DECEMBER 1, 1899.] 
where a is the measure on the mental scale, 
T the natural period, t any other period, and 
ca personal constant. By this formula the 
various periods may be laid off according 
to their mental differences from the natural 
period. Every difference from the natural 
period is mentally a positive matter. [With 
the mental scale the law of difficulty becomes 
p=P(1+ cx) 
where p and P are the probable errors for ¢ 
and 7 respectively, « is the measure on the 
mental scale and ¢ is a personal constant. 
This is the equation of a straight line. 
The law states that the difficulty of any 
arbitrary period is directly proportional to 
its mental difference from the natural 
period. This is the statement which I 
tried to make in the note published in Scr- 
ENCE, 1896, N. S., IV., 585. 
This law of difficulty as depending on the 
period is, of course, only one of the laws of 
free rhythmic action. It is quite desirable 
that other laws of difficulty and of fre- 
quency should be determined. For ex- 
ample, observations on ergograph experi- 
ments tend to show that the irregularity 
and the natural period both change with 
the weight moved; they also change with 
the extent of the movement. 
Such a series of well established laws might 
be useful in regulating various activities to 
the best advantage. It is already recog- 
nized that it is most profitable to allow 
soldiers on the march to step in their nat- 
ural periods ; it is also known that on the 
contrary sudden and tense exertion is 
favored by changing the free rhythmic 
action into regulated action by marching in 
step and to music. More definite knowl- 
edge might perhaps be gained concerning 
the most profitable adjustments of the 
rhythm and extent of movement in bicycle- 
riding to the person’s natural period ; at 
present only average relations are followed 
in the adjustment of crank-length, gear and 
SCIENCE. 
81h 
weight to bicycle-riders, individual and sex. 
differences not being fully compensated. 
Other examples will suggest themselves. 
Not only does every simple activity have. 
its own natural rhythms; combinations of- 
activities have rhythms that are derived 
from the simpler ones. In fact, it may be 
said that the individual, as a totality, is 
subjected to a series of large rhythms fox- 
his general activity (e. g., yearly, monthly, 
weekly, daily, and so on), and also to a 
series of smaller rhythms for his special 
activities. The natural periods do not al-. 
ways correspond with the enforced periods. 
The daily rhythm is unquestionably too- 
slow for some persons and too rapid for 
others ; the unavoidable enforcement of the- 
24-hour period works a loss to all who would 
naturally vary from it, and diminishes the 
total amount of work that could be pro- 
duced by them. For large numbers of brain- 
workers the 24-hour period is too long ; for- 
many of them the natural period is prob- 
ably about 18 hours. Although about one-- 
quarter of the day is not efficiently used, 
there is little relief in splitting up the day 
into parts, because (1) the 12-hour period 
would be naturally even less advantageous 
than the 24-hour one, and (2) the rhythm 
of the environment cannot be made to 
fit. 
The progress of civilization and the 
changes in life are undoubtedly tending to 
shorten the natural period from 24 hours 
by encouraging a greater discharge of energy 
at shorter intervals. Since the 24-hour 
rhythm is a fixed one, there must be a con- 
stant effort at adjustment in this respect by 
those individuals most susceptible to the 
new influences. The survival of the fittest 
will, of course, tend to keep the natural 
rhythm not far from the 24-hour period. 
E. W. Soriprure. 
PSYCHOLOGICAL LABORATORY, 
YALE UNIVERSITY, 
August 1, 1899. 
