111 
July 21, 1845. (Adjourned Extra Meeting.) 
SIR Wu. R. HAMILTON, LL.D., President, in the 
Chair. 
Reav,—The following Resolution of Council, passed on 
16th July, 1845: 
‘¢ ResotveD,—That at the Adjourned Meeting of the 
Academy, summoned for Monday, 21st July, it be recom- 
mended to the Academy to authorize the Treasurer to sell 
Stock to the amount of £400 sterling, for the purpose of dis- 
charging existing liabilities.” 
Resotvep,—That the Academy do approve of and adopt 
the recommendation of Council, as now read; and that the 
Treasurer be authorized to sell Stock to the amount of £400, 
for the purposes described. 
Mr. Perris, V.P., having taken the Chair, the President 
continued-a paper on the Applications of Quaternions to some 
Dynamical Questions.—See Appendix, No. ILI. 
The President having resumed the Chair, the Rev. Charles 
Graves read the following paper on two methods of solving 
Biquadratic Equations. 
I.—An equation being supposed to have a pair of imagi- 
nary roots, a+ VY —1.b and a— / —1.b, if we diminish all 
its roots by the quantity a, the transformed equation would 
plainly have two roots differing only in their signs. This 
consideration suggested the following mode of solving the bi- 
quadratic equation, 
a+ aw? + a,a+a,= 0. (1) 
Let its roots be diminished by a, a quantity to be determined 
by the condition that the transformed equation, found by sub- 
stituting y + a for v, shall have two roots which differ only in 
