76 
no distinguished celebrity as a regal city; and hence its 
omission from the map of Ptolemy, who wrote in the century 
preceding. 
Another fact, derived both from historic evidences and 
existing remains, is, that, with the exception of the cahir 
erected by the Tuatha Dedananns, all the works appear to 
have been of earth and wood; though forts and houses of 
uncemented stones are found in other districts of equally 
ancient or even earlier date. From the uniform character 
which pervades these remains, the author concludes that 
they are the monuments of one people; and he thinks that 
the fact above mentioned may help to elucidate the origin 
of that Scotic race, which ruled in Ireland at the period of 
their construction. 
Sir William Hamilton laid before the Academy an ac- 
count of some investigations, in which he had recently been 
engaged, respecting Equations of the Fifth Degree. They 
related chiefly to three points: first, the argument of Abel 
against the possibility of generally and algebraically resolving 
such equations; second, the researches of Mr. Jerrard; and 
third, the conceivable reduction, in a new way, of the original 
problem to a more simple form. 
1. The argument of Abel consisted of two principal 
parts; one independent of the degree of the equation, and 
the other dependent on that degree. ‘The general principle 
was first laid down, by him, that whatever may be the degree 
n of any general algebraic equation, if it be possible to ex- 
press a root of that equation, in terms of the coefficients, by 
any finite combination of rational functions, and of radicals 
with prime exponents, then every radical in such an expres- 
sion, when reduced to its most simple form, must be equal 
to a rational (though not a symmetric) function of the roots 
of the original equation; and must, when considered as such 
a function, have exactly as many values, arising from the 
