Excerpt from Proceedings of the National Academy of Sciences of the United States of America, 1915, Vol. 1In treating similarly the formal invariants of l modulo S, we would employ the symmetric functions of the fourth powers of our values a, b, a b, and not the values themselves. For, (1, (2, (3, (4, 0) give the same point and yet lead to the values a, 2a, 3a, 4a of l, we take the fourth power to secure a value uniquely defined by the point. In the case of a quadratic form modulo S, we need only take the squares of the values.The method is applicable to invariants of several forms in any number of variables and to semi-invariants, as shown in the paper cited, which gives also a novel method of deriving modular invariants from semi invariants.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully, any imperfections that remain are intentionally left to preserve the state of such historical works.