312 
Variation in Chrysanthemnm leucanthemum 
the Nova Scotia lot represents a mid-season condition, somewhat later than my Figure 1, 
and the Massachusetts lot represents a condition late in the season, like that of my Figure 2. 
The criticism of Ludwig, that if Lucas had counted more heads he would have found modes on 
the series of Fibonacci, 8, 13, 21, 34, &c., is only partly true. Lucas's polygons of distribution 
are even in outline and evidently contain a sufficient lumiber of variates, and I doubt very much 
if a much larger number of heads taken at the same time would have materially changed his 
results. If Lucas had made counts of material taken at different times during the generation he 
would in all probability have found modes corresponding to those found by Ludwig in Germany 
or to those at Yellow Springs, 0.* 
From the above observations upon C. leucanthemum L. and Shull's results upon Asters, 
together with an exactly similar series of observations upon several species of insects, it seems 
that the determination of a " place-mode " on the mode of any character is not a simple matter. 
The following definition of a "place-mode," given by Davenport (1898), seems to me inadequate 
in view of the evidence. He says : " I use the word ' i:>lace-mode ' to embody a well known idea, 
namely, that a species has a different mode in different localities It fixes the 
condition of a species in a particular locality at a particular time ; it affords a base from which 
we may measure any change which the species has undergone in the same locality after a 
certain number of years." The statement " It fixes the condition of a species in a particular 
locality at a jmrticular time ," does not express, I believe, the idea contained in the word 
" place-mode." Thus, either of my lots 1 or 2, or Lucas's lots fix the condition of the rays for 
C. leucanthemum for a particular locality at a particular time, and therefore each of my two 
polygons represents a "place-mode" for the rays of C. leucanthemum at Yellow Springs. If 
this is true then there are tw'o difiTerent " place-modes " for the rays of this species at Yellow 
Springs during one and the same season. It is not thinkable that there should be two 
" place-modes " for the same species and character, at the same place and during the same 
season. Consequently, my two lots as well as Lucas's are not " place-modes," but are, as I 
have before stated, momentary states in the pyrogressive variation of a given season. 
It is well known that the several climatic factors are potent in producing variation, not only 
in the characters of animals and plants, but also in the dates between which a given species will 
appear. Thus, seasons vary, are hot or cold, ea,r\y or late, moist or dry, &c., and species of 
plants and animals are governed largely by these conditions. For example, C. leucanthemum 
may in favorable years begin to blossom by May 15, or even earlier, or in unfavorable ones the 
blossoming period may not begin until June 15 ; hence, if, in two successive seasons, one early 
and the other late, collections of this species were made on July ], the two collections would not 
represent homologous points of time in the two seasons. It is evident that the data obtained 
from such material would not represent " place-modes," neither would the two lots be comparable 
in any way, so that indications of change could be detected. I believe, therefore, that the 
"place-mode" for a species or for a character of one sjiecies should represent the average 
prevailing condition at a given place during a jieriod of observation continued through years or 
long enough to eliminate the effect of secular climatic fluctuations. 
To determine the prevailing condition for a given place and time, the variates should be 
taken uniformly throughout the season and with as little selection as possible. This would 
give a " secular-mode," since it would reveal the condition as regards variation as it exists for 
the place and season and we should then know just how much abmodality is exhibited by 
different parts of the same lot of variates, their relative strength and permanency, and the 
direction of variation from year to year, or from decade to decade. 
* It has been shown by Ludwig (1895) that C. leucanthemum has a strong mode on 21 in the 
lowland counties of Germany, and that lots from the mountain region have modes on 13 or even 8 
strongly developed. In some extremely fertile places he found strong modes on 34. This variation of 
modes with locality, soil and climate Ludwig believes to be largely due to nutrition. He has observed 
the same facts in other species of plants. 
