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DUEATION OF THE SEVEBAL MITOTIC STAGES IN

THE DIVIDING ROOT-TIP CELLS OF THE

COMMON ONION

BY

HARRY HAMILTON LAUGHLIN, Sc. D.

Eugenics Record Office, Carnegie Institution of Washington

Published by the Carnegie Institution of Washington
Washington, 1919

CARNEGIE INSTITUTION OF WASHINGTON
Publication No. 265

Paper No. 30 or the Station for Experimental Evolution at
Cold Spring Harbor, New York

IS'olH

PRESS OP GIBSON BROTHERS, INC.
WASHINGTON, D. C.

CONTENTS.

Summary chart Frontispiece

Index to charts, diagrams, and tables 4

roof of principle : Hypothetical case 6

Applicability of plan 7

Stage index 9

Mitotic stage duration and time-complex found in dividing root-tip cells of the onion. 9

Formula for determining the average relative duration of a given mitotic stage 9

Procession index 11

Mitotic synchronization in homologous tissue-samples 13

Cautions in method 13

Adequacy of the procession index 14

Formula for the average absolute duration of a given mitotic stage 15

Measure of accuracy 16

PreUminary experiments 18

Average relative durations of the several mitotic stages; PreUminary experiments .... 18

Probable errors 19

Other sources of possible error 21

Average absolute durations of the several mitotic stages: PreUminary experiments. ... 22
Experiments to determine the effects of temperature increments upon the several

mitotic stages 24

The velocity of chemical reactions: Response to temperature differences 24

Material for the experiments 25

Apparatus : Thermostat 26

Sampling and counting 27

Further development of the statistical method 29

a. Probable errors 29

6. Procession index 30

c. Coefficient of mitotic homogeneity 30

Further analysis of the dynamics of mitosis by the stage-timing method 30

a. Quantitative increase in data 30

b. Effects of agents other than temperatiu:e 31

c. Possible mitotic models 31

d. Cell-division in development 31

e. Relation of mitosis to other activities 31

Results and discussion 31

A. Rhythm in mitosis 32

(a) General 32

(6) Ward's work 33

(c) Additional evidence ■ 33

(d) Summary of evidence of mitotic periodicity 34

B. Heat factor in growth 35

(o) General 35

(6) Phenology 35

C. Nature of the complex in growth and mitosis 36

D. Physico-chemical aspect 37

(a) IndividuaUty in velocity reactions of the several mitotic stages to the

same temperature changes 37

(6) van't Hoff's law 39

(c) Isolation of factors 40

Elimination by comparative experimental evidence 40

A single index for two factors 41

8

4 ' CONTENTS.

Results and discussion — continued. p

(d) Difference between physiological and piu-ely chenaical temperature-

velocity reactions 42

Physiological processes 42

Growth or permanent bulk increase 42

Mitosis 43

(e) The reactions of definite mitotic stages 44

General survey 44

The movement of chromosomes 45

The peculiar reaction of mitotic stage No. 6 45

Summary 4q

References 47

Charts, Diagrams, and Tables measuring the relative and absolute durations of the several
mitotic stages, and determining the relation between temperature and velocity of each
definitely marked stage of the mitotic cycle. (All but the frontispiece in serial order
following page 48.)

Summary chart. Frontispiece.
First series: Principles.

1. Method chart.

2. Properties of four condition-complexes.

3. Principles and formulas.

Second series: Preliminary study— Based upon 13,000 cell-counts distributed among
11 stages, through 13 observation-instants (from 10 a. m. to 12 noon),
at approximately 18° C.

4. Stage index table.

5. Graphs showing mitotic and stage indices.

6. Procession index table.

7. Graphs showing orderly succession of procession indices.

Third series: Final study — Based upon 55,000 cell-counts distributed among 11
stages, through 19 observation-instants (from 10 a. m. to 1 p. m.),
one-third at 10° C, one-third at 20° C, and one-third at 30° C.

A. Average relative durations of the several mitotic stages.

8. Stage index table. 10° C.

9. Stage index table. 20° C.

10. Stage index table. 30° C.

11. Graphs showing mitotic indices at 10° C, 20° C, and 30° C.

B. Average absolute durations of the several mitotic stages.

12. Procession index table. 10° C.

13. Procession index table. 20° C.

14. Procession index table. 30° C.

15. Table: Summary and comparison by stages and temperatures.

16. Comparison at 10° C, 20° C, and 30° C. of average relative durations.

17. Comparison at 10° C, 20° C, and 30° C. of average absolute durations.

18. Graphs showing comparative average absolute durations at 10° C, 20° C,

and 30° C.
Table: Qio values (on page 38 of text).

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the duration of the several mitotic stages in the
diyidinCt root-tip cells of the common onion.

The ends sought in these studies are, (1) to devise and to prove an
accurate method for measuring the relative and aboslute average dura-
tions of the several mitotic stages in cell-division; (2) to make use of
this method in determining such durations for each of ten arbitrarily-
marked stages in the mitotic cycle of the dividing cells of the root-tips
of the onion {Allium cepa), at three different temperatures, namely,
10°, 20°, and 30° C, and thus to learn the effects of such temperature
increments upon the duration of the mitotic process as a whole and
upon each of its specifically marked stages, with the ultimate view
to aiding the analysis of the dynamics of mitosis.

The text-books generally describe the mitotic sequence in consider-
able detail; but so severe and abnormal an environment for Uving
tissues are the microscopic shde and staining fluids that only recently
has special technique developed to the extent of permitting the direct
observation of mitotic changes. Especially difficult has been the
direct observation of mitosis in any cells other than the first divisions
in the transparent fertiUzed egg in a few organisms. Consequently,
most of the data descriptive of mitotic details have been secured from
dead samples. This has given a series of pictures of situations at the
several instants of killing, which when articulated have restored the
whole cycle in correct detail, with these special advantages, that up to
instants of kilhng the tissue may be living in practically normal envi-
ronment and the high staining may bring out mitotic details as yet
unseen in living cells. But this lack of data on the timing and meas-
uring of mitotic processes under definitely controlled environments
has prevented the building up of an extensive body of facts on the
dynamics of mitosis. The existing knowledge of mitosis is largely
descriptive of structure and structural changes.

Ultimately, a process of better staining and viewing live cells may be
developed. It may then be possible to trace the normal and unham-
pered mitotic process in a single living cell and, from direct observa-
tion, to time the actual normal duration of each of its successive mitotic
stages, and thus from a large series of similar cells easily arrive at the
correct average relative and absolute durations of each stage; and
further, for the purpose of analysis, to time durations under definitely
governed and measured abnormal conditions. But for measuring the
velocities of normal activities, it is necessary, in the present stage of
development of microscopic viewing of living cells, to find some other
method of attack, one in which data are based upon mitotic processes
as nearly as possible normal and unhampered up to the instant of

5

6 DURATION OF THE SEVERAL MITOTIC STAGES

sampling, one in which the mitotic stages may be definitely marked
according to arbitrary but fixed standards, and one which will yield
numerous samples in order that the average values calculated may
have relatively small probable errors.

The method herewith presented is a statistical one based upon stage
counts and their classification, within selected microscopic fields taken
from closely related and similarly active tissues through a regular suc-
cession of observation-instants. The calculations and comparisons
shown on the accompanying Method Chart demonstrate the generality
and vaUdity, for the purpose designed, of the principle so based, and
which is employed in determining the measurements reported in
this paper.

PROOF OF PRINCIPLE: HYPOTHETICAL CASE.

The principle here employed is as demonstrable as a geometrical
theorem. For the purpose of such proof the case here first presented
(see L Method Chart) is an hypothetical one in which the mitotic prog-
ress is plotted for each of a series of related cells, through an evenly
graduated time-scale. Among the cells thus plotted there is fluctuation
in (a) the mitotic index^ (M. I.), (6) the duration of successive stages
within the same cell, and (c) the duration of stages of the same order
in different cells. This situation, as will be seen later, approximates
the actual condition of mitosis in the dividing root-tip cells of the onion.
Then transversely across the stage-duration diagram, and parallel to
the time-interval lines, are drawn at three time-intervals distant a
series of fines marking observation-instants. This graphical presenta-
tion of the stage-durations (A. Diagram plotting the situation) lends
itself to the actual counting of stages and to measuring their several
lengths, thus providing data adequate, by simple arithmetical calcula-
tions, to determine the average relative duration (A. R. D.) and the
average absolute duration (A. A. D.) of each stage type plotted. Also,
it makes possible the construction of Table B, which appears on the
lower half of the same chart. The data for this table are secured
solely by counting the different mitotic stages (including the resting
stage) at the successive periods passed through by the observation-
instant lines. From the data thus secured the average relative and
absolute durations of the several mitotic stages are calculated.

It is evident that the calculations of the average relative and abso-
lute durations made from actual counting and measure are the correct
ones for the particular case presented. The general applicability of
the results thus obtained depends entirely upon the representative
nature of the sample used; but the reliance which we may place upon

'Professor C. S. Minot first used and defined the term mitotic index, "Age, Growth, and
Death." Pop. Sci. Mo. 71: 510, 1917. It is the percent-measure of the total number of cells
showing mitotic activity in a given sample tissue.

IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 7

the determinations derived from Table B depends wholly upon the
degree of their approach to the results obtained from the actual count-
ing and measuring of the diagrammed stage durations (Diagram A, on
the upper half of the chart).

APPLICABILITY OF PLAN.

Since we may, from the study of mitotically homogeneous tissues
reared under the same conditions and killed instantaneously at regu-
larly successive intervals, construct a table with all the mathematical
properties of Table B at the bottom of the Method Chart, but can not,
from directly observed timing of a mitotically active living tissue, plot
the details of stage-successions as is done in Diagram A at the top of
the chart, it is the immediate task to establish the reliability of meas-
urements calculated from statistical data, as in Table B, and to demon-
strate the general applicability of the principles and formulas used.

It is evident that if one kills and mounts, in accordance with modern
histological practice, a tissue whose cells are actively dividing, the
relative numbers of cells found in the several successive mitotic stages
will be dependent upon two factors: (1) the percentage of cells actually
dividing at the instant of kilhng; (2) the mitotic progress each particu-
lar cell has made since it began to divide.

If all mitotically active cells began to divide at exactly the same
instant, and all had made the same progress, then but a single mitotic
stage would be seen in the sample. If in, not a single tissue, but in
many tissues wherein mitosis had begun at the same instant and
had made the same progress, samples are taken at short time-intervals
(shorter than the duration of the shortest mitotic stage), it is evident
that, if the total counts per sample be equal, the summations of counts
of each of the several types of cells in the whole series of samples will
show the greater number of cells to have been killed while passing
through the longer stages, and similarly a lesser number during the
shorter stages. In such case it is further evident that if in the stage-
sequence there is a stage whose length is shorter than the time interval
between the observation-instants, it is possible that such a stage may
be missed in the sampling, and since under the conditions above referred
to all cells of the same sample are in the same mitotic stage, an in-
crease in the number of cells counted in the sample would not supply
a chance of including it, nor would such increase in the size of the
sample have any bearing upon its representative character.

If, however, most of the cells had begun to divide at about the same
time, and had progressed about evenly, an observation early in the
process would reveal a relatively high number of early stages; simihrly,
a late observation would reveal a relatively large percentage of the
late stages. The term relatively is here very important, for the cell-

8 DURATION OF THE SEVERAL MITOTIC STAGES

numbers of an observation-instant selected at random, when the mitotic
index has not been constant, depends (a) upon the number of cells in
the sample having begun mitosis previously to the observation-instant,
and (b) upon the mitotic progress each has made prior to the observa-
tion-instant. Thus, if a large number of cells had begun dividing at
about the same time, but sufficiently remote and properly timed to
bring each of them to a certain very short stage at the time of killing,
and also the same number of cells had begun dividing at a different
period of time, but properly removed so as to bring their mitotic pro-
gress to one of the longer stages at the instant of kiUing, the numbers
of cells actually counted in these two stages in this one sample would
be equal and would not, therefore, measure the relative duration of the
two stages. If, however, in closely related tissues behaving mitoti-
cally in exactly the same manner, a series of samples be taken, both
earlier and later than the sample above named, in the later samples the
earlier stages become rarer and the later more numerous, and vice
versa the earlier samples show a rarer number of the later stages and a
greater number of the earUer ones.

