302 
By permission of the Chairman, Mr. Hennessy explained 
some results at which he had arrived since the last meeting of: 
the Academy, relative to the influence of latitude on the posi- 
tions of the isothermal lines at the surface of the earth. Set- 
ting out from the general laws of radiant heat, he had arrived 
at a mathematical expression for the quantity of solar heat 
received at a limited area of the earth’s surface, which depends 
on an elliptic function whose modulus is the sine of the incli- 
‘nation of the equator to the ecliptic. From this he was able 
to deduce the theorem already announced as to the transpor- 
tation of the closed isothermal lines of an island towards the 
pole, by introducing the influence of latitude. It follows 
also, that the isothermal lines will be crowded more closely 
together towards the poles. He has found that the parallel 
of either hemisphere, which receives the greatest amount of 
heat from direct solar radiation, while the sun is at the same 
side of the equator, has a latitude of 7° 24’. 
Rey. Dr. Graves read a paper on the extension of Taylor’s 
theorem to non-commutative symbols. 
The Secretary read extracts of a letter from Mr. James 
Gilmour, of Coleraine, explaining the exact locality where the 
ancient gold fibula, called the Dalraida brooch in the Ulster 
Journal of Archeology, No. 13, was found. He also stated 
that Dr. Aquilla Smith had ascertained its specific gravity to 
be 15:45, and not 16°248. By permission of Mr. Gilmour, 
the brooch was exhibited. 
Dr. Petrie made some remarks on the ornamentation of 
the brooch, and explained that it was chiefly interesting as 
being made of gold, and gave it as his opinion that it could 
not be earlier than the end of the eleventh or beginning of the 
twelfth century. 
