278 Prof. J. R. Young on the decomposition of Functions 



I have already alluded to the influence of the sea in equal- 

 ising the temperature of places in its vicinity in my remarks 

 on the quarter ending June 30, IS^?. It moderates the se- 

 verity of winter and the heat of summer, but does not seem to 

 exercise any influence over the mean annual temperature. 

 Hence we perceive the same annual temperature may be dis- 

 tributed in various ways in the different seasons of the year. 



At Uckfield, the yearly, monthly and daily ranges are in 

 excess, which must be owing to local perturbations. By re- 

 ference to column 13, it will be seen that the annual tempe- 

 rature has been uninfluenced by these large ranges. 



The only other places at which considerable differences are 

 show^n between the calculated and observed ranges are White- 

 haven and Liverpool ; and the smallness of the ranges at those 

 places are evidently to be attributed to the vicinity of the sea. 



In conclusion, I have merely to remark, that I am persuaded 

 the spirit of the above method of reducing meteorological ob- 

 servations, and deducing from them general formulae, will 

 some day lead to empirical laws, showing the reciprocal de- 

 pendence of each subject of research. I would, however, 

 impress upon observers generally the absolute necessity of 

 using good instruments, and ascertaining their errors by com- 

 parison with standards ; such would save me a great deal of 

 labour and anxiety, which I have experienced in the past 

 year. These exertions, it is evident, could not be long con- 

 tinued ; and it must be borne in mind, that no system of cal- 

 culation can deduce good results from imperfect observations. 

 I must beg, however, to offer my sincere thanks to the gen- 

 tlemen who have furnished the observations, for their ready 

 acquiescence at all times to my wishes. 



This is the first annual report upon the meteorology of En- 

 gland. May it be followed by many, more ably conducted 

 and more valuable to meteorology! 



XXXIX. On the decompositioTi of Functions into Conjugate 

 Factors ,- isoith some co7iseguences deducible therefrom. By J, 

 R. Young, Professor of Mathematics, Belfast College"^. 



I THINK that by decomposing a function of an even de- 

 gree into its constituent conjugate factors, some interest- 

 ing results in analysis may occasionally be deduced. It will 

 be seen, from the expressions below, that this decomposition 

 is very easy ; and as the component factors involve an arbitrary 

 function, common to each pair, we are at liberty to fix its 

 value so as to fulfill certain prescribed conditions that may 

 * Communicated by the Author. 