But if cells of the tissues sampled had begun mitosis at different
instants throughout the cycle of the mitotically most advanced cells
sampled, at a random instant of sampling there would be found a con-
fusing variety of mitotic stages. This is the situation plotted, and
analyzed in the method chart, because (as previously stated) it approx-
imates most closely the actual mitotic condition in the growing root-tips
of the onion. As a matter of common knowledge, these differences are
known to represent a cross-section and instantaneous view of many
cells in varying stages of mitotic progress. Because in the plan fol-
lowed (a) the series of samples is fairly representative of the whole
mitotic sequence, and (b) the total number of cell-counts per sample,
regardless of the mitotic stage, is large and constant,^ an examination
of the method chart shows that even when the mitotic index (M. I.)
fluctuates greatly, and the successive stages are of varying durations,
these differences coincide and average so that throughout the sampling
the summation of the counts of a given definite mitotic stage measures,
in proportion to the total number of cells counted for all stages, the
average relative duration (A. R. D.) of this particular stage. Thus,
not only the duration of the stage but also the mitotic progress which
each cell has made up to the instant of sampling must be provided for
in any statistical analysis of mitotic progress.

Further, if in this same set of mitotic conditions, sampling and
counting, the observation-instants are further removed from each
other than the duration of the shortest mitotic stage considered, it is
possible that the sampling may omit such stage altogether, but the
probability of its being included increases with the number of counts

1 If not constant, correction can be made by means of the Stage Index (S. I.) (see p. 9).

IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 9

per sample; and even in this case of very short stage-length, if the
sample be large, the stage-length is proportional to the summation of its
corrected counts. Unlike one of the hypothetical conditions earlier
described, wherein mitotic progress runs exactly parallel in all of the
mitotically active cells, in the present case of fluctuating mitotic indices
and variously beginning mitoses, the representative character of the
sample and the accuracy of the determinations are increased with the
number of cell-counts per sample.

STAGE INDEX.

The stage index (S. I.) simply casts into percentage the actual count
of each of the several mitotic stages observed in the sample. Thus, for
arithmetical purposes, correction is made for the population or size of
the sample and for fluctuation in the mitotic index, if the resting stage
be not included in the cycle. Mathematically the formula is stated as

„^ T 1 /CI T \ No. of cells in given mitotic stage.
Stage Index (S. I.) =

Total number of mitotically active
cells observed in the same fields.

If in each sample the cell-count continues until 100 dividing cells are
counted, the stage-counts are directly proportional, each to each, to
the stage indices. If, however, the count be continued until 100 cells,
including the resting cells, are tallied, and the stage index refers to the
percentage of the cells actually dividing, i. e., if the resting stage be not
included in the cycle, then, as in the first treatment of the actual
studies presently to be set forth on mitosis in the root-tip cells of the
onion, such simple proportion does not hold good and the stage index
must be calculated for each count.

MITOTIC STAGE DURATION AND TIME COMPLEX FOUND IN THE
DIVIDING ROOT-TIP CELLS OF THE ONION.

Finally, we come to the actual complex of mitotic conditions found
in the growing root-tips of the onion, namely: (a) fluctuating mitotic
index, implying variation in the numbers of cells beginning and ending
mitosis at successive instants; (6) stage-lengths varying in successive
order in the same cell; (c) variations also among stages of the same order
in different cells; (d) closely parallel mitotic processes in different but
similarly appearing root-tips of the same bulb.

FORMULA FOR DETERMINING THE AVERAGE RELATIVE DURATION
OF A GIVEN MITOTIC STAGE.

Having determined the effect of each of these complicating factors
a, h, and c (factor d is treated on p. 13) upon the cell-count of successive
mitotic stages, and made corrections for each, we find that if samples
of tissues mitotically active as above described be taken at regular and
short intervals throughout at least a considerable portion of one cycle,

10 DURATION OF THE SEVERAL MITOTIC STAGES

and if corrections be made by means of the stage index for mitotic index
fluctuation and the size of the samples, the sunmaation of the percent-
age-frequencies (that is, of the stage indices) of a given stage in the
several successive samples will measure the average relative duration
(A. R. D.) of that particular stage. The one additional compHcation
(factor c) not present in the last hypothetical case does not change the
rule for this particular type {i. e., average) of measurement. Mathe-
matically stated, the formula for this determination is:

S S. I. of the given stage in all

Average relative duration (A. R. D.) ^ observations.

of a given mitotic stage. s S. 1. of all stages included in the

cycle, in the same fields.

This equals also the average stage index for the particular stage in the
series of samples.

Let us now consider the average absolute duration (A. A. D.) of the
several mitotic stages. If the mitotic index did not vary, but remained
constant throughout the day, and the coefficient of variabiUty for the
duration of stages of 'the same order were low, a single root-tip sample,
just as accurately as many samples, would supply data for measuring
the average relative durations of the several stages. The accuracy of
such measurements would vary with the square root of the number of
cells counted within the sample or samples. While such a condition
of constant mitotic index would, if it existed, greatly simplify the
determination of the average relative durations, it would debar entirely,
by the method herein used, the determination of the average absolute
durations of the several stages.

It is fortunate, therefore, for the particular investigation in hand,
that such fluctuation in the mitotic index really exists in the growing
root-tip of the onion. For, in order to make this latter measurement
(A. A. D.), it is necessary first to trace through a succession of mitotic
stages and time-intervals a definite, recognizable mitotic wave. The
conditions conducive to an accurate measurement of the average abso-
lute duration of the several mitotic stages depend upon (a) the sud-
denness and greatness of change in the number of cells beginning the
mitotic process during the period of observation; (b) the greatness of
the number of such waves; (c) the greatness of the number of stages
traced through each individual wave (if fractional lengths of waves are
used and if they are not equally distributed over the whole cycle, they
must be applied only in determining the A. A. D. within their respec-
tive sections); (d) the greatness of distance apart of these waves,
especially if some of the stages involve a high percentage of the entire
cycle; (e) the approximation to constancy in durations of the mitotic
stages of the same order.

\A^ile variations in none of these five factors would impair in the
least the determination of the average relative duration of the several

IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 11

mitotic stages, the character of each is vital in finding the average
absohite duration. And, since the relative duration for all of the
several stages is so readily and accurately determinable, it suffices to
find only the average absolute duration for a few stages, whereupon
determining these latter durations for the whole cycle of stages is a
matter of simple calculation. This, also, is indeed fortunate, for, if
the waves were closer together than the time-period measuring the
duration of the longest mitotic stage, the curves marking their progress
would in the longer stages become inextricably tangled. The phenom-
enon of one wave running into another, thus destroying the recogni-
tion of the identity of both in their further progress, may well be called
jamming. Thus, in the studies made on the onion root-tip it was
found ad\dsable to eliminate (for the purpose of tracing definite waves,
but not for measuring the average relative durations) the resting stage,
which consumes a large percentage of the duration of the entire cycle.
In some cases even stage 1 (which, in the onion, when the growing
temperature was 30° C, was found to be of even longer duration than
the resting stage) may have to be eliminated in order to prevent
jamming, but, as was seen above, such elimination does not preclude
the determination of the absolute duration of a definite portion of the
mitotic cycle, and thence by simple calculation of each definite stage.

PROCESSION INDEX.

Throughout the actual studies on the onion, as in the Method Chart,
it was found necessary for the purpose of locating mitotic waves, to
calculate for each stage-count not only the stage index (S. I.), but also
a procession index (P. I.). The stage index corrects the deviations
from the actual wave-course in the stage index table in so far as such
are caused by differences in the size of the samples and by variation in
the mitotic index. Such correction lends itself directly to the purpose
of calculating the average relative durations, but it does not possess
properties enabling one, by connecting high values in a succession of
such indices (S. I.), to trace a mitotic wave through a succession of
time-intervals and stages in which the stage-lengths of different orders
vary to any considerable degree. It is necessary, then, for wave-
tracing purposes, further to correct the stage-index values by tak-
ing into consideration the average length of each stage into which
the cycle is divided. This correction is accomplished by means of a
Procession Index (P. I.). In order to secure this (i. e., the P. I.) for a
given count, the stage index (S. I.) is divided by the average rela-
tive duration (A. R. D.) of the particular stage. Thus cross-section-
ing partially corrects the differences in magnitude of the successive
values of stage indices in the path of the mitotic wave, due to the dif-
ferences in length of the several stages. The correction is complete
in latitude and longitude, but is only partial in altitude; it suffices to

12 DURATION OF THE SEVERAL MITOTIC STAGES

trace the wave much as one follows a mountain range, with consid-
erable certainty, but not expecting each successive peak to reach a
uniform altitude. In this connection the critical student will examine
the procession index tables (Nos. 12, 13, and 14) with the greatest
care. He will satisfy himself concerning the definiteness — i. e., the out-
standing clarity and unbranching continuity of the waves as indicated
by the connecting lines. Also he will seek especially to determine
whether the absence of data for observation-instant number 12 in the
20° C. series and for number 2 in the 30° C. series impairs or destroys
the possibihty of accurate range-tracing.

Theoretically, the proper correction of the stage-length, in order to
eliminate the difference due to variation in the duration of the several
stages, would consist in subtracting from an increased stage index of a
given stage, at a given instant of observation, the stage index of the
same stage for the next previous observation-instant. Thus corrected,
the stage indices would provide a wave of procession indices passing
through successive stages and time-intervals and connected by points
registering the same magnitude. But such mathematical procedure
would be possible only in case the normal stage index (that is, of those
cells not in the new wave) of each stage in every sample were always
proportional to the average relative duration of its own stage. In
such a case the procession indices for all stages and time-intervals
not in the new wave would be zero, while those for the new wave
would be marked throughout by points of equal magnitude. It is
easily determined by the actual counting and classifying of mitotic
stages in onion root-tip cells that there exists no such condition as fol-
lows: Uniformity in the mitotic index for a considerable number of
minutes, then suddenly a much larger and a definite number of cells
begin to divide and progress in a thoroughly parallel manner to the end
of their several mitotic processes, then at the completion of mitosis, by
the suddenly increased number of cells, the mitotic index drops to
exactly the same level as existed before the sudden beginning of the
new wave. But rather, the facts are, in the material studied, that
the mitotic index rises and falls continuously and in small increments,
only occasionally presenting a major wave, and even then none too
easily recognizable.

All this comphcates but does not prevent the location of definite
mitotic waves; but we have to be satisfied with a mountain-range
effect instead of a dead level in the corrected heights of the points
tracing such waves. The formula finally developed for the procession
index is not the subtraction-rule above referred to — the actual mitotic
complex in the material used precludes that — but is a ratio-rule which,
as demonstrated immediately hereinafter, accounts for all of the com-
plicating factors and gives the wave-effect sought. Mathematically

stated, the formula for the procession index used is:

s. I.
Procession Index (P. 1.) = . ^ „
A. R. D.

IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 13

MITOTIC SYNCHRONIZATION IN HOMOLOGOUS TISSUE-SAMPLES.

In connecting procession indices of highest values, one observes that
such connecting lines run in the direction expected — that is, they trace,
as on the crest of an actual mitotic wave, progressively through suc-
cessive tinie-intervals and mitotic stages. This is one of the cardinal
proofs of the adequacy of the scheme of attack here followed, because
it demonstrates conclusively that the greatest theoretical handicap of
the plan (namely, the possibility that the mitotic processes are not
running approximately parallel in the homologous tissues sampled) does
not exist. For if such parallelism did not exist, no such orderly pro-
cession, as is here traced, would be possible.

