386 
nomenon observed by Dr Keller on the Aar Glacier so closely 
resembles that given by me of the water-holes on the Gorner 
Glacier, that there can be no doubt that they refer to the same 
phenomenon, and that therefore it was first noticed by Dr 
Keller, and described by him in 1847. 
T cannot however think that Dr Keller’s explanation of the 
phenomenon is satisfactory. He speaks of the holes as semi- 
circular with the arc towards the north, and attributes the 
greater depth of the northern portion of the hole to the longer 
time for which the sun will fall upon the gravel on the north 
portion of the bottom. 
This does not explain the much more striking phenomenon, 
the east and west elongation of the hole. Moreover, the holes 
are so deep in the latter part of the summer that the gravel at 
the bottom must be in shade all day. No explanation is given 
of the accompanying hummocks of ice, which are spoken of as 
if they existed before the water-hole, whereas my observations 
of last summer make it clear that they are formed subsequently. 
I therefore still adhere to the explanation given in my paper, 
which seems to me to explain all the phenomena. 
October 25, 1875. 
THE PRESIDENT (PROFESSOR BABINGTON) in the Chair. 
The following communication was made to the Society: 
On Herwart ab Hohenburg’s Tabule Arithmetice 
TpoolaharpEer€ws universales, Munich, 1610. By 
J. W. L. Guaisuer, F. R.S. 
The title more at length is ‘‘Tabule arithmetice mpoo- 
Oadarpecéws universales, quarum subsidio numerus quilibet, ex 
multiplicatione producendus, per solam additionem: et quotiens 
