The Rev. H. Lloyd on the Mean Results of Observations. 65 



Hence the error committed, in taking the mean of the temperatures at any two 

 equidistant hours as the mean temperature of the day, is expressed nearly by 

 the term 



0°-70 sin (2.( + 6 7"-2); 



and consequently cannot exceed O'-TO. To obtain the pairs of homonymous 

 hours, whose mean temperature corresponds most nearly with that of the day, 

 we have only to make sin {2x + 67°.2) = ; which gives for ./; the values 



X = 56^4, ,v = 146°-4, 

 corresponding to the times 



f = S* 46'", t = 9* 46'". 



Accordingly, the best pairs of homonymous hours, so far as this problem is con- 

 cerned, are 3* 46-" a. m. and 3" 46'" p. m., or 9" 46"" a. m. and 9" 46-" p. m. 



The error committed, in taking the mean of the temperatures at any three 

 equidistant hours as the mean temperature of the day, is, very nearly, 



+ 0°-26 sm (3x + 73°-5) ; 



and cannot therefore exceed 0^26. The best hours are those in which the 



angle, in tlie preceding expression, is equal to 180° or 360^ The corresponding 



values of ,x are 



.V = 35°.5, X = gS'-S ; 

 whence 



t = 2* 22", f - 6* 22'". 

 Accordingly, the best hours of observation are 



2" 22-" A. M., 10* 22"" A. M., 6* 22" p m. • 

 and ' 



6*22'"A.M., 2' 22-" P.M., 10* 22" P.M. 



By taking the mean of any four equidistant observed values, the hmit of 

 error will, of course, be less. Its amount, which is the coefficient of the fourth 

 term of the preceding formula, is only 0°.03 ; and, accordingly, the mean tempe- 

 rature of the day is inferred from the temperatures observed at arey four equi- 

 distant hours with as much precision as can be desu-ed. 



7. The law of the diurnal variation of the atmospheric pressure is contained 

 in the following equation : 



VOL. XXII. K 