Additional evidence that, in homologous samples, mitotic processes
do run parallel is found in the work of Ward,^ Kellicott,^ and Kar-
sten.^ They show that in mitotically active tissues there is rhythm and,
moreover, that the high points of such pulsations occur, more or less
specifically, for the same tissues grown under the same conditions, at
definite periods of the day. Further evidence consists in the fact that
in the growing root-tips of the onion the different tips from the same
individual onion, grown under the same condition and having attained
the same length and appearance in the same period of time, must have
passed through processes of cellular growth and mitosis practically in
a parallel fashion. A discussion of an index of mitotic homogeneity
is presented later in this paper (p. 30).

CAUTIONS IN METHOD.

There are two other features of the mitotic cycle which should be
considered in their bearing upon the relation between stage-count and
average relative duration:

(1) The cycle begins in a single cell, while at the end of stage 10 we
find, in place of one mitotically active cell, two resting cells. Must
rectifications be made looking toward a correction in the determination
of the average relative duration of the resting or other stages on this
account? The origin of the cells observed makes no difference in the
fact that the longer they, on the average, remain in the resting or in any
other stage, the more apt they are to be found in that stage at a subse-
quent random observation-instant. If (a) the number of cells in the
tissue sampled be small, and (b) all must be counted, and (c) all mitotic
sequences in all cells synchronized exactly, the law of averages would
not take care of this doubling factor in its bearing upon average relative
duration; but in the tissues studied only a small fraction of the cells
were used, and the mitotic indices of these tissues had been fluctuating

^ Ward, H. M. "On the biologj' of Bacillus ramosus (Fraenkel), a schizomycete of the River
Thames." Pro. Roy. Soc. 58: 265-468, 1895.

^ Kellicott, W. E. "The daily periodicity of cell-division and elongation in the root of Allium."
Bui. Torr. Club, 31: 529-550, 1904.

^ Karsten, G. "tJber embryonales Wachstum und seine Tagesperiode." Zeit. Bot. 7: 1-34,
1915.

14 DURATION OF THE SEVERAL MITOTIC STAGES

greatly for many previous generations, so that this otherwise sudden
doubling effect is entirely lost — scattered over long time-intervals —
in the average. The fact that there is a mitotic cycle is, in the kind
of study here made, of biological import only. Mathematically, the
resting stage and the ten arbitrarily marked subsequent divisions of its
mitotic course might just as well have been eleven successive sections
from the middle of an indefinitely long process.

(2) There is always a chance that a cell permanently — so far as
mitosis is concerned — set aside in the root-structure may be included
in the counting. Such inclusion, in the statistical method here fol-
lowed, would tend to lengthen the average duration of the resting
stage, as indeed it should (but would not make it indefinitely long, as
would actually timing each cell by the direct observation method) ; but
since this study is primarily one on mitotically active cells, it was
sought to eliminate this factor by (a) confining the cell-count to cells
within two root-tip diameters of the extreme tip, and thus to avoid the
region where many non-dividing cells are being left behind; and (b)
by basing the calculations first upon the ten mitotically active stages
and later upon the cycle as a whole.

ADEQUACY OF THE PROCESSION INDEX.

The adequacy of the procession indices and the inadequacy of the
actual counts and of the stage indices, to trace mitotic waves which are
plotted graphically in Diagram A of the Method Chart, are shown in
Table B of the same chart. The solid line through Table B traces an
attempt to follow a mitotic wave through successive time-intervals and
stages by connecting the high points in the actual count. It can be
seen at a glance that by this method, in the situation here plotted, one
wave is early confused with the other, and that thereafter the whole is
incapable of further analysis.

The line of dashes indicates a similar attempt to trace the same
mitotic wave by connecting the highest points of the stage indices. In
this case the correction is made for difference in (a) size of the sample,
and (b) variation in the mitotic index. If several successive stages
were of approximately the same length, this indeed would suffice to
trace the wave (as would in fact the actual cell-count, if also the sam-
ples consisted of the same number of counts) ; but in the stage index a
processional correction is not made for variation of length of successive
stages of the same cell. One sees, by examining the Method Chart, that
tracing by count or by stage index is satisfactory until one comes to
stage 4, a very short stage compared with the previous ones. Neither
the actual count nor the stage index can, in tracing a wave, cross such a
stage — the bridge is shorter (1.2 min. to 4.7 min.) than the width of
the chasm (10 min.). Thus, not only the stage-count but also the
stage-index method of wave tracing fails.

IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 15

The dotted line attempts successfully to follow a mitotic wave
through successive time-intervals and stages, as one may judge by
comparing the actual plotting of the stage successions in the diagram
with the wave traced in the table, for here the final correction (in addi-
tion to that of the S. I.), namely, that for variation in the average
relative duration of the several stages, is partially made. One may
glance at this diagram and with the eye readily trace the course of two
mitotic waves; first the complete wave (No. 2) in the middle of the
plot, and second, earlier than this one, what appears to be the ending of
another (No. 1). Then, comparing such actual waves with their
mathematical treatment in the table below them, one's confidence in this
statistical method of tracing mitotic waves is established, especially
since the later stages of the earUer wave overlap, in the same observa-
tion-instant, the earlier stages of the later wave. In counting and
classifjdng cell-stages in an isolated sample, this overlapping presents
hopeless confusion; in the diagram the counts of successive samples
begin to coordinate in orderly manner; but only in the procession
indices (P. I.) of the statistical table (B) are the analysis and reorgan-
ization of the mitotic pulsations definitely achieved.

FORMULA FOR THE AVERAGE ABSOLUTE DURATION OF A
GIVEN MITOTIC STAGE.

The locations of the waves having been established, the duration of
definite sections of the cycle is determined in each particular case by
counting the number of time units passed through by the particular
wave traced, and the average duration of a single stage by dividing the
number of time units by the number of stages the wave passes through.
In case sections of cycles are included in such determinations, they
must on the average equably cover the entire cycle, for in each case a
given section of a wave subtends its component stages which may be of
varying durations. The average is then made of these several determ-
inations. The average absolute duration for the cycle is calculated by
multiplying the number of stages in the cycle by the average absolute
duration per stage. The average absolute duration of a particular
stage is then determined by multiplying the percentage measuring the
average relative duration of the particular stage by the number of
time-intervals measuring the average absolute duration of the entire
cycle. Mathematically stated, the formulas for the average absolute
duration of the entu-e mitotic cycle and for a particular stage are:

Average absolute durationi
of entire active mitotic I
cycle (A. A. D. of C.) ... J

Time periods elapsing between two points
in a recognizable procession of P. 1

No. of stages covered.

No. P. 1. waves followed.

No. 1

of

>xj

stages

in
cycle.

Average absolute duration]

of a given mitotic stage [■ = A. A. D. of C. X A. R. D. of S.
(A. A. D. of S.) J

16 DURATION OF THE SEVERAL MITOTIC STAGES

MEASURE OF ACCURACY.

Reverting once more to the Method Chart, we find that by actual
count and measure from the diagram, the average relative durations of
the five stages run: 0.3213, 0.2609, 0.2167, 0.0398, 0.1611. The same
measurement, that is, the average absolute durations of the several
stages calculated from the stage indices of Table B, are: 0.2912, 0.2843,
0.2171, 0.0352, 0.1719. Similarly, by actual count and measure from
the diagram, the average absolute duration of the stage series measures,
in tune-units: 13.84, 11.24, 9.70, 1.78, 7.66; a total for the cycle of
44.25; an average of 8.92. While the same measurements calculated
through Table B give: 13.32, 13.00, 9.93, 1.61, 7.86; a total of 45.74;
an average of 9.14. The close approximation in this test case, of
the series of results derived from the table to those calculated from
first-hand count and measure in the diagram, establishes the general
vaUdity of the principle followed and demonstrates that results secured
from such tables alone may be expected to approximate the truth
within a relatively small error, provided that the size and representa-
tive character of the sample and the closeness and number of observa-
tion-instants in an actual case are comparable (in relation to their
stage and cycle durations) to the same relations in the hypothetical
case. Or, presenting the principle in another manner, granted that the
diagram is correct (an exact picture of a representative sample actually
taken). Table B derived from it will approximate it in proportion to
the greatness of the number of observation-instants. Only by chance
would the determinations of the table and the diagram be exactly the
same.

The relatively small fluctuation in the duration of average stage
length among the waves actually traced (see lower left-hand corner of
charts 12, 13, and 14) indicates a consistency in turn indicative of
accuracy in measurements and deductions.

We know that if in an actual case we find a definite percentage of
cells in a given stage at a given observation-instant, and at the next
observation find this percentage changed, there is a net difference, but
just where in the interim between observation-instants each particular
cell-stage changed we do not know. The closeness of the observation-
instants tends to lessen the error due to this fact.

The facts bring us again (see p. 7) to this: From the data secured in
observing homologous dead material killed at regularly successive
time-intervals, we can not plot an exact diagram of mitotic stage suc-
cession in a given cell ; nevertheless we can construct the exact anolog
to Table B (Method Chart) with all of its mathematical properties,
including its characteristic close approach to the actual facts. This is
what was done, and thus the data are supphed for the determinations

IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 17

in both the preliminary and the fuller investigations reported in this
paper.

The governing maxim in these studies has been: A maximum of
biology and a minimum of mathematics. Continual recourse was had
back to actual biological fact. Biometrical formulas mathematically
derived are mathematically correct, but if in course of their develop-
ment a single false biological factor enters, all subsequent derivations
are false. Full cognizance of this danger is in mind as the accompany-
ing principles and formulas are set forth. They are nevertheless pre-
sented with the confidence that they are sound, both biologically and
mathematically. We may safely say that although we can not see the
mitotic details in actual process of transformation we may determine
the average duration of the successive mitotic stages with fully as great
accuracy as would be possible if we were able to follow the normal
and unhampered mitotic train directly with our eyes (see charts 1
and 6).

The work of developing the statistical method of interpreting from
dead material the facts concerning stage duration in live material and
that of conducting a series of preliminary cytological experiments were,
of necessity, carried on at the same time; for thus only could these two
phases of the investigation mutually suggest and correct. The work
was undertaken with the feeling that there must exist a definite mathe-
matically determinable relation between the number of cells found in a
given mitotic stage at a given time and the relative duration of that
particular stage. The purpose was to find, demonstrate, and formulate
such relationships.

To begin the work the only thing to be done was to count and classify
the cell-stages in comparable samples of mitotically homogeneous
tissues killed in successive order. So far as development of the sta-
tistical interpretation was concerned, it was possible only to construct
charts and diagrams plotting different hypothetical condition-com-
plexes in reference to mitotic activity, and then inductively from these
to work out the mathematical properties of each factor contributory
to the complex relationship between the cell-counts as distributed among
specific stages and the average and absolute durations of their respec-
tive stages. Unless, indeed, one can see and retain in mind the set of
comphcations involved in each different situation, it would seem that
such plotting and coordinating of situations in accordance with known
biological facts constitute the only safe method of procedure in devel-
oping formulas adequate to solving this particular problem. The
properties and usefulness, for the end sought, of several of these situa-
tion-complexes are summarized in an accompanying table (No. 2) bear-
ing the title ''Properties of four condition-complexes in reference to
mitotic indices and stage durations." These are way stations reached
in seeking the final solution.

18 DURATION OF THE SEVERAL MITOTIC STAGES

PRELIMINARY EXPERIMENTS.

In the first experiments the samples used were the growing root-tips
of a reddish commercial onion about 1.5 inches in diameter. They
were sprouted in water at an ordinary room temperature which during
their period of growth fluctuated around 18° C, thus preventing the
possibiHty of eliminating the temperature factor, but that was not the
purpose of the initial study; temperature effects were to be considered
in a later investigation. After 5 or 6 days the root-tips had reached a
length of 5 to 10 mm. Thirteen samples were taken at lO-minute inter-
vals, from 10 a. m. until 12 noon on the same day early in February
1916. Each sample was dropped immediately into a numbered vial
of Fleming's fluid, and each was duly prepared, sectioned longitudinally
(6 microns), mounted and stained with Heidenhain's hematoxyhn.
Then, within two root-tip diameters of the extreme tips, that is, in the
mitotically most active region, microscopic fields were selected at ran-
dom in which the cells were counted and classified as to the stages of
their mitotic progress. In each of the 13 successively cut root-tips
1,000 cells, including both those mitotically active and resting, were
observed and classified. The same 10 active mitotic stages which were
used in the subsequent and fuller study constituted the basis of classi-
fication.

