E. L, DeForest on a method of correcting monthly means. 155 
1 : : 1 
‘elaceie Bisin ($n.-+-n,) —sin alt C[eostn, —cos($n2--n5)], 
M,=A+- B cosz, sin bef C sinz, sin de. 
Let the above be written for brevity 
m,=A-+Béb,+Ce,, 
m,—A-+Bd,, 
m,—A+Bb,+Ce,, 
M,=A+Bb"-LCe", 
Eliminating A, B and C, and employing K and L as auxiliary 
letters, we shall find this expression for M, : 
Kao (2 —5)—¢3(b2— hy 
€,(b,-6,)—¢,(6, -45) 
c,(b2 — 6") —c'""(b, —b,) 
¢3(6—b,)—c,(b,— 03) 
M,=m,+(K+L)m,—Km,—Lm,. 
We may now proceed to compute for each of the twelve months 
separately, the numerical values of b,, d,, 5, ¢,, Cy, 6” and ec”, 
and from them the numerical coéfficients K and L, with the fol- 
lowing result: 
|S awe 
M, =m, +0036 m, +0031 m,,—-0067 m, 
M, =m, —-0127m, —-0030m, + 0157m, 
M, =m, +'0028m, —-0248m, +°0220m, 
M, =m, —:0042m, ~—-0199m, +0241 m, 
M, =m. +'0016m, —-0217m, +0201 m, 
M, =m, —-0039m, —-0179m, +0218 m, 
M; =m, +:0025m, —-0199m, +:0174 m, 
M, =m, +0025m, —-0103m, +0078 m, 
M, =m, —-0027m, —-0067m, +:'0094m,, 
M,o=m,,+'0030 m,,—"0085 m, +0055 m,, 
M, =m, , —0026 m, , ~—°0046 m, +0072 m,2 
M, 2==m,.+'0032 m,, ~°0064 m, ,+°0032 m, 
A comparison of this system of equations, found by using a 
‘trigonometrical curve, with the former system which was found 
by using an algebraic curve, is interesting as showing how far 
the values of the numerical coéfficients are independent of the 
nature of the curve employed. The fact that these two sets of 
coéflicients differ but little, tends to establish the general aecu- 
racy of both methods, and gives a high degree of pechebiiey 
the results derived from them. These results are almost iden- 
tical. For the climate of St. Paul, where the great range of 
