203 



transform it into 



t/J^Zey^—QyJrgx^% 

 and proceed as before. Or we might start at once with 



y^J^Sey^—^yJr^x^Q, 

 and regard x as the independent variable, and e as constant. 



The simplicity and beauty of the results obtained by Mr. 

 Harley in the case of trinomial biquadratics and quintics 

 suggested to me the following investigation, which I think I 

 communicated to him some months ago. Let 

 J'V , dry 



r being taken from to n, and A being constants. Then 7i 

 particular integrals are obtained from the formula 



by giving to m the values 0, 1, 2,, ,n, successively; z being 

 taken from to go , and zi being defined by 



where 



P=:2 A^ TT,. (m-\-zn), 



The symbol tt here introduced is such that 

 ^J=l (^_i) (1—2). .(/— r+1) 

 is its defining relation. 



Mr. Egbert Eawson, Honorary Member, read the First 

 Part of a Memoir of the late Professor Eaton Hodgkinson, 

 F.R.S. Thanks having been given to Mr. Rawson, on the 

 motion of Mr. Binney, seconded by Dr. Smith, 



The Rev. Mr. Kiukman said, " It is no ordinary renown 

 that the late Professor Hodgkinson secured to himself, and 

 for ever will reflect on Manchester. It is a great thing to 

 outstrip one's cotemporaries in commercial competition, and 

 to accumulate fairly-gathered wealth ; it is a great thing to 