The accompanying Summary Chart figures and describes each of these
arbitrarily marked sections of the mitotic cycle. Since the mitotic
process is a continuous one, there are as many stages in its course as one
may care to mark ; nevertheless there are striking transformations which
appear to occur with relatively great rapidity, and hence their begin-
nings and ends make suitable mile-posts for studying and comparing
absolute and differential progress. When less numerous divisions are
required, cytologists generally have named the stages of the mitotic
cycle as follows: (1) resting, (2) prophase, (3) metaphase, (4) ana-
phase, (5) telophase. In these studies ten stages were marked off
with arbitrary but definite boundaries in order to provide a more re-
fined analysis of the mitotic cycle than the usual fewer and more indefi-
nite stages just named imply.

AVERAGE RELATIVE DURATIONS OF THE SEVERAL MITOTIC STAGES.

PRELIMINARY EXPERIMENTS.

Applying the principles demonstrated in the method chart, the stage
index chart of the preliminary work gives for the average relative dura-
tions of the successive stages the following series:

0.4473, 0.2218, 0.0933, 0.0266, 0.0077, 0.0096, 0.0089, 0.02S1, 0.0367, 0.1196

These results are based upon 13,000 individual cell-counts, and if the

IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 19

total population of the several samples were the one controlling factor,
these findings would consequently be much more to be relied upon than
the total of 708 counts recorded in the Method Chart ; but in evaluating
the accuracy of these results it must be borne in mind that (a) the num-
ber of individual cell-counts, the greatness of which tends to increase
accuracy, must be considered; (6) the greater the number of stages into
which the mitotic cycle is divided the greater the chance of error; (c)
the greater the number of observation-instants the greater the accuracy
of the determination; and (d) the shortness of intervals between
observation-instants conduces to greater accuracy.

PROBABLE ERRORS.

These four factors all tend, in so far as their bearing upon accuracy is
concerned, in the directions above indicated, but their incorporation
into a single accuracy-measuring mathematical formula has not yet
been accompHshed. Indeed, none of the several probable-error formu-
las now used in biometrical study will apply here. In planning the
later studies cognizance was taken of the directions in which all of the
aforenamed accuracy-factors operate, and the conditions of experimen-
tation, so far as possible and feasible, were modified in accordance with
these teachings to make for greater precision in the determinations.

The probable error is a measure of accuracy for certain classes of
data, but when (a) the data in hand are not from material homogeneous
throughout the sampling, or (b) the values involved fall below 5 or 6
per cent, or (c) if the absolute numbers of individuals in the several
classes of the series are low, the probable errors as now calculated are
not valid.

The mitotic index is found by applying the following rule:

. Number of cells dividing.

Total number of cells (both resting and
dividing) observed in the same fields.

In these studies on the duration of the several mitotic stages in onion
root-tip cells only the mitotic indices lend themselves to the usual
probable-error corrections. This is because they alone, of all ratio-
results here presented, are measured by high percentages derived from
relatively large numbers. But even in case of the mitotic indices each
probable error so calculated is comparable with no other like determi-
nation of the series, because in each case the material is characteristic
of a given time of day, i. e., of a given instant in the mitotic rhythm, and
of a given temperature — that is, the population is homogeneous in the
given sample only. Nevertheless, the probable-error formula appli-
cable in each particular case is :

20 DURATION OF THE SEVERAL MITOTIC STAGES

In which Po= percentage of cells dividing, Pi = percentage of cells
(dividing and active) in the same field, N= population of sample. The
determination of standards with which to compare such probable errors
would naturally be a part of any investigation seeking to develop a
coefficient of mitotic homogeneity. (See p. 30.)

If a probable error could be calculated for each of the several stage
indices of these determinations, it would greatly simplify the calcula-
tions of such a measure for all of the subsequently calculated values,
because a stage index is an element in each of them. While the stage
index is of the same nature as the mitotic index, and normally should be
subject to the same probable-error formula, still it is not so easily cor-
rected, for, as a general rule, the values of the stages indices fall
below the critical point, namely, 5 or 6 per cent.

The fundamental principles upon which the determination of this
study are based are demonstrably sound, but it is not possible, in the
present stage of biometrical science, to supply formulas which will
measure mathematically the approximation to the actual values of the
several calculated determinations. Some other common-sense method
of estabhshing our confidence in their degree of accuracy must be
applied; so let us continue by the comparative method to gage the
accuracy of the determinations of the hypothetical case, the preliminary
study, and the completer experimentations.

It is quite evident that the determinations of the average absolute
duration will possess a greater relative error than do those of the average
relative duration, because the absolute value of a given stage is based,
(1) upon the absolute duration of the whole cycle, which itself is subject
to an error, and (2) upon the average relative duration of a given stage,
which also possesses an error. An element in reducing error in the
average absolute duration is the greatness of the number of waves
traced. In the hypothetical studies, in which temperatures were con-
stant, 6 waves were traced through the series grown at 10° C, 6 through
that at 20° C, and 7 through that at 30° C.

Taking into consideration only the total populations of the samples,
we find that if the populations sampled be homogeneous throughout,
accuracy (or the approximation to the truth) is not directly a function of
frequency or numbers, but is a function of the square root of such fre-
quency. One must, therefore, if he would halve his approximation to
the truth, quadruple the quantity of his observational data. Since in
the preliminary study there were 13,000 cell-counts, or 18.35 times the
708 of the Method Chart, it is clear that if the data were taken from
a homogeneous population (which is not the present case) the determi-
nations based upon the 13,000 counts would in their approximation to
the truth deviate on the average only :;^== as far as those based upon
708 counts. In the final studies of this investigation, the first series
consisted of 19,000 counts, 26.77 times the number of the Method

IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 21

Chart, and consequently deductions from such data would be expected,
on the average, to vary only ;7^= as far from the actual values; but
other factors enter.

In the hypothetical study 708 cell-counts were distributed among 27
observation-instants and 5 mitotic stages. In the preliminary study,
which was made on onion root-tips, 13,000 cell-counts were distributed
over 13 observation-instants, and classified among 11 stages (10 active
and 1 resting) ; while the final study consisted of a total of 55,000 cell-
counts divided into 3 subordinate studies, the first with 19,000 counts
and the second and third with 18,000 each. In the first the counts
were distributed over 19 observation-instants and among 11 (10 active
and 1 resting) mitotic stages; the second and third were each distributed
over 18 observation-instants and among the same 11 stage- types. As
was earlier pointed out, until all these factors have been joined in an
accuracy-measuring formula, we must be content to balance in judg-
ment the factors which later may be balanced mathematically and
with the highest efficiency. In our experimentations we can, there-
fore, in the interest of accuracy, only increase as much as feasible the
quantity of each type of data in the direction proven to make for
the reduction of error.

OTHER SOURCES OF POSSIBLE ERROR.

But it must not be concluded that all of the sources of error in a study
of this sort are traceable to lack of extreme refinement in statistical
methods. For instance, the matter of judging the individual cells and
classifying them into their previously determined stages is important,
especially since it is indeed difficult to draw a sharp line of demarcation
between the end of one stage and the beginning of another. Moreover,
in counting and classifying so many (55,000) cells, on the basis of
mitotic condition (10 active and 1 resting stage) there is a possible
source of error of interest both to biologists and psychologists; the
criterion for classification are apt to undergo evolution in the ob-
server's mind. This diflBculty was attacked by establishing the criteria
set forth in the three figures (see Summary Chart) for each stage marked
off. From the examination of these it will be seen that the difference
between the last condition of one stage and the first of its successor
is very slight and is determined in most cases by a single point of differ-
ence, the principle being to characterize these stages not by general
conditions descriptive of their means, but to set them off by clean-cut
lines. If error crept into the determinations because of this difficulty,
it would probably have come in between stages 1 and 2 — that is, where
the criteria for distinctions are the least well marked. We find in stage
1 but Httle acceleration in the 20° to 30° C. rise, while in stage 2 in the
same temperature rise we find the largest velocity increment in the
whole series. This compensating coincidence may lend color to the

22 DURATION OF THE SEVERAL MITOTIC STAGES

theory that a confusion actually occurred here. If stages 1 and 2
actually respond about the same to heat changes, a clean-cut differen-
tiation in classifying them in the early countings and a gradual uncon-
scious evolution of conscious criteria in the later thousands, in which
stage 2 was crowded in favor of stage 1, would give the phenomena
recorded. At no other point in the determinations is there such a diffi-
cult distinction to miake, nor is there such another adjacent pair of
values that might be accounted for by such an error. However, the
much greater duration of stage No. 1 over stage No. 2 precludes the
possibiUty of errors in then* distinction, greatly changing the determi-
nations for No. 1, the longer one. When we test this possible error
by uniting stages 1 and 2 into a single stage, we find the following:

A A D.atlO°C. = 74.36min.; at 20° C.= 67.49 mm.; at 30° C. = 52.67
mm. Qio 10° C. to 20° C.= 1.10; Qio 20° C. to 30° C.= 1.28

still giving a stage, sluggish hke No. 1, in the 20° to 30° C. temperature-
rise response. This indicates strongly that the values calculated for
stage 1 are certainly quite correct and those calculated for stage 2 can
not be challenged on the grounds of the immediate criticism, and
therefore that the striking difference in their calculated temperature
reactions is real.

AVERAGE ABSOLUTE DURATIONS OF THE SEVERAL MITOTIC STAGES.

PRELIMINARY EXPERIMENTS.

A further examination of the Stage Index Table (No. 4) of the prelim-
inary study reveals no recognizable mitotic wave passing through a suc-
cession of mitotic stages and time-intervals. This confirms the evidence
of the Method Chart that connecting the high points of the stage index
sequence through mitotic stages and time-intervals will not, in the
situation-complex existing in the material used, suffice to determine the
average absolute durations of the several stages. The procession indi-
ces of the preliminary study were worked out in accordance with the
principles analyzed in detail in the Method Chart, and the result shows
clearly 3 different progressive waves passing, as would be expected, in
an orderly manner through successive mitotic stages and time-inter-
vals. The calculations from these 3 waves give the average dura-
tion of the entire mitotic cycle of these 10 active stages to be 172.2
minutes. Dividing this value in proportion to the average relative
duration of the several stages, the average absolute duration of the
10 successive stages is as follows (in minutes) :

77.02, 38.19, 16.06, 4.58, 1.32, 1.65, 1.53, 4.83, 6.31, 20.59

These results are based upon large portions of 3 waves, while those in the
Method Chart were based upon only 2 waves. If, as is seen, the average

IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 23

absolute durations of the several stages of the Method Chart thus cal-
culated approximate so closely the correct values obtained through
actual counting and measure, one is justified in concluding that por-
tions of 3 waves based upon 16 times as many individual cell-counts,
although upon twice as many mitotic stage types, and ^ as many
observations, would probably as closely approximate the actual facts.

The average relative duration of the resting stage in this prelimi-
nary work proves to be 66.12 per cent of the entire cycle, when such
cycle is conceived to consist of both the resting stage and the 10 mitotic
stages, thus crowding the 10 active stages into 33.88 per cent of the
11-stage cycle. Consequently, the average absolute duration of the
resting stage, during the period sampled, is 336.06 minutes, and
that of the entire cycle (including the resting stage and the 10 active
stages) is 508.26 minutes,^ which (so far as the number of cells of
the region sampled is concerned) means a doubling in about 8 hours,
near neither the minimum nor the maximum for such processes.

