xl 
AMERICAN PREFACE. 
he kesitate about giving an explanation of the laws and conditions 
of animal or vegetable growth? No, indeed. He will assert that 
he knows much about these matters which can be described and 
taught with the utmost certainty. Ask the chemist whether he 
can inform you what gives to food that peculiar davor, lacking 
which food is not appetizing and life-supporting, and he will reply 
that it is beyond the reach of Chemical analysis, and that no 
chemically compounded food can be substituted for the natural 
product. But he will not hesitate to say that he can give a vast 
deal of other and useful Information about food ; that he can teil 
what ingredients to add to any given soil to improve the wheat 
crop, and with what to feed animals to keep tkem in health and 
to improve their flesh for the table. 
Just so it is with those who have made a study of what is called, 
for the want of a better name, Art-science. While tliey realize 
and acknowledge that many things pertaining to art have not yet 
been explained, and that some of them probably never will be, 
they, on the contrary, hold that other things have been definitely 
settled, and can be taught with precision. This ‘teachable art- 
knowledge has been derived from a study of art as illustrated in 
the works of the past, also from the study of nature as the 
original source of art. Some of it has come, indirectly, from a 
study of nature for other purposes, as for the purposes of Chem 
istry and physics ; indeed, it is impossible to draw a clear line of 
demarkation between art and Science. Art is not wholly independ 
ent of other lines of human endeavor. It may not be out of 
place to enumerate some of these teachable elements of art. 
l’ORMS AND LINES. 
All art involves the representation of forms. The simplest and 
elemental forms, those upon which rest all the varied forms of 
art and nature, are geometric. It is essential to know these as 
they really are, and the power to draw them should be acquired 
before an attempt is made to draw forms of greater intricacy. 
But the representation of forms by any method calls for lines, and 
not unfrequently for mathematical lines, that is, lines which are 
expressed by an equation. Mathematical lines are especially em- 
ployed by those who are engaged in designing the buautiful forms