66 kepobt— 1879. 



I can only regret that so little help is to be got from the text-books 

 on electricity in these observations. They appear to devote most of their 

 space given to atmospheric electricity to a picture of Franklin holding a 

 kite under a shed, and another picture of a waterspout. 



Report of the Committee, consisting of Professor Sylvester, F.R.S., 

 and Professor Caylet, F.R.S., appointed for the purpose of 

 calculating Tables of the Fundamental Invariants of Algebraic 

 Forms. 



With a portion of the grant made last year, the valuable services of 

 Mr. F. Franklin, of the Johns Hopkins University, have been obtained 

 to aid in computing, under Professor Sylvester's inspection, the ground 

 forms (otherwise called the fundamental invariants and covai'iants) of 

 binary quantics of the 7th, 8th, and 10th orders respectively, thus ren- 

 dering the list of tables of such forms complete for quantics of all 

 orders up to the 10th inclusive. 



The sbeets containing the calculations referred to are deposited pro- 

 visionally in the Library of the Johns Hopkins University at Baltimore, 

 where they remain subject to the direction of the Council of the British 

 Association as to their future disposal. 



The tables of the ground forms of the seventhic are published in the 

 Comptes Bendus of the Academy of Sciences at Paris, 1878 ; the table of the 

 ground forms of the ninethic in the ' American Journal of Mathematics, ' 

 March, 1879, and in a future number of that Journal will shortly also 

 appear the intermediary tables of the Generating Functions from which 

 such ground forms are deduced, as also the ground forms and generating 

 functions connected with the tenthic. 



These tables, in addition to those previously constructed, will, it is 

 believed, form a valuable, and (for the present) a sufficient basis for the 

 prosecution of this kind of research in what regards the theory of single 

 binary quantics, leaving a wide field still open for computations of a 

 similar nature connected with systems of binary quantics and ternary and 

 quaternary quantics, single or in systems. 



Report of the Committee, consisting of the Eev. Samuel Haughton,. 

 M.D., and Benjamin Williamson, M. A., appointed for the Cal- 

 culation of Sun-Heat Coefficients. Drawn up by Dr. Haughton. 



The calculation of the quantity of sun-heat received at a given place, 

 and in a given time, on the earth's surface, neglecting the heat absorbed 

 by the atmosphere, was solved by Lambert in the middle of the last 

 century, and the researches of Poisson, Meech, and others have added 

 very little to the work done by Lambert. 



I have myself published a simple solution of Lambert's problem, 

 depending on trigonometrical series, well known and readily applied, 1 

 copies of which are now offered to Section A. 



1 Proceedings, Koyal Dublin Society, 1878. 