A word of explanation is perhaps necessary concerning that chart (No.
7) of the preliminary study entitled '' Graphs showing orderly succession
of procession indices." This chart is simply another method of show-
ing the data tabulated in the Procession Index Table (No. 6) of the
same study. The 3 recognizable mitotic waves are traced by the heavy
lines connecting successive stages through time-intervals. A heavy
line begins at the highest point in the early periods of sampling attained
by one of the highest indices of the region. If, by chance, as in wave 1,
this happens to be the index for stage 1, at 10^20"^ a. m., the next crest
touched must be later than 10*'20'°, and must be that for stage 2, and
so on. Thus we connect stages 1, 2, 3, 4, and 5 in one of the straightest
lines of the tangle. Wave 2 begins with stage 4, at 10 a. m. This pre-
sents a single backward step in that the crest of stage 6 is not quite so
far advanced as for stage 5; but, on an average, this line, too, is relatively
level. Similarly, wave 3 begins at lO^'lO" a. m. with stage 7, connect-
ing the highest point in the region successively for stages 8, 9, and
10, in not so level a manner as waves 1 and 2, but still relatively so.
Indeed, the comparison of the high points of the mitotic wave to the
peaks of a definitely traced mountain range holds good in this first
actual study. The procession index corrects the stage indexes through
the successive periods of a given mitotic wave strongly in the direction
of uniformity, but never completely reaches it. They (the procession
indices) are the best available means of unraveling the mitotic tangle
in the material used, for if, as in the Method Chart, one attempts in this
actual study a similar wave tracing in the chart (No. 5) " Graphs show-
ing mitotic and stage indices," he is hopelessly lost. (See pp. 11 and 14.)

1 If comparison be made with the determinations of the final experiments reported in this
paper, account must be taken of the facts that the two experiments differed in temperature, in
season of the year, and in variety of onion used (see p. 26) .

24 DURATION OF THE SEVERAL MITOTIC STAGES

EXPERIMENTS TO DETERMINE EFFECTS OF TEMPERATURE INCRE-
MENTS UPON THE SEVERAL MITOTIC STAGES.

The results of the preliminary study with the 13 successively taken
samples of 1,000 cells each accord with common-sense expectations in
reference to the durations of the several stages. Also the ends sought
by this investigation lend themselves so completely to a simple cyto-
logical and demonstrable mathematical method that it appeared invit-
ing to continue the study with a view to making practical use of the
method developed in measuring accurately the effects, in an actively
growing tissue, of some selected and controlled environmental factor
upon the relative and absolute durations of the several successive
mitotic stages and upon the mitotic cycle as a whole.

THE VELOCITY OF CHEMICAL REACTIONS: RESPONSE TO TEMPERA-

TURE DIFFERENCES.

The mitotic process is, no one doubts, a complex of physical and
chemical activities. It is known that, in homogeneous chemical sys-
tems, within Umits generally from 10° to 40° C, the velocity of a chem-
ical reaction is about doubled or trebled for each rise in temperature
of 10° C. This is van't Hoff's law, which experimental physiologists
have tested out in reference to so many vital phenomena. It was,
therefore, decided to select the temperatures 10°, 20°, and 30° C. for the
purpose, not only of determining the effect of these different tempera-
ature-increments upon mitosis, but also in order to make comparison in
reactions to temperature-increments between mitosis and homogeneous
chemical reactions. Furthermore, the temperatures selected present
two periods of 10° C. each, both still within the growing temperature-
range for plants, 30° C. approximating, but still a little lower than the
optimum, and 10° C. well above the minimum for growth in the species
selected for study. In general the botanists claim that the range for
protoplasmic activity in plants varies from zero to about 50° C. As a
rule, at a temperature below zero the protoplasm is killed by freezing,
and above 50° C. is killed by ''heat rigor." Of course, it would have
been possible to have tested out van't Hoff's law by making studies
with smaller temperature-differences and applying the formula,^

_( h \^'

Q

but in the same quantity of sampling and counting it seemed ad-
visable to increase the cell-count per sample rather than, at the expense
of cell-count, to lessen the temperature-intervals. In the absence of a

» Snyder, Charles D., "A comparative study of the temperature-coefficients of the velocities of
various physiological actions." Am. Jour. Physiol. 22: 311, 1908.

IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 25

biological necessity of having to resort to the smaller differences, it
seemed advisable also to select three temperatures, all between the
minimum and optimum for plant growth, and also near the mean
temperature most often found in reactions which obey van't Hoff's
law. Another reason for basing the first practical measurements (in
accordance with the method developed) upon temperature is that the
latter is known to exert great influence upon growth, implying bulk
increase and mitosis. It is, moreover, one of the external conditions
most readily and precisely manipulated.

MATERIAL FOR THE EXPERIMENTS.

Advantage was taken of the facts presented and the experience
gained in the preliminary study in planning and executing the com-
pleter one. The temperature-range having been decided upon, it is
next necessary to select suitable material. The onion, having proven
to be so well adapted to the sort of study in hand, was chosen for the
completer investigations. Not only has it long been known to show
mitotic rhythm, but it presents a homogeneity of samples not so easily
obtained in other types of organisms. Their root-tips closely resemble
each other and their mitotic processes were shown to synchronize.
(See p. 13.) Moreover, one sample may be taken without disturbing
the activity of the others, at least during the few hours of sampling.
They are not difficult to prepare cytologically. Furthermore, the
cells constituting the growing root-tip show comparatively little differ-
entiation. Each possesses a large number of chromosomes, which fact
(when the cells are longitudinally sectioned) makes the determination
of arbitrarily marked mitotic stages an easy and definite matter.
Finally the cells are large and the rate of mitotic activity permits
convenient (lO-minute) sampling intervals.

Bacteria, such as Ward^ used in his investigations, divide rapidly,
but their smallness and the imperfections of the views obtainable of
their transformations render them inferior to many other materials.
If one desires to learn how the details of certain other mitotic struc-
tures— for example, centrosomes which are not present in plant cells —
are influenced during their mitotic transformations by various external
agents, other materials would be necessary; but, taking all factors into
consideration, the onion presents a very satisfactory source of material
for the type of investigation here reported.

Many of the quantitative studies on growth have been based upon
the lengthening root-tips of plants. This is suitable material, whether
growth proper — i. e., permanent bulk-increase — is considered alone or
in relation to mitosis, for the root-tip grows chiefly in one dimension,
namely, length. But very rarely do the cells divide other than trans-

iSeeref. No. 1, p. 13.

26 DURATION OF THE SEVERAL MITOTIC STAGES

versely, and all are about the same size. Thus the cell number, on
the average, is roughly proportional to root-tip length in this actively
growing tissue.

The onions used in these experiments were uniform in size and exter-
nal appearance and, while they were purchased in the open vegetable
market without their pedigree being known, they were of sufficiently
uniform type and sprouted with sufficient uniformity to convince one
that their genotypic constitution was quite uniform. An effort was
made to divide a single onion into 3 equal vertical sections and to sprout
the roots from each section under the 3 different but constant tempera-
tures, thus eliminating a possible genotypic difference. It was found,
however, that there were not enough root-tips of uniform size in each
section to supply the demands of the study, 57 being required. Five
onions were grown in each temperature-constant chamber. The 19
samples required for each temperature-series were cut from these five
onions on the basis of uniform length and appearance.

APPARATUS: THERMOSTAT.

Constant temperatures in growing conditions were required and,
in the absence of laboratory rooms with equipment especially designed
for maintaining constant temperature, a special apparatus had to be
built. This consisted of a battery of 3 constant-temperature boxes,
each 1 foot by 1 foot by 1| feet in size, mounted longitudinally about
a foot apart upon a board. Each box had a wooden top, bottom, and
ends, but the front and back were inclosed with double glass doors.
Underneath these chambers ran a wooden tunnel, heated at the extreme
right with a small kerosene lamp. Since the CO2 contents of the 3
chambers must be constant, the fumes from the lamp were not allowed
to enter the tunnel, which was separated from the lamp-container by a
zinc partition. Aloxig the top of the chambers ran a similar tunnel,
connecting from above with a well-insulated ice-box in which the cool-
ing substance (crushed ice and salt) was confined to three-fourths of the
space (left-hand) by a wire netting. From each tunnel into each box was
an opening covered by a small copper lid slightly controlled by thermo-
stats taken from Hoover incubators. The lids and thermostats were
so adjusted that a rise in temperature lowered the lid which covered the
warm-air opening, and uncovered further the opening from the cold-
air tunnel. When the temperature fell, the reverse action was induced.
A centigrade thermometer was inserted through a cork which filled a
hole in the top of each chamber; the thermometer was long enough to
extend into the water in which the onions grew. In each tunnel on
each side of each box were hand-dampers controlling the size of the
tunnel. It must be confessed that, even at best, this contrivance was
was only partially automatic. In order to keep the temperature of each
compartment within the range of 1° C. from the desired standard, it

IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 27

required to be attended once every 3 or 4 hours during the entire 24;
but it worked, and that was the essential thing. Thus the three com-
partments maintained temperatures at 10°, 20°, and 30° C, respectively,
each with a fluctuation throughout the growing period of less than 1° C.
above and 1° C. below the standard set. All other environmental
factors, including lighting, were apparently very uniform in the three
chambers. The machine was set in a cellar admitting light from the
north only. In this room the temperature during the period of 3 weeks
in which the thermostats were used did not vary more than 2° or 3° C.
This aided the maintenance of constant temperatures in the three
chambers.

The onions were sprouted in earthen quart crocks and were supported
by floating wooden frames so that only the root base of each bulb ex-
tended into the water. When onions were first grown, February 1916,
for the preliminary work, they sprouted most readily, but in August of
the same year, when the constant-temperature apparatus had been
built and was in working order ready to receive the onion, the sea-
sonal conditions under which this bulb normally sprouts, or can be
induced to sprout, evidently were past. In all 5 varieties of onions were
tried out, but after 10 days none sprouted, but this time was well spent
in learning to maintain constant temperatures. By the time constant
temperatures had been attained in the three chambers, it was found
that, after scoring them deeply, the small white onions of quite uniform
character, commonly found in the fall vegetable markets, could be
induced to sprout roots. (See p. 35.)

SAMPLING AND COUNTING.

As was seen earUer (see p. 22), at a temperature of 18° C. (preliminary
study) the whole sequence of these 10 active stages of the mitotic cycle
for the onion root-tips, studied during the approach to the natural
growing season, occupied approximately 3 hours. This, together with
the fact that the highest point in their mitotic activity appeared at
11^40™ a. m., suggested that the most appropriate time for samphng, if
one wished to cover a whole active mitotic wave, would be from about
10 a. m. until 1 p. m. This succession was, therefore, decided upon and
19 observation-instants were chosen, each 10 minutes removed from its
predecessor, beginning and ending as above suggested. It is clear that
a completer and more refined analysis could be made if the observation-
instants were less remotely distant from each other; but it was desired
to cover as large a portion of a whole mitotic cycle as possible and to
make the cell-counts per individual sample as great as possible; hence
the necessity, in the interests of accuracy, to continue the observation-
instants in a series 10 minutes removed from each other. \Vhether
this is really economy working for accuracy can be determined only
when the relative influences of various factors (previously mentioned)

28 DURATION OF THE SEVERAL MITOTIC STAGES

upon the probable error of the determinations are known. (See pp.
19 and 29.)

One thousand counts per observation having proven satisfactory, the
plan of making similar counts was decided upon for the subsequent study.

The task of working out a coefficient (see pp. 13 and 30) of nodtotic
homogeneity, or synchronization in the mitotic area, was not under-
taken, because the preliminary investigation showed in the Procession
Index Tables an orderly succession of high points in mitotic waves
through successive mitotic stages and time-intervals that would not
have appeared had there not been a high degree of parallelism in the
mitotic processes in the several samples taken. Judgment, therefore,
dictated that it was necessary, in order to make for adequate accuracy,
to include in the actual temperature-studies as many cell-counts as
possible. Against this one possible handicap of having to use different
cells to restore the sequence series, instead of being able to trace the
succession of stages in the same cell — that is, in case the index of
mitotic homogeneity or synchronization proved to be low — one must
balance the fact that many hundreds of stained dead cells can be classed
by the statistical method during the time that would be consumed by
directly observing and definitely timing, even if it were possible, only
a few cells actually moving through their mitotic stages. Remembering
that numbers make for accuracy or, to be exact, that accuracy is a
function of the square root of the population of the sample, we have only
to increase the number of samples counted in order to increase the true-
ness of our statistical picture. In addition, as was stated earlier (see
p. 5), the statistical method has the advantage of taking fresh and
naturally developing tissue and killing it almost instantaneously, thus
insuring relatively untampered-with normal samples.

