302 DISCUSSION or THE SECULAR VARIATION 



Investigation of the Secidar Variation — The following discussion, which is based 

 upon the preceding tabular numbers/ will be limited to the examination of the 

 secular variations of the temperature for places within the United States or 

 for adjacent stations. To ascertain in general the character of these variations a 

 number of stations were selected possessing the requisite length of series or from 

 which, by proper combination from several stations at no great distance apart, such 

 a series could be produced having as few interruptions as possible. These separate 

 or combined series were plotted (see accompanying illustration); this could be 

 done either by plotting directly the annual means, as in the case of New Haven 

 (see isolated dots), or by smooth curves, as shown for all the stations which resulted 

 from the application of the process of successive means (to the 4th order) which 

 has been explained before. This process, while it preserves all the characteristic 

 features of any systematic progression of temperature during a succession of years, 

 also relieves us in a great degree from the embarrassing presence of the accidental 

 and minor irregularities. The 4th order of means was found quite sufficient ; the 

 8th is given for New Haven. 



Further, the process of combination of the results from several adjacent stations, 

 either for the purpose of producing a more extended series, or for filling up gaps, 

 must be such as to preserve exactly any feature or features common to all the 

 stations, whether of a progressive or a periodic character as might be produced by 

 a disturbing influence of a general or cosmical nature. This will be done by the 

 method of differences, as will be explained further on. If we examine any of the 

 numerical and graphical results, for instance those for New Haven, we recognize 

 in the first place certain apparently altogether irregular fluctuations in the annual 

 means, their influence will be greatly reduced or destroyed by successive means and 

 by combination of series (since they are equally liable to -|- and — deviations, which 

 will tend to cancel themselves) ; in the second place, we notice certain systematic 

 changes or undulations of irregular epochs and extent which will be subjected to 

 further study with respect to their character and geographical distribution. If all 

 the series, proposed for combination to a normal series, were of equal extent and 

 complete, the simple mean for each year would be all that is needed, but for 

 indirectly connected, overlapping, or defective series, the combination is more 

 laborious, as we must take account of all possible differences or combinations," which 

 can only be done by application of the method of least squares. After the series 

 have all been rendered homogeneous, by application to each of the corrections 

 indicated with consideration of all possible combinations and their weights, the 

 means for each year can be taken as before. A full example of the method is 

 given below,'^ and the same is intended to show also the amount of local variation 

 in the annual means after they have been reduced to a uniform series. 



^ The tables contain altogether about 1210 stations with an aggregate of about 8500 annual means. 

 The general tables are estimated to represent nearly 11|- millions of individual observations. 



' The number of combinations of n elements by twos is expressed by — ^^r— -, 



^ Suppose it be proposed to combine to a uniform system the results of the mean annual temperature 

 of the 49-year series at Brunswick, the 37-year series at Portland, the 31-year series at Grardiner, 

 the 40-year series at Castine, and the 14-year series at Cornish, all in the State of Maine, for which 



