28 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 94 



that expected for the first interval, the mean values as thus reduced 

 run as follows : 



. , Mean form _ 



Assumed period a Kange 



8 m. o d 0.1 —0.6 —I.I — i.o 0.3 0.4 0.6 —0.3 1.7 



8 m. plus I d 1.9 1.0 —0.1 —0.6 —1.9 —0.3 1. 1 1.4 3.8 



The average range of the 8 months minus i day periodicity is almost 

 o.°4 Centigrade (see fig. 12, L). This range is more than twice as 

 great as for the periodicity 8 months o days. 



Pairing is not so well marked in these curves as appears in figure 12. 

 ai to ki. It, indeed, shows strongly as between curves ha, u, and J2, kg, 

 but the curves aa to go seem inclined to change form at every sun-spot 

 period of 11+ years instead of every second period, as in former 

 cases. We shall note this tendency frequently in other connections. 



Curves as to Cs of figure 12 relate to intervals when the Wolf 

 numbers generally exceeded 80. As in the corresponding case of the 

 ii-month periodicity, they show no definite deviation from the origin- 

 ally assumed period, 8 months o days. There is on the whole a good 

 agreement between the curves. Only the curve da runs counter to 

 all of the others, but it is at the same time one of the weakest, repre- 

 senting the mean of but four lines. The general mean is represented 

 in the curve, I3 and runs as follows : 



2.2 — 1.0 — 2.6 — 1.7 0.0 I.I 2.6 2. 9 



Its range is over o.°5 Centigrade. 



c. The 7-MONTH Periodicity 



The 7-month periodicity, as already stated is much modified by 

 the 5-month smoothing. However, in the curves representing intervals 

 with sun-spot numbers between 40 and 80 there is such an excellent 

 case of the pairing which starts with the year 181 9 that these curves 

 are given, ag to ka annexed to figure 12. There is no exception to the 

 similarity of the pairs from curve ba to curve ko. Two excellent pairs 

 are found corresponding to low sun spots, but generally these forms 

 change with each new sun-spot period. 



There i§ no indication in any of the analyses of the 7-month peri- 

 odicity of a departure in length from the period assumed. The fol- 

 lowing are the mean forms and ranges. The ranges may be assumed 

 to be only about half as great as would be found without 5-month 

 smoothing. 



Sun-spot Seven m. o d. mean periodic forms 



numbers ^ A , Kange 



Below 40 0.7 1.8 0.0 — o.i 0.4 — 0.6 — 1.4 o!3 C. 



40 to 80 0.8 0.3 —0.4 —0.9 —0.9 0.1 0.7 0.2 C. 



Above 80 1.2 0.8 — 1.2 — 1.9 — 0.6 0.6 1.7 0.4 C. 



