RECORD AND DISCUSSION OF TEMPERATURES. 



The following is an example (of a somewhat extreme case) of the method of 

 interpolation adopted in the preceding abstract. Required, the hourly temperatures 

 between, 1854, April 2d, 20 h -, and April 3d, 13 h -. The monthly means of each 

 hour (omitting the observations on the 2d and 3d) were first compared with their 

 monthly mean, when the mean diurnal variation (for the 15th of the month) 

 became known. In like manner, the variation for the preceding month was ob 

 tained; and then, by a simple interpolation, the mean diurnal variation for the 



time between the 2d and 3d was found. Let v^ v 2 v s v 4 v 2i equal the hourly 



values of the diurnal variation, t equal the mean temperature, and T resulting or 

 interpolated temperatures ; then T= t+ v j), where p a factor depending principally 

 on the transparency of the atmosphere. To find the hourly values of t and p for 

 the above interval, we select a convenient number of consecutive observations before 

 and after the interval, which, in the present case, gives the equations 



April 2, 15 h - 

 16 

 17 

 18 

 19 

 20 



21.2 = t+3.1p 

 22.3 = t +3.2 p 

 23.0 = &amp;lt;+2.8 p 

 25.0 = t+2.1p 

 28.0 = t+l.l p 

 27.0 =t + 02p 



April 3, 13 h - 

 14 

 15 

 16 

 17 

 18 



Mean 24.4 = t +2.2 p 

 And from comparison ( t = 29.1 



with each equation \p = 2. 14 j 

 Hence, hourly variation in t 0.35, and in p 0.04. 



for 17i h - 



26.9 = +3.4p 

 26.5 = t +4.0p 

 24.0 = t +3.7 p 

 25.8 = t +3.2 p 

 29.0 = t + 2.Sp 

 30.4 = t +2.1 p 



27.1 = &amp;lt;+3.2^&amp;gt; 

 = _36.8 I 



The above sets of equations were then corrected for this hourly change of t and 

 p, when the following corrected results were obtained : 



t = 27.9 

 p= 1.60 



t = 33.2 

 p= 1.90 



These values, when substituted in the equations, leave the following residuals : 



In first set 0.1 0.1 -fO.2 0.3 1.3 +1.5 Prob. error of each +0.6 



In second set 1.1 1.5 +2.0 +1.5 0.5 0.3 &quot; &quot; +1.0 



The true hourly variation in t becomes 0.24 



p &quot; 0.01 



The following table contains the interpolated values of t and p, and the result 

 ing hourly temperatures for the interval. 



Which values in the last column will be found in their proper place in the preced 



ing abstract. 



