Polytechnic Association Proceedinos. 959 



Greeks made all their statues according to this rule. The face, 

 from the highest point of the forehead where the hair begins, to 

 the end of the chin, is one-tenth of the whole stature. The hand 

 from the wrist to the end of the middle finger, is the same. From 

 the top of the chest to the highest point of the forehead, is a seventh. 

 If the iength of the face from the roots of the hair to the chin, be 

 divided into three equal parts, the first division determines where 

 the eyebrows meet, and the second the place of the nostrils. The 

 navel is the central point of the human body, and if a man should 

 lie on his back with his arms extended, the periphery of the circle 

 which might be described around him, with the navel for its center, 

 would touch the extremities of his hands and feet. The height 

 from the feet to the top of the head is the same as the distance 

 from one extremity to the other when the arms are extended. These 

 are the general measures of the species. The lecturer then spoke 

 of geometrical forms and solids in trees, flowers, plants, fruits- and 

 vegetables. 



Common beholders, he said, see these things constantly without 

 observing them, and yet there is not a leaf nor a blade of grass 

 which does not present a treasure of geometrical beauty; for Ave 

 have leaves that are round, circular, cylindrical, oval, ovate, oblong, 

 triangular, leaves that have five angles, and so forth. The seeds 

 of .flowers have the same resemblance to geometrical solids. Among 

 fruits we have the apple, the peach, the pear, the plum, the grape, 

 the nut, and many others of a spherical or conical form. In a 

 carrot we find the cone, which cut transversly, shows concentric 

 rings and circles. The tranverse sections of trees present similar 

 rings — and the whole trunk is full of cylindrical pores for the con- 

 duction of sap. The forms of trees are conical and cylindrical; 

 the branches and twigs taper ofl" in a conical manner for evident 

 reasons. Again, in animals and their products, we remark the 

 display of geometrical provision, accuracy and beauty. The ovate 

 form of eggs; the spider's web; the heads of fishes; the cycloidal 

 flight of the eagle when pursuing his prey; the zig-zag lines made 

 b}' the hare when chased by enemies; the graceful outline of the 

 greyhound and of many other animals; in short, from the largest 

 elephant to the most diminutive animalculse, we trace geometrical 

 figures and forms. 



The hexagonal cell of the honey-bee has ahvays been a subject 



of wonder and of interest. In every regular hexagon the distance 



' from its center to any one of its angles, is exactly equal to any 



