity, and by 

 attracting the eye of the beholder from the lower parts of the 

 l)uilding to the higher, to raise his thoughts from the things of 

 earth to the mysteries of heaven. He looks upon the foundation, 

 and has his eye carried forward by some molding, or line developed 

 in the material of the structm'e, until, on the outside, it is carried 

 up to some pinnacle, or a tower or spire; the leading lines all tend 

 upward. The ornaments are all designed according to the unerring 

 laws of geometry; so that Gothic tracery is symbolic of the unerring 

 government of Providence. The circle symbolizes eternity — imvhig 

 neither beginning nor end. The trifoliated leaves and tricuside 



