423 
Monpay, May 9ru, 1853. 
THOMAS ROMNEY ROBINSON, D. D., Presipent, 
in the Chair. 
Tue Rey. Dr. Todd presented the following donations to the 
Museum : 
1. From William Acheson, Esq., copies of two ancient 
brooches,—one, Irish, found at Roscrea, and now in the cabi- 
net of George Petrie, LL. D.; the other, Scotch, found in the 
parish of West Kilbride, Ayrshire. 
2. From the Very Rev. Richard Butler, a steel arrow- 
head, found on Cromwell’s Hill, close to Towneley, on the 
Boyne. ; 
The Secretary reported that the conditions upon which 
the Academy’s consent to exhibit their Museum, as amended 
by the vote of the Academy at its last meeting, having been 
communicated to the General Executive Committee of the 
Exhibition, were approved of, and signed by their Chairman. 
The Rev. Dr. Graves read a paper on the properties of the 
functions of two variables employed by him in the interpreta- 
tion of his theory of triplets. 
“In interpreting my theory of algebraic triplets I was 
led to the conception of a calculus, whose formule bear a 
close resemblance to those of trigonometry. In this latter 
calculus there are two primitive functions of a single variable, 
named its sine and cosine, between which the equation 
sin? 9 + cos? @ = 1 
holds good, whatever be the value of the variable 0. Besides 
these primitive functions, there are other derived ones, such 
as the tangent, secant, cotangent, cosecant, &c., which may 
VOL. V. 2T 