On Saturday, September 9, 1916, the samples were taken. The
root-tips were 5 to 10 mm. in length and varied but little in this respect
in the three different constant-temperature chambers; but it must be
remembered that growth and mitosis are different processes. The
sampling began at 10 a. m. and, as was planned, continued at 10-
minute intervals until 1 p. m., 19 observations in all. There was one
person at each temperature-box and at the given signal an onion was
lifted out and the root-tip quickly snipped with a pair of scissors and
dropped immediately into Fleming's fluid. The temperature in the
growing compartments did not vary so much as 0.5° C. during the 3
hours of sampUng, although each chamber was opened 19 times;
doubtless the volume of water in which the onions were sprouted aided
in maintaining the constancy. The root-tips were embedded in paraffin
and cut in longitudinal sections 6 microns thick, and were stained with
Heidenhain's hematoxylin, due precautions having been taken, as in
the preliminary work, carefully to label the vials in which the specimens
were prepared, and finally to label the slides upon which the series were
mounted.

IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 29

In order to prevent confusion in counting and classifying the cells,
which were viewed under the oil-inunersion lens, the field was divided
into quarters by means of hairs crossed in the eye-piece of the micro-
scope. Thus in a field containing from 50 to 100 cells it was easy to keep
one's bearings. No cells were counted twice, and all cells within a
selected field were counted and classified.

Special attention is called to the Procession Index Tables (Nos, 12, 13,
and 14). In calculating the average absolute durations of the several
stages, only those waves were used which traversed in a definite manner
at least three-fourths of the stages of the entire mitotic cycle. Some
waves were cut off in their prime by the termination of the sampling at 1
p. m., and because the sampling had a beginning (namely, at 10 a. m.)
other waves were found already well advanced. The portions of waves
unused in the calculations are indicated by dotted lines.

There are two blanks in these tables, one in the 20° series for the
sample at 11^50™ a. m., and the other in the 30° series for the
sample at 10^10™ a. m. These samples were duly taken and fixed, but
were ruined in preparation, so that while the results of the 10° series are
based upon the determinations of 19 samples of 1,000 cells each, in the
20° and 30° series each is based upon only 18 samples of 1,000 cells.

In studying the results given in the several tables, attention is cglled
to the fact that, for better comparison between mitotically active and
mitotically inactive stages, in some cases the percentages are based
upon a cycle consisting of the 10 mitotically active stages only, omitting
the resting stage. In other cases the resting stage is considered as a
part of the mitotic cycle. Thus, in making comparisons other than
those set forth in the same tables, one must make sure that the data
apply to the same definition of the mitotic cycle.

FURTHER DEVELOPMENT OF THE STATISTICAL METHOD.

The results of the experimentation reported in this paper invite
future statistical investigations as follows:

(a) To work out with more mathematical refinement the measure for
accuracy {prohahle errors) of the formulas here given. — This involves the
determination of the interrelation between the accuracy of the calcu-
lations and (1) the size of the individual samples, (2) the number of
observation-instants per series, and (3) the closeness of observation-
instants; and the working out, as hereinafter suggested, of a coefficient
of mitotic homogeneity or synchronization in the successive samples —
all of which would permit not only the calculation of probable errors for
the several determinations, but also would supply the basis for sound
judgment in planning experiments. For example, if only a limited
number of observations were feasible, it would enable one to choose, in
the interests of accuracy, between closer observation-instants covering

30 DURATION OF THE SEVERAL MITOTIC STAGES

less time and observation-instants farther removed but covering more
time.

(6) To find, if possible, a theoretically perfect procession-index. — ^The
one used in these studies is highly practical and reliable, but, as was
pointed out (see p. 11) in the early part of this paper, it lacks certain
theoretical refinements.

(c) To work out a coefficient of mitotic homogeneity or synchronization. —
This could be done by sampling a number of similar-appearing root-
tips from the same plant at the same instant, counting a large number
(say, 1,000) of cells from each, classifying their stages, and calculating
the percentage-frequencies of each, as was done in the study herein
reported for successive samples. Then one should calculate through
the series of samples, for each stage, the average percentage-frequencies.
For each calculation, because the material sampled would be homo-
geneous, the usual probable error of the mean would apply. Then

%-E%

applying the formula — ^7 = 1. H., we would have a good index of

/o
mitotic homogeneity, for each stage. These values could then be
coordinated into a single index of mitotic homogeneity for the entire
cycle of mitotic stages.

Karsten,^ in his studies, appears to have taken 4 or 5 samples at
about the same time and to have taken data from each of them, but
from each sample his cell-counts are low, generally ranging from 50 to
100; which being distributed over the 5 mitotic stages which he used
as a basis of classification, would make the calculation of their probable
errors valueless. But by further inspection of his tables, one finds a
constancy fully in accordance with expectation within the comparative
smallness of his samples. This would lead one to expect, in a determina-
tion based upon large samples, a low probable error in a coefficient of
homogeneity or synchronization. (See pp. 13 and 19.)

FURTHER ANALYSIS OF THE DYNAMICS OF MITOSIS BY THE
STAGE-TIMING METHOD.

It would be desirable:

(a) To conduct experimentations similar to those here reported,
but in which every qualitative feature would be more precise and every
quantitative factor making for accuracy greatly increased. For in-
stance: Temperature difference of 2° C. from 8° C. to 45° C. (or from
the awakening to the maximum temperatures for growth in the
particular plant selected), all other environmental factors constant;
sampling at 5-minute intervals for 24 hours; 3 or 4 samples per
observation-instant; genotypically uniform material; possibly a revi-
sion of the successive stages of the mitotic cycle used in this study; at

1 See ref. No. 3, p. 13.

IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 31

least 1,000 cell-counts from each sample. This would be a long
and arduous task, possibly to be carried out best on a cooperative
plan, but it would supply valuable and accurate standards for the further
quantitative analysis of mitotic processes.

(b) To make studies on the duration of the several mitotic stages at
the awakening and end of mitotic activity as affected by temperature
changes; also on the effects of light, electricity, moisture, pressure,
gra\'ity, foods, and poisons upon stage-durations. Much qualitative
work, but none of a quantitative nature, has been done in this direc-
tion; for instance, V. Sabline,^ in subjecting the roots of Vicia Jaba to
different temperatures, lack of oxygen, quinin sulphate, sulphuric ether,
and other substances and conditions, noted their effects upon mitosis
up to the instant of killing. The analysis of vital phenomena by
timing mitotic stages thus modified is most promising.

(c) To follow the clue presented by the effect of temperature on stage
6, in constructing working models simulating this stage of mitotic
activity, seeking by a temperature rise to weaken the tension of strands
appearing to pull the chromosomes toward the different poles. Indeed,
if such strands could be made to appear in a gelatine cell, by a current of
electricity, the simulation would be all the more promising as a possible
real parallel to mitotic force. (See p. 45).

{d) To time in detail the mitotic process, not only in cell-division
characteristic of growth in undifferentiated tissue, as in this study, but
also in cell-division in tissues undergoing differentiation.

(e) To make studies in cell-size, cell-number, mitotic activity, and
bulk-increase in the same tissues as affected by temperature-differences.
Tissue growth consists in an alternation of cellular bulk-increase and
mitosis. The experimentation herein proposed would determine the
proportion of the limitation set upon growth by lowering temperatures
due to (a) slowing-down the mitotic process, and to (6) reducing the
absorption of food materials and delaying the metabolism necessary to
creating the chemical potential which must precede mitosis.

RESULTS AND DISCUSSION.

The accompanying tables and charts give in detail the cell-countings,
the mitotic stage-classification, and the determinations derived from
them; they give also the formulas used, and finally they set forth
graphically and comparatively the results of the experimentation and
calculations for each temperature series. Nevertheless, a short dis-
cussion is perhaps permissible.

1 Sabline, V. "L'influence des agents externes sur la division des noyaux dans les racines
de Vicia faba." Rev. Gen. Bot. 15:481-497, 1903.

32 DURATION OF TQE SEVERAL MITOTIC STAGES

A. RHYTHM IN MITOSIS,
(a). GENERAL.

The beginning of the mitotic process in plants is conditioned upon
the state of cell-turgor, which in turn impHes that under conditions
normal to the growing tissue the cell has not only absorbed a definite
quantity of water, but also an amount of food materials and oxygen
sufficient to set up the necessary physical and chemical potential de-
manded, in the particular setting of things, to start the mitotic train.

Strictly speaking, growth and mitosis are two distinct processes;
growth refers only to permanent increase in bulk; mitosis, on the other
hand, refers to cell-division regardless of increase or decrease in the size
of the end product. Not only are they distinct processes, but in the
same cell at the same time the one practically precludes the other.
But while mitosis and increase in bulk are different processes, they must
cooperate, if either is long to continue. Cells must divide, because
their contact with the external world is through their surfaces and is
therefore proportional to the square of their diameters; but their bulk
and consequently the amount of metabolic work they are called upon
to do vary with the cube of their diameters. A cell active mitotically
is resting from its normal metabolic activities; conversely, while a cell
is metabolically highly active it can not undergo mitosis. Sachs,^ in
his "Text-book of Botany," says:

"This relation of growth, which is dependent on cell-division, to assimila-
tion, is especially clear in algae of simple structure (as Spirogyra, Vaucheria,
Hydrodictyon, Ulothrix, etc.), which assimilate in the daytime under the
influence of light, while cell-division proceeds exclusively or at least chiefly
at night

"We have here a case of division of physiological work which shows us that
the cells which have to do with chemical work (assimilation) can not at the
same time perform the mechanical labor of cell-division ; the two kinds of labor
are distributed in the higher plants in space, in very simple plants in time.
Provided there is a supply of assimilated reserve-material, cell-division can
therefore take place either in the light or in the dark. Whether there are
special cases in which light promotes or hinders cell-division is not known
with certainty."

Quoting Famintzin,^ Sachs continues:

"The cell-division of Spirogyra has been proved to be dependent on light
to the same extent as the formation of starch ; but relationship in the former
case differs from that in the latter in the following respect : The formation of
starch is induced by a very brief exposure to light (about half-hour) and
requires that its action be direct; starch is formed only under the influence of
light ; in its absence the formation at once ceases. Cell-division, on the other
hand, is induced only after light has acted for some hours; it then commences
in the cells, whether these have been exposed to light for some time or have
been removed into the dark."

1 Sachs, Julius, "Text-book of Botany." (Tr. by A. W. Bennett.) Ch. 3, pp. 659-689.
^ Famintzin, Melanges phys. et chim. Petersbourg, 1868, Vol. III.

IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 33

(6). WARD'S WORK.

A very important step in the analysis of vital phenomena was made
in 1895, when W. M. Ward/ in his classical experiments " On the biology
of Bacillus ramosus (Fraenkel), a schizomycete of the River Thames,"
determined that growth {i. e., permanent increase in bulk) while in the
long run dependent upon cell-division, does not synchronize but rather
alternates with it. He measured quantitatively what other investiga-
tors had only caught glimpses of.

(c). ADDITIONAL EVIDENCE.

In 1904 W. E. Kellicott^ pubHshed, in a bulletin of the Torrey Club,
his paper "The daily periodicity of cell-division and of elongation in
the root of Allium J' In the experimentation upon which this paper was
based Kellicott grew onions in wet sawdust until the roots were from
50 to 100 mm. in length. Then, at 2-hour intervals throughout the 24
hours, with the temperature ranging from 14° C. at 1 a. m. to 27° C. at
3 p. m., he took samples of the root-tips and at the same intervals made
measurements of the rate of elongation of similar tips. His purpose was
to trace the rhythm in cell-division and the rhythm in growth, with a
view to determining whether (as Ward nine years previously had found
in Bacillus ramosus) the maximum of mitotic activity alternates with
the maximum of root-tip elongation. His work seems to have con-
firmed for the root-tip of Allium the conclusion of Ward in reference
to Bacillus ramosus, and thus tended to suggest the generality of the
principle.

