in the State of New York. 251 



On the subject of the lime at which the observations are 

 made, the report states, " that they are taken as early as pos- 

 sible in the morning (say 6 a. m.) ; — at 3^ p. m., and an hour 

 after sunset. The mean is calculated by adding together the 

 morning's observation, twice the afternoon's and evening's, and 

 the next morning's, and dividing the amount by six." 



The learned individuals who have prepared the report do 

 not state upon what grounds the preceding hours have been 

 adopted, and we can scarcely conceive a reason for adopting 

 two fixed hours, viz. about 6 a. m., and at 3 p. m., and the 

 variable time of an hour after sunset Professor Dewey found 

 that 7^ A. M., 2^ p. M., and 9^ p. m., gave in North America the 

 same result nearly as that of 24 hourly observations ; and in 

 the Edin. Phil. Journal^ vol. vi. p. 352, we have shown, frona 

 the observations made by Professor Dewey, that tzco ohsewa- 

 tions at 10 a. m. and 10 p. m. gave a result still nearer the 

 mean daily temperature. Since that time the hourly meteoro- 

 logical journal has been kept at Leith ; and on the authority 

 of its results we would recommend to the Regents of the Uni- 

 versity to fix for the hours of observation any two similar 

 hours, such as 8*^ a. m. and S^ p. m. ; or 9^ a. m. and 9^ p. m. ; 

 or lO'^ A. M. and lO** p. m. ; or, what is still better, adopt the 

 two instants of the mean daily temperature, viz. 9^ 13' a. m., 

 and 8h 27 p. m. 



With regard to the rule for calculating the mean adopted 

 in the report, we think there must be some oversight ; for the 

 equation which expresses it seems to us to be identical with 

 that which gives the simple mean of the three observations. 

 Thus let a, b, c, d, be the four observations employed, and M 

 the mean daily temperature, the rule for the mean given in the 

 report is 



a j^ <2 h -\- '-Z c -\- d r= M 

 6 



Now, since a and d are observations made at the same hour 

 in the morning of two consecutive days, they must be nearly 

 the same, or, what is more correct, in the calculation of averages, 

 their difference must be inappreciable. Hence we may make 

 a =z d and a -{- d = 2 a, and the equation becomes 

 2a-\-2b-\-2c — M or a >)- 6 -f c = M 

 6 3 



