2 
Proceedings of the Royal Irish Academy. 
These experiments conclnct to tlic three following eqnations, which 
constitute a solution of the problem : — 
l\ X X 0-24 + y X 0-086 + s x 0-182 = 0 
2°. - X X 0-24 + y X 0-086 + z x 0-182 = 0' 
3°. X X 1-16 + y X 1-1 + z = w. 
X, y, 2 are respectively the weights of the cane, the inverted, and 
the grape sugars in the syrup ; 6, 6', the rotative powers of the syrups 
before and after inversion. 
In equation 1°, the numerical coefficients of ^, y, z, are the rotative 
powers of a unit weight of the respective sugars. 
In equation 2°, 0-36 is the coefficient of inversion of cane sugar. 
In equation 3°, iv is the combined weight of the three sugars, each 
being estimated as grape sugar. 
II. — On the Foemation op Thenardite m Connexion with the 
DATE OE THE GlACIAL PeEIOD, AND THE TeMPEEATUEE THAT PEE VAILED 
DUEING IT, AS DEDUCED EEOM THE InELUENCE OF THE ExCENTEICITY 
OF THE EaETh's OeBIT ON THE LeNGTH OE SuMMEE AND WiNTEE IN 
Aphelion and Peeihelion. By "William K. Sullivan, Ph. D., 
Secretary to the Academy. 
[Read December 13, 1869.] 
It seems to be now generally admitted that at a time immediately an- 
terior to the human period, if not actually within it, a low tempera- 
ture prevailed over a large portion of the temperate regions of Europe 
and N'orth America, and that the cold was accompanied by a considerable 
development of glaciers. There is, however, much difference of opinion 
as to the geographical range of the low temperature, and the degree 
of cold. Both have perhaps been exaggerated, and this exaggeration has 
greatly influenced the character of the hypotheses proposed to account for 
the Glacial Period. Sir Charles Lyell and many of his followers look 
upon changes in the relative amount of land and water, and their 
distribution on the surface of the globe, as the dominant cause of changes 
of temperature in geological time. But the difficulty of admitting that 
changes in the extent and distribution of land and water sufficient to 
account for phenomena usually attributed to the action of ice, or which 
are assumed to indicate a low temperature, could have occurred over so 
large an area in geological times so recent, has led geologists to seek a 
cause in astronomical changes, especially in the influence of the pre- 
cession of the equinoxes and the revolution of the apsides on the sea- 
sons. 
Although the actual amount of heat which falls upon the northern 
hemisphere in summer, whether the latter occurs in aphelion or peri- 
helion, is equal to that which falls upon the southern hemisphere, M. 
Adhemar argues that the climatal effects are different, because the 
average temperature does not depend alone on the amount of heat re- 