Besides counting the resting stages in selected areas, he counted also
the mitotically active stages, classifying them as early, middle, and
late. He reports no further use of this classification other than to add
their counts together for determining periods of comparative mitotic
activity. His data would hardly suffice for a study of stage duration,
for the observation periods were too far apart and the total number of
cells counted approximated only 3,000.

Kellicott summarizes his investigations as follows:

" 1. In the root of Allium there are two maxima and two minima in rate of
cell-division during the 24 hours.

"2. The primary maximum occurs shortly before midnight (11 p. m.) and
the primary minimum about 7 a. m. The secondary maximum occurs about
1 p. m. and the secondary minimum about 3 p. m.

"3. There is no correspondence between the rate of cell-division and slight
variations in temperature.

*******

"6. Under nonnal conditions of growth the rate of elongation of the root of
Allium exhibits a daily rhythm, showing two maxima and two minima durmg
24 hours.

1 See ref. No. 1, p. 12. ^See ref. No. 2, p. 12.

34 DURATION OF THE SEVERAL MITOTIC STAGES

"7. Elongation is most rapid (primary maximum) about 4 or 5 p. m., the
secondary maximum occrn'ring about 7 a. m. The primary minimum is about
11 p. m., and the secondary minimum about noon.

"8. Periods of rapid cell-division coincide with the low rate of elongation
and during rapid elongation the rate of cell-division is lowest."

Finally G. Karsten^ records his investigations of the mitotic rhythm
through successive intervals under constant temperature. He traced
the fluctuations in mitotic activity through long periods of the day,
for the most part through the hours of daylight only. The intervals
between his observations were not equal, but varied from 30 minutes
to 2 hours. His plants were grown in a thermostat, maintaining a
temperature constant at 25° C. From 6 a. m. to 6 p. m. the thermostat
was lighted electrically, and from 6 p. m. to 6 a. m. it was permitted to
remain dark. His purpose was to eliminate the influence of temper-
ature fluctuations upon the degree of mitotic activity. He determined
particularly that the fluctuations in mitotic activity during the course
of the day are not due solely to variation in temperature.

In making his cell-counts, Karsten noted five stages, viz., Auflock-
kerung, prophase, metaphase, anaphase, and telophase, and counted
for each species studied a total of from approximately 100 to 400 cells
per observation-period. Like Kellicott, he apparently made no further
use of his division of stages of mitotic progress other than to sum them
for measuring the height of mitotic activity at the given instant of
observation. Karsten's view that root-tip cells do not show mitotic
periodicity is not well founded, nor is Kellicott's conclusion^ in refer-
ence to temperature and cell-division.

id). SUMMARY OF EVIDENCE OF MITOTIC PERIODICITY.

To sum up the evidence in relation to periodicity, we may say that in
growing tissue, so far as the individual cell is concerned, there is a
definite alternation between permanent increase in bulk and mitosis.
Indeed, if bulk-increase is largely anabolic and cell-division catabolic,
as is most probably the case, then opposing activities can not synchro-
nize in the same cell each as a dominant factor of activity. But syn-
chronization of the same activities among many neighboring cells is a
different matter. This exists and its degree determines the character of
the pulsation observed in rate of growth in actively growing tissues.
Even if growing cells did not have to experience this alternation in
growth and mitosis, but responded directly and constantly to their
environment, we should expect periodicity nevertheless, for the daily
cycle of illumination, heat, and moisture, with their concomitant influ-
ences, direct and indirect, upon nutrition and metabolism, would make
for a rhythm in growth. (See p. 30.)

^Karsten, G. " IJber embryonales Wachstum unci seine Tagesperiode." Zeit. Bot. 7: 1-34, 1915.
^See No. 3, p, 32.

IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 35

Not only would we look for rhythm, as caused by the complex of
envh-omnental factors, but the internal organization of the plant permits
response at one time or season, but not at another. That is, besides
the daily response in mitotic and growth rhythms, due chiefly to ex-
ternal influences, there is a seasonal rhythm due chiefly to internal
organization. Thus in February and March the cured onions, which
have been stored through the winter, sprout very readily upon being
given moisture and light; but in August the same type of onion, as was
earlier reported, is hard to awaken to growth. (See p. 27.) Then, too,
each individual tissue of each individual animal or plant would be
expected, under a definite complex of environmental factors, to present
its own specific train of mitotic phenomena, the parallelism in re-
sponse being governed in such cases by the degree of constancy in the
en\aronment-complex and in the genotypic constitution of the tissues
compared.

B. HEAT FACTOR IN GROWTH.
(a). GENERAL.

Heat is known to exert an important influence upon the velocity (see
p. 38) of chemical reactions, and also upon the reaction-rate or strength
of practically all of the measurable physical forces known in both the
inorganic and the organic worlds. Growth (bulk-increase and mitosis),
which is a complex of chemical and physical reactions, can take
place only under appropriate temperature-conditions. Other things
being equal, the growth response of a specific plant is specific for a given
temperature. Many experiments have been conducted upon the rate
of growth for the purpose of working out physiological constants for
given and various situation-complexes of nature and nurture. So far
as temperature-relations are concerned, there have been found cardinal
points, specific temperatures, at which growth in a specific plant
responds at its mimmum, its optimum, and its maximum rates. As a
rule, these points are found to vary from slightly above zero to approxi-
mately 50° C.

ib). PHENOLOGY.

The phenologists have found a certain relationship between the quan-
tity of heat (that is, the number of centigrade-degree days) and the stage
reached by a given plant in its development from the dormancy of mid-
winter. Linsser,^ in 1867, attempted to formulate this relationship.
His conclusions were based upon the theory that a definite quantity
of heat is required in order to affect the internal reactions necessary to
reach a definite developmental stage; regardless of whether this quan-
tity be distributed over a long or a short season, its end effect was
thought to be the same. In general, phenology is an attempt to har-
monize the known facts of energy transmutation and conservation in

1 Linsser, Carl, "Die Periodischen Erscheinungea des Pflanzenlebeas in irhem Verholtniss zu
den Warmeerscheinunzen." Mem. Acad. Sci., St. Petersb., Ser. VII, Vol. XI, No. 7, 1867.

36 DURATION OF THE SEVERAL MITOTIC STAGES

chemical reactions with the phenomena of growth. It does not, how-
ever, take into consideration the differential effect of heat at different
temperatures, nor the possibility of physical shock in raising and lower-
ing the temperature, nor the possible wastage and excretion of products
before the measured stage is reached.

Ward^ calls attention to a fact of interest to those who seek to estab-
Ush physiological constants, namely:

"That the variation in rate of growth which has been going on at an hith-
erto constant temperature is more pronounced when the rise or fall is 2° C. than
when it is only 1° C. will be obvious, and similarly for any other range; but,
again, it must be noted that the amount of deflection of the curve for any
range of variation depends on the amount of temperature, or the hitherto con-
stant temperature at which the growth has been going on The external

factors are : (1) Temperature. Variations in the curve are produced by sudden
variations in the temperature, and apparently the variations are the more
pronounced the quicker the temperature changes and the more extensive their
range; but the amount of variation in the curve due to any given rise or fall of
temperature in constant time appears to depend on the distance of the tem-
perature (from which the variations is reckoned) from the optimum. In other
words, the sensitiveness of the organism to a rise or fall of a degree centigrade
varies according to the temperature from which the rise or fall occurs; for if it
has been growing at 30° C. constant temperature, for an hour, it shows a more
marked deflection in the curve for a sudden rise or fall of 1° C. than for the
same sudden rise or fall from 25° C."

He then discusses other factors wdth which we are here not so con-
cerned.

C. NATURE OF THE COMPLEX IN GROWTH AND MITOSIS.

Physiologists often have attempted to treat the complex of bulk
increase and mitotic activity as a unit, fitting in its end-product the
simple formula followed by reactions in homogeneous chemical systems.
If, by any chance, in a special case, growth (impljdng an alternation in
(a) the absorption of food materials, cell turgor, and (6) mitotic poten-
tial and its consequent mitosis) should be found to follow the same rule
in response to one or more external agents as is obeyed by the simpler
organic reactions, it would indeed be a matter of chance and not an
homologous response due to types of chemical activity being parallel
throughout. The one is a relatively simple and direct reaction, and the
other a vast complex of inhibitions and activations, with their interplay,
giving finally a single measurable resultant of forces. In mitosis we
see different structures and can trace their dissolution and reorganiza-
tion; this shows clearly that mitosis is not a homogeneous chemical
reaction. There are many different substances distributed throughout
the cell, but their distribution is not so homogeneous as not to require
the consideration of the diffusion factor before completing their chem-
ical reactions incident to mitosis. The fact that different structures and
substances in the cells, both Uving and dead, take different stains proves

1 See ref. No. 1, p. 13.

IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 37

their different chemical composition and makes possible the micro-
chemical analysis of cell structures, but the same evidence of com-
plexity demands the greatest refinements in measuring unhampered and
elementary vital processes. The mathematical formulas for physio-
logical constants are, as a rule, not nearly so dependable as are such
velocity-reaction formulas for substances in the world of non-living
protoplasm. Doubtless the reason is that in living protoplasm there is
a more complex interplay of forces and the consequent manufacture of
new products which, in turn, by their presence affect their differential
influences upon the whole subsequent course of vital activity. Such
can not, without great difficulty, be resolved into its elements and given
mathematical interpretation.

D. PHYSICO-CHEMICAL ASPECT.

(a). INDIVIDUALITY IN VELOCITY REACTIONS OF THE SEVERAL MITOTIC
STAGES TO THE SAME TEMPERATURE CHANGES.

It should be noted that there is a differential response characteristic
of each of the several mitotic stages here listed. This is not surpris-
ing, for each mitotic stage possesses its own individuality so far as its
physico-chemical complex is concerned. This is most strikingly shown in
chart No. 18, in the parallelism between the graphs plotting the velocity
reactions of the successive stages at 20° C. compared with the velocities
at 10° C, and those for 30° C. compared with the velocities at 20° C. as a
standard. If the specimens had been grown at temperature-intervals
of 2° C, one would expect, from the response shown in table on page 38,
through the temperature series a characteristic and orderly increment or
decrease in the velocity-response of each arbitrarily marked-off section
(mitotic step or stage) of the mitotic cycle, the same as from the cell-
organization as a whole, only in slightly less complex manner.

With the microscope it can be seen readily that the mitotic process
involves gross molar movements and, as the cycle progresses, differ-
ential staining proves the change of minute cellular structures, "the
production of structure from metabohsm," involving chemical change.
In a homogeneous chemical system it is possible to measure the quan-
tity of the homogeneous reaction-product produced in a given amount
of time; but in mitotic activity it is the progress of the complex-train
with all of its many products that is measured by dividing it into
arbitrary but recognizable progress-stages. It is not the mass of its
reaction-products that is measured. Thus the end speed of the whole
mitotic process is the resultant of many cooperating and conflicting
forces; but, regardless of the number of complications, a thing that is
measurable and is varied by the change in complicating factors shows
orderly change and rhythm. Such measuring is a step in advance
because it admits of analysis further than has been made and points
the way toward still greater refinements.

38

DURATION OF THE SEVERAL MITOTIC STAGES

Owing to the individuality of the physico-chemical complex char-
acterizing each mitotic stage herein set off, we do not expect orderly
fluctuation in the reactions of the successive stages (see chart 18) to
the same temperature any more than we expect serial order in the
reactions of different organisms selected at random and unseriated;
but (see also charts 16 and 17) we do expect to find, in the same
organism, that a characteristic and orderly curve plots the reactions
to orderly increments in temperature, of the same mitotic stage, of
any given combination of mitotic stages, of the entire cell as a unit,
or of the more complex organism as a whole.

The effect of temperature increments of 10° C. upon the velocity of each of the several
mitotic stages in the dividing root-tip cells of the onion. Qio values.

Mitotic stages

(see summary chart for definite

limits) .

Velocity at 20° C.

compared with
velocity at 10° C.

Velocity at 30° C.

compared with
velocity at 20° C.

