232 
Royal Irish Academy. 
It will be perceived that this theory employs the general pro- 
cesses of analytical mechanics, as delivered by Lagrange. The first 
attempt to treat the subject of reflection and refraction in this man- 
ner was made by Mr. Green, in a very remarkable paper, printed in 
the Cambridge Transactions, vol. vii. part 1. After stating the 
dynamical principle expressed by equation (1), (though with a dif- 
ferent hypothesis respecting the density of the eether,) Mr. Green 
observes, that, supposing the function v to be known, ‘'we can im- 
mediately apply the general method given in the Mecanique Analy- 
tique, and which appears to be more especially applicable to problems 
that relate to the motions of systems composed of an immense num- 
ber of particles mutually acting upon each other.” Such is cer- 
tainly the great advantage of starting with that general principle ; 
but the chief difficulty attending it, namely, the determination of 
the function v, on which the success of the investigation essentially 
depends, has not been surmounted by Mr. Green, who has conse- 
quently been led to very erroneous results, even in the simple case 
of uncrystallized media, to which his researches are exclusively con- 
fined. In this case Mr. MacCullagh’s theory confirms the well- 
known formulae of Fresnel, one of which Mr. Green conceives to be 
inaccurate, and proposes to replace by a result of his own, which, 
however, will not bear to be tested numerically. The present theor}^ 
applies with equal facility to all media, whether crystallized or not, 
and is distinguished throughout by the singular elegance and sim- 
plicity of its analytical details ; a circumstance which the author 
regards as a strong indication of its truth. 
A paper was read by Mr. J. Huband Smith, descriptive of certain 
porcelain seals, amounting to upwards of a dozen, found in Ireland 
within the last six or seven years, and in places very distant from 
each other. 
He exhibited to the Academy one of these seals, with impressions 
of several others in sealing-wax. He stated that they were all 
uniform, consisting of an exact cube, having hy way of handle, 
some animal (probably an ape) seated upon it ; and that they were so 
precisely similar in size and general appearance as to be undistin- 
guishable, except by the characters on the under surface. Little is 
known respecting these seals beyond the mere fact of their having 
being found in this country. 
An extract from the Chinese grammar of Abel-Remusat showed 
that the inscriptions on these seals are those of a very ancient class 
of Chinese characters, “ in use since the time of Confucius,” who 
is supposed to have flourished “ in the middle of the sixth century, 
before J. C.” The remote period to which these characters are 
assigned, leaves open a wide field for conjecture as to the time in 
which these porcelain seals found their way into this country. 
The situations in which some of them have been found are re- 
markable. One was discovered in ploughing a field near Burriso- 
kane, county of Tipperary, in 1832; another was found last year at 
Killcad, in the county of Down ; another in the bed of the river 
