330SCHOOL SCIENCE AND MATHEMATICS

Hence

(n�\)ll=n, as required.

We conclude with the mention of some other results easilydemonstrated.Let k denote the ratio primary A’.central A. Then k=7 when

n = 2, as in corollary 5. This is the only case in which both n andk are integers. To make this clear note that, for n> 1, k increasesor decreases according as n decreases or increases. Now whenu==l there is no central triangle (corollary 4). Hence n is not an

integer for any integral k>7. For k=2, 3, � � � ,-6 we may con-sult the equation

n^+n+lk-

(^-l)2

This, when solved for n, has the discriminant 12k� 3. Substitu-tion of the above integers for k indicates n irrational in eachcase. The uniqueness of n = 2, k == 7 follows.

If n takes any of the values f, i, i, - �

� , the corresponding kis integral. In fact, if n-= (a+l)/a or o/(a+l), thenk =3a2+3a +1. Any other integral k requires an irrational n.

NEW PRESIDENT OF GINN AND COMPANY

At the February meeting of the directors of Ginn and Company, Mr.Frederick A. Rice, a director, and manager of the San Francisco office, waselected President of the company. Mr. E. K. Robinson was re-electedTreasurer and Mr. E. N. Stevens, Clerk and Secretary.Mr. Rice as President succeeds Mr. Henry H. Hilton who in his fifty-two

years with the organization has played a leading part in its affairs. Mr.Hilton was Chairman of the partnership for some years and has beenPresident since the incorporation of Ginn and Company in 1939. He willremain active in the company as Chairman of the Board.Mr. Rice, the new President, was born in New Jersey. His early educa-

tion was in the schools of New York City. After graduation from CornellUniversity in 1908 w-ith Phi Beta Kappa honors, he became a graduatestudent, holding the Fellowship in American History in 1908-09. As high-school teacher and administrator in the State of Washington from 1909 to1911, he gained his first experience in the field of public-school education.In 1912 Mr. Rice joined the staff of Ginn and Company’s San Franciscooffice. For many years he was assistant manager of this office under Mr.Selden C. Smith and, on Mr. Smith’s death, he became manager. In 1937he was admitted to partnership in Ginn and Company. Mr. Rice is a trus-tee of Mills College, and he has been active in various civic affairs. "He plansto move his residence from Berkeley, California, to Boston or its vicinity.