204 
FIFTH REPORT -1835. 
abscissae referred to the line C C as the general line of the or¬ 
dinates represent the deviations of the temperature of any point 
q for any time p taken on that line. The ordinates C B, B G, G E, 
E C make up the mean temperature line of 24 hours, or 1440 
minutes. One degree of temperature in the projection is con¬ 
vertible into 60 minutes, being equal to an hour of time. We 
may hence readily obtain the abscissae in terms of the ordinates 
or reciprocally, by merely converting degrees into time. 
It is not therefore difficult from the known equation to the 
parabola, or y~ = 4 ax, to calculate the temperature of any point 
q which should arise at any point of time p , on the supposi¬ 
tion that the four curvilinear branches are semi-parabolas, and 
so compare the observed temperatures with those of calculation. 
For this purpose the following formulae may be employed, which 
are easily arrived at. 
Let T = the temp, for any point q at any time p ; m = the 
min. = 49°; M = max. = 58° ; y = any ordinate taken on the 
line C C = variable in time. 
Then for the morning branch A B we have T = m + 
for the noon branch B D.T = M — 
for the afternoon branch D E.T = M — 
A C x y\ 
(C B) a ’ 
PGx/. 
(B G) 2 ’ 
D G x ?/ 3 . 
(GE)*"’ 
for the night branch E A.T = m + 
AC x/ 
(CEP* 
By these formulae the curvilinear branches A B, B D, of the 
* These formulae, as shown by Sir David Brewster in his investigation of the 
Leith observations, are deducible in the following way: 
Taking one of the branches, as BD, Plate X. we have by the property of 
the parabola GD «(B G) 2 . If therefore q be any point of temperature at any 
given point of time p, then in drawing p q and n q 
D G : D » :: (G Bf : (n ^ n = G D j 
• (#) (G B) 2 ' 
Now it is to be observed that G D is the deviation of the maximum = M from 
the line of mean temp. = p, and p q— Gn= (G D — n D) the deviation at time 
p ; hence temp, at point D = (p + GD) = M, and for any other point q at any 
other time p we have T = (p, - f- G D) — D n. Substituting therefore the values 
of (^4 -j- G D) and D n in this equation, we get for the branch B D, 
T = 
M — 
GD.j/ 1 
(GB) 5 
and for D E T = M — 
DG.jf- 
'(GE ) 2 ’ 
By a similar process we arrive at the formulae for the branches below the 
line of mean temperature C C in substituting m for M, the value of m being 
m = (p — A C). 
