122 Report S.A.A. Advancement of Science. 



second and third order annul each other, and therefore the mean 

 of the four observations from either set, six hours apart, will be 

 equal to the mean of the day. Since, however, the fourth component 

 is practically zero at any hour, the mean of any four observations 

 equi-distant at six hour intervals will give the true mean. 



The annual normal curve of temperature is repre.sented by the 

 formula : — 



T = t+ 12-247 sin (ni50 + 23iO-o) 

 + 3-068 sin (n3oO + 6iO-8) 

 + •741 sin (n450 + 230-9) 

 + •803 sin (n6o° + 2260-2) 



Following the same line of reasoning here as we did for the 

 pressure, we see that the second component vanishes at 3h. 56m., 

 and gh. 56m., a.m. and p.m. Hence, since for either homonymous 

 pair the value of the fourth constituent is approximately 0^-8, it 

 follows that the mean of the temperatures of either pair will exceed 

 the true annual mean by about three-quarters of a degree. 



The term of third order vanishes for the epoch 3h. 28m., 7h. 

 28m., iih. 28m., a.m. and p.m.; and, therefore, we may consider 

 the mean of the obser^'ations at (3h. 30m., iih. 30m., iph. 30m.), 

 or (7h. 30m., i5h. 30m., 23h. 30m), as giving the mean temperature 

 of the year. 



The fourth component vanishes at 2h. 4m.. 5h. 4m., 8h. 4m., 

 iih. 4m., a.m. and p.m.; and, therefore, the observations at 

 (II., VIII., XIV., XX.), or (V., XL, XVII., XXIII.). may be con- 

 sidered the equivalent of the true normal mean. 



The annual normal curve of dew-point is given by the formula : 



D = d-i- 1-223 sin (ni5° + 25i°-2) 

 + ■554 sin 01300+1580-9) 

 + O439 sin (n450+ 6O-2) 

 + -068 sin (n6oO + 3420- j ) 



In the same way as before, the second component of dew-point 

 vanishes for the epoch oh. 42m., 6h. 42m.. a.m. and p.m. And at 

 these times the fourth constituent is barely 00-03 in magnitude. The 

 mean of either pair of homonymous times will, therefore, give a 

 fairly true annual mean. 



The term of third order vanishes for the epoch 3h. 52m.. 7h. 

 52m., I ih. 52m., a.m. and p.m. ; and, therefore, we may regard the 

 observations at (IV.. Noon. XX.) or (VTll.. XVI.. Midnight) as 

 turnishing the equivalent of the normal mean. 



The term of fourth order vanishes at oh. 18m., 3h. 18m., 6h. 

 ]8m., 9h. 18m., a.m. and p.m. With sufficient exactness, then, the 

 mean of the observations at (Midnight, VI., X'oon. XVIII.). or (III.. 

 IX., XV.. XXL), may be called the true mean. 



