423 



Monday, May 9th, 1853. 



THOMAS ROMNEY ROBINSON, D. D., President, 

 in the Chair. 



The Rev. 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 then' 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 wa8 

 led to the conception of a calculus, whose formulae 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 2 8 + cos 2 0=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. 2 T 



