434 
Proceedings of the Royal Society 
directs its eyes each to a separate object, but habitually, when 
about to strike its prey, brings both eyes to bear upon it. Several 
experiments, mostly suggested by Wheatsone’s inquiries, were 
cited, and the conclusion was arrived at, that, although the adjust- 
ment for direct vision concur in the formation of the estimate of 
distance, the convergence of the eyes plays the principal part. 
3. On the Fall of Rain at Carlisle and the neighbourhood. 
In this communication, the author offers remarks on journals 
kept by Dr Carlyle, in the city of Carlisle, from 1757 to 1783 
inclusive; by the Rev. Joseph Golding, at Aikbank, near Wigton, 
Cumberland, from 1792 to 1810 inclusive ; and by himself at Bun- 
kers Hill, two and a half miles west of Carlisle, which is situate 
184 feet above the sea-level. The author gave tables showing the 
quantity of rain of each month and year included in these periods. 
From the averages, it appears that about twice as much rain falls 
in each of the latter months of the table as in the month of April ; 
and about one-third less rain falls in the first six months of the 
year than in the last six months, and that April is the driest month 
of the year. 
4. Mathematical Notes. By Professor Tail. 
1. On a Quaternion Integration. 
A problem proposed to me lately by my friend T. Stevenson, 
C.E., for constructing what he calls a Differential Mirror , when 
attacked directly led to the equation 
where a is a unit-ve ctor, perpendicular to fi. 
By another mode of solution it was easy to see that the integral 
must be of the form 
It may be instructive to consider this question somewhat closety, 
as the form of the unintegrated expression is certainly (to say the 
least) at first sight unpromising. 
By Thomas Barnes, M.D. 
Tp - T(/3 + a Yap) = constant. 
