Meteorological Observations. 121 



minimum shade temperatures — usually represented by -^ (M + m)-— 

 is rather more than a degree above the mean. Readings at XX. 

 would give much closer approximations to the true means. In 

 fact really excellent normals might be obtained thus by dropping 

 the third decimal place in the pressure, taking the temperature 

 equal to -^ (M + m + t ,1), the dew-point and humidity not requiring- 

 alteration. 



For single daily observations at a fixed hour, to give the annual 

 means, we have the following : — 



Pressure II.. <ir XXI. 



Temperature 8.45 a.m., or 7.30 p.m. 



Dew-point VII.. XVI.. or XX. 



Humidity 8.45 a.m.. or XX. 



If we resolve the annual normal curve of pressure into its har- 

 monic constituents, we may represent it by the following formula: — 



P = p + -o276 sin (ni5° + 357°-5) 

 + •0245 sin (n3oO-f 1580-7) 

 + •0017 sin (n450 + 357°-i) 

 -r '0002 sin (n6o° + 330°'o) 



Here the term of second order vanishes for the epochs 

 oh. 43., a.m. and p.m. Also for any pair of homonymous hours the 

 sum of the terms of first and third (in fact any odd) constituent 

 will annul each other, so that the mean of the observations at 

 either pair of hours will be equal to the mean of the day, plus the 

 value of the fourth constituent. This last, being '0002 inch at 

 most, at any hour, and, in fact, only .oooo4inch for the times in 

 question, may be neglected. So that for two obsen-ations per diem, 

 these will give a true annual mean. The night hour, however, would 

 not be convenient enough to all(;w the pair to which it belongs to 

 come into general use. 



Again, the term of third order vanishes at oh. 4m.. 4h. 401., 

 8h. 4m., a.m. and p.m. Also for any triplet of hours eight hours 

 apart, it is easy tO' prove that the sum uf the terms of the first, 

 second and fourth order annul each other ; and, therefore, the mean 

 of the three observations at either (oh. 4m., 8h. 4m., i6h. 4m.) or 

 (4h. 4m., i2h. 4m.. 2oh. 4m.) will be equal to the mean of the dav. 

 It will be sufficient to outline the proof for the first — and most 

 important — constituent ; those for the others being constructed upon 

 similar, though simpler, lines : — 



Let t be any hour : Then 



sin [Vi^(t+i6) i50] + sin [V, +(t + 8) 15O] . 



==2 sin [Vj H-(t+i2) 15O] cos6o° 

 = sin [V] +(t+i2) 15O] 

 = — sin (V + t -150) 



Again, the fourth component vanishes eight times a dav, at 

 oh. 30m., 3h. 30m.. 6h. 30m., gh. 30m.. a.m. and p.m. Also for 

 any four hours, six hours apart, the sum of the terms of first, 



K 



