of Reducing Observations of Temperature. 23 
The angle whose tangent is equal to P divided by Q is e, 
the “epoch” or “date of phase ;” and @ multiplied by the 
secant of this angle is a the amplitude in degrees of tempera- 
ture. 
_In finding a and e by logarithms, it will be sufficient to 
carry these to four places of decimals. 
A check against large errors in determining a is afforded 
by knowing that if P and Q are the sides of a right-angled 
triangle, a is the hypotenuse. 
If the year be supposed to consist of 360°, then e represents 
the interval from that day in autumn which forms the boun- 
dary between the warm and cold halves of the year to the 
15th of January. The amplitude a is approximately equal 
to the difference between the mean temperature of the year 
and that of the warmest or coldest group of thirty days. 
More accurately,* it 1s proportional (but not equal) to the 
difference between the mean temperatures of the warm and 
cold halves of the year, bearing to this difference the constant 
ratio of 1 : 1:2879. In speaking of the warm and cold halves 
of the year, I suppose the year divided at two opposite points 
in such a manner, that the greatest possible amount of heat 
shall be contained in one half, and (consequently) the greatest 
possible amount of cold in the other. 
I shall now give instances of the comparison of climates. 
The subjoined table (Table I.) exhibits the results of the 
proposed method of reduction, as applied to all those stations 
of the Scot. Met. Soc. whose observations embrace the three 
years 1856-57-58. The data are the mean temperatures of 
the stations for each calendar month on the average of the 
three years above named, as contained in the Society’s report 
for the quarter ending June 30th, 1859. 
* This definition, and also that above given for ¢, are very close approxi- 
mations to the truth as regards the actual temperatures, being true not only 
for a simple harmonic curve, but also for that more complex curve whose 
equation is given in the note, page 3. The first definition here given of a is 
only true for a simple harmonic curve. 
