293 
This curve, a correct figure of which was exhibited, has its 
extreme horizontal limit when 0=33°, 32', 03", from which 
the utmost horizontal span of a uniform chain is found to be 
s x 1-325 4838, the height or versed sine being x 447 5659, and 
the length of the chain sx 1*667 1130 when 5 is taken equal to 
the modulus of strength of the material. 
This, however, does not show the absolute limit ; for, by reducing 
the thickness of the chain at each point till it be just able to bear 
the strain to which it is subjected, we shall remove all redundant 
weight. The form which such a chain assumes may be called the 
catenary of regulated strength. 
Its equations are — 
. x 
s 
X 
z=s . nep log sec — 
l = s . nep log tan 
i being the inclination of the curve to the horizon. This curve has 
two vertical asymptotes placed at the distance crs from each other, 
which distance is thus the absolute extreme horizontal span that can 
be reached by a chain having s for its modulus of strength. A correct 
drawing of this curve was also shown. 
2. On the Climate of Edinburgh for Fifty-six Years, from 1795 
to 1850, deduced principally from Mr Adie’s Observations ; 
with an Account of other and earlier Registers.— -On the 
Climate of Dunfermline, from the Registers of the late 
Rev. Henry Fergus. By Professor J. D. Forbes. 
The paper on the Climate of Edinburgh is divided into seven 
sections. 
The First Section includes an account of the earliest records of the 
thermometer at Edinburgh which are to be found in the Edinburgh 
Medical Essays . They date from 1731. They were made with a 
thermometer having an arbitrary scale, which is described In Mar - 
tine’s Essays , and they appear to have been recorded with much 
2 R 
VOL. IV. 
