J.D, Everett on Reducing Observations of Temperature. 173 
Arr. XVI.—Further Remarks on a method of Reducing Observa- 
tions of Temperature; by Professor J. D. Everert, of Kings 
College, Windsor, Nova Scotia. 
J 
In an article in the January number of this Journal, I recom- 
mended for general use a method of comparing climates, as 
regards temperature, by reference to the curve whose equa- 
tion is ‘ 
=A,+A, sin (z+E,) 
We must first prove the following proposition: Any m num- 
bers, (m being either 2n or 2n+1,) can be exactly expressed by 
an equation of the form 
=A,-+A, sin (2+E,)+A, sin (2e++E,)+ ....-+-A, sin (nz+-E,), 
in such a sense that, by giving x the successive values, 
o, -<360°, 2 x360°.... = 360°, 
m ™m ™m / 
the resulting values of y will be the given numbers in order. 
We shall hereafter denote the terms on the second side of the 
above c. To prove the 
proposition, let the series be transformed, (see p. 25 of my former 
oy * 17S) g 
term, Q, sin nz, is to be omitted; and we shall have 2n equations 
to determine 2n constants. Hence, by the theory of equations, 
there will always be one and only one solution. = —__ 
The rule for obtaining the solution is extremely simple:— ~ 
To find the value of any one of the constants, multiply each 
quation by its coefficient of that constant, and add the m equa- 
tions thus obtained.’ It will be found that all the terms on the 
* It is worthy of remark that this rule is identical with that 
D 
quantities from a greater number of simple equations, when the latter are 
all of equal weight. This general rule is thus given in “Airy on Errors of Obser- 
vations,” p. 80: “Multiply every equation by its coefficient of one unknown quan- 
eicuhk ack oe Gaie cisee ouar, ott eonlh sages Bens ete 
ty; so on for every unknown quantity; and thus a number of equations 
iPM bs fitaid aegial 4a the teaser of vaknowe quantities” ie 
