EEPOETS 



ON THE 



STATE OF SCIENCE. 



Report of the Committee, consisting of Professor Sylvester, Profes- 

 sor Cayley, and Professor Salmon, for the calculation of Tables 

 of the Fundamental Invariants of Algebraic Forms. 



The principal work performed by aid of tlie grant to the Committee 

 during the past year has been the calculation of the irreducible invariants 

 and covariants appertaining to the binary quantics of the 12th order by 

 Mr. F. Franklin, of Baltimore, under the direction of Professor Sylvester, 

 A brief synopsis of the result of this enormous computation is annexed. 



Table of the Ground- forms to the Binary Octavic Form. 



Total No. of Ground-forms (counting in the quantic itself and the absolute constant) 



= 949. 



It may be noticed that the highest order in the variables which ap- 

 pears in this table is 34, coinciding with the ' superior limit ' furnished 