0.8818 (i. €., -1.1340)
+2.6832
+2.9599
+ 1.3859
+ 1.4071

0.8546 (i. e., -1.1701)
+ 1.1523
+ 1.6334
+ 1.3329
+ 1.1240
+ 1.2215
+2 . 0476
+ 1.1990

+ 1.1525
+4.9406
+2.6404
+2.7593
+3.0663
+2.3440
+2.7571
+2.6038
+2.1694
+3.0931
+4 . 9463
+3.2311
+ 1.3962

9. Early telephase or di-spireme

2 to 10 inclusive

1 to 10 inclusive

Entire cycle, i. e., the 1 resting and
the 10 active stages

+ 1.2139

+2.6218

Note. — Each of the above values when preceded by a + or a — sign constitutes
the usual Qio calculation.

The above shows, in terms of velocity rather than of duration, the
effects of temperature increments of 10° C. upon the increased rapidity
of each of the several mitotic stages in the dividing root-tip cells of
the onion. (Table 15 and charts 16, 17, and 18 give in detail the
comparative effects of temperature upon the duration of the several
individual mitotic stages.) In two instances it will be seen that
mitotic velocity is slowed down by the 10° C. temperature-increase,
while in all other cases it is speeded up. On the whole the increased
velocity exceeds the retarding influences, so that a rise in tempera-
ture increases the rate of mitotic activity. Stages 1 and 6 are, to a
greater degree than any other stages, slowed down by a rise in tem-
perature, while stages 2 and 8 are greatly accelerated by the same
change. The former pair (stages 1 and 6) apparently have little in
common, while in the latter pair stage 2 is constructing chromosomes
and stage 8 is breaking them down.

IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 39

(6). VAN'T HOFF'S LAW.

If van't Hoff's principle is taken to apply only to simple chemically
homogeneous reactions, it finds little direct application to the measure-
ments herein reported for the influence of temperature-increments
upon mitotic velocity. However, determining the Qio values, i. e., the
coefficients for simple or complex physical, chemical, or physiological
activities, is a very useful method of analysis. But when we find
Qio values of the magnitude of van't Hoff's expectation, namely, of
from +2.0 to +3.0, we must not consider therefore that we have of
necessity located a simple homogeneous chemical reaction. We may
or we may not have found such. As many as possible of the con-
tributing factors must be taken into consideration and each duly
weighted. Every chemical and physical activity has its characteristic
velocity-response to a 10° C. rise in temperature. Generally these val-
ues vary from —2.0 to +5.0. Because in these experiments with mito-
sis the value of Qio is never greater than +4.95 and never less than
— 1.18, the evidence points strongly toward the nature of mitotic
forces being chiefly chemical and physico-chemical, but without
further analysis this evidence tells little more as to what combina-
tion of a great repertoire of activities may be involved in the mitotic
stage-complex whose activities are measured as a unit.

The fact that influences are both specific and measurable is the
encouraging thing. The measuring of two complexes differing only in
one factor supphes a measure of this differential. If finally a vital
reaction is analyzed and one of its elements closely accords in behavior
with some simple reaction, well and good, for such indicates approach
to the elementary, and elemental formulas relating to such a
complex can be synthesized; but calling a patently and unanalyzed
complex elementary because it responds like such in one or more
respects hardly makes for progress. Doubtless the component proc-
esses of mitosis are of a chemical and physico-chemical nature and
their individual responses to temperature-changes are of the expected
nature and degree. But the interplay of activities may cause the
complex as a unit to synchronize with certain selected elements or the
conflict of forces may greatly retard or accelerate the common progress.
For instance, the production of enzyme A may be proceeding at a
chemically expected rate in response to its surrounding temperature.
But when enzyme A comes in contact with enzyme B, which is being
similarly produced, their interaction may introduce another factor,
accelerating or retarding general or specific progress. Also, anti-
catalysis (or the influencing of the velocity of production of a chemical
product by the unremoved product itself) is a factor. It is a mass of
such individual activities that we measure in most physiological
activities, and especially is this true in mitosis.

40 DURATION OF THE SEVERAL MITOTIC STAGES

While the experunents and discussions of this paper are confined
to the method of mitotic analysis based upon velocity-responses
characteristic of definite temperatures, which method doubtless will
continue to yield profitable returns, the study of specific mitotic stage-
duration as affected by other physical forces, such as light, electricity,
pressure, and gravity, and by chemical agents, and finally by given
complexes of these forces and agents, must be resorted to for a better
determination of the details of mitotic dynamics. The method of
measuring the durations of mitotic stages presented in this paper is
applicable equally well to each of these situations.

Gradually the physiological complex of the cell is being analyzed,
each factor measured, and coefficients and indices of reaction of
definite living organisms to controlled environmental conditions are
being worked out so far as velocity-reactions to temperature are
concerned. The fact that mitosis in its complexity does not behave
throughout like a uniform and simple chemical reaction is to be ex-
pected. In mitosis there exists a microcosm of chemical and physical
forces, each with its characteristic response to temperature-increments.
Indeed the differential reactions of the several stages of the mitotic
process-train present the only possible but nevertheless a most prom-
ising key to further analysis of the forces involved in cell division by
the method of measuring velocity-response to temperature-changes.
Especially valuable will this key be if used under a wide range of con-
trolled conditions and applied to mitotic stages of very definite but
small differences. Finally, of course, velocity-analysis in its various
relations will (like temperature-analysis) reach its Hmits of usefulness,
but its possibilities in determining the nature of the dynamics of
mitotis are thus far only sampled.

(c). ISOLATION OF FACTORS.

Elimination hy comparative experimental evidence. — When a physi-
ologist confines his investigations to a definite, localized, relatively
homogeneous reaction, he may expect results more closely approxi-
mating those of the chemist deahng with homogeneous systems. But
even then the varying factors may act upon processes controlling the
one sought to measure alone. Riddle^ experimented with four species
of cold-blooded vertebrates, with a view to determining the velocity of
digestion in relation to temperature. He recognized the difficulty in
measuring the effects of temperature upon the digestive process alone.
In regard to complicating factors he says:

"The data indicate that the effects of temperature on the digestive proc-
esses must be considered under two heads: First, the accelerating action of
increased temperature on the chemical processes involved; and second, the
retarding action of very high or very low temperatures due (a) to the pro-
duction by the animal of smaller amounts of digestive enzymes under these

' Riddle, Oscar. "Rate of digestion in cold-blooded vertebrates." Amer. Jour. Physiol. 24:
447 et seq., 1909.

IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 41

conditions or (6) to the actual destruction of enzymes by these extreme
temperatures."

After executing his experiments in a manner as nearly as possible
eliminating these perturbing influences, he finds:

"Within certain not very wide ranges of temperature the rule of van't Hoff
applies to the digestive processes in living cold-blooded vertebrates, the aver-
age of eight vahd coefficients being 2.62."

And, in further interpretation of his results in which the velocity in-
crease for a 10° C. temperature-increment varied from 0.93 to 7.81 , he says :

" Those numbers which are greater than 3.00 indicate that the lower temper-
ature of the two temperatures compared exercises a destructive or inhibitive
action on the digestive secretions; whereas numbers smaller than 2.00 indicate
that the higher temperature of the two temperatures compared likewise
inhibits or destroys ferment action."

It is clear that he regards uncomplicated peptic digestion as a simple
and purely chemical process which would, therefore, for moderate tem-
peratures, show the characteristic Qio value of from +2.0 to +3.0.
For these reasons, of the 13 determinations made 5 were rejected as
not valid. His 8 valid coefficients, above mentioned, were determined
for temperatures approximating the optimum for peptic digestion in
each of the several species experimented with. Thus the cardinal
temperature-pomts for the particular activity characteristic of the
particular species and individuals used in the experiment and must
be taken into account in interpreting temperature-indices based upon
physiological systems.

A single index for two factors. — Livingston^ attacked the problem
of physiological constants. As he points out in his investigation, he
"takes account of the principle of temperature minima, optima, and
maxima." Thus, ''basing the indices upon a physiological rather than
an exponential system," he finds ''the van't Hoff-Arrhenius principle,
upon which is based the exponential series, appears to hold for the
elongation of young maize shoots only for a temperature range from
about 20° to about 30° C. (Lehenbauer), and the physiological system
is approximately true for all temperatures from 12° to 43°C., at least
for the conditions of Lehenbauer's experiments." Subsequently the
same author (Livingston) worked out "A single index to represent both
moisture and temperature conditions as related to plants."^

There is always great difficulty in attributing to an elementary and
uncomphcated physiological process the Qio values found in any given
measurement, so great in the Uving organism is the interrelation of
activities. The analysis must, however, strive to isolate the factors
and thus seek data based upon relatively simple processes. Formulas
duly weighing each factor can then be synthesized.

1 Livingston, Burton E. "Physiological temperature-indices for the study of plant growth in
relation to climatic conditions." Physiol. Res. 1: No. 8: 399, 1916.

2 Physiol. Res. 1: No. 9: 421-440, 1916.

42

DURATION OF THj: SEVERAL MITOTIC STAGES

Temp. (C).

Qio.

18° to 28°

2.40

19 29

2.24

20 30

2.08

21 31

1.93

22 32

1.82

23 33

1.73

24 34

1.58

25 35

1.41

26 36

1.25

27 37

1.10

28 38

0.96

(d) DIFFERENCE BETWEEN PHYSIOLOGICAL AND PURELY CHEMICAL
TEMPERATURE-VELOCITY REACTIONS.

Physiological processes. — Harvey/ in his inves-
tigations of the rate of conduction of the nerve
impulse in the medusa Cassiopea, calls attention
to the fact that within medium temperatures —
that is, from 18° to 38° C. — the velocity-increment
per definite temperature-rise for physiological
processes declines as the temperature increases,
whereas in purely chemical reactions the velocity-
increment increases as the temperature rises. He
gives the accompanying table showing the former
principle for the experiment above named.

In interpreting this behavior Harvey says:

"If the rate of nerve conduction depends on the velocity of some chemical
reaction in the nerve, the above-mentioned difference in its temperature curve
remains to be explained. It is possible, indeed probable, that yet another
factor than reaction velocity determines conduction rate, and the resultant

curve of the two factors is the one actually observed Different enzymes

exhibit maxima at different temperatures. Most of these are rather high,
much higher than the maximum for nerve-conduction, which lies at about
33° C. The same ferment obtained from different sources may exhibit dif-
ferent maxima .... we may say that the propagation of the nerve impulse
is not only dependent on the velocity of a chemical reaction, hut that the reac-
tion is further accelerated hy the presence of an enzijme. Thus the characteristic
difference in the form of curve from that of a simple reaction."

Growth or permanent hulk increase. — Lehenbaur,^ presents the table
shown herewith. The purpose of his experiments was to test the appli-
cabihty of van't Hoff's principle to the rate of growth in the stem-
shoots of maize seedlings. He points
out that his results approximate van't
Hoff's law in the medium temperatures
only, that is, from 20° to 30° C, where
the concomitant temperature-coefficients
range from H-1.88 to +2.40. The table
is indeed a most interesting one, for
growth alone is considered, and this he
studied in its more restricted sense,
namely, permanent increase in bulk
disregarding mitotic activity. There is
no constant velocity-increment with each
temperature-rise of 10° C, but it will be

1 Harvey, E. Newton. "Effects of different temperatures on the medusa Cassiopea, with
special reference to the rate of conduction of the nerve inpulse," Carnegie Inst. Wash. Pub. No.
132, pp. 27-39, 1910.

2 Lehenbauer, Philip A. "Growth of maize seedlings in relation to temperature." Physiol.
Res. i:No. 5:281, 1914.

Temp.

Range of

Coeffi-

range.

growth-rate.

cient.

mm.

°C.

1.01

12 to 22

9 to 59

6.56

13 23

10 64

6.40

15 25

20 75

3.75

18 28

28 98

3.50

20 30

45 108

2.40

21 31

53 109

2.06

22 32

59 111

1.88

25 35

75 86

1.15

32 42

111 11

0.09

33 43

101 6

0.06

IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 43

seen that the lower the temperature the higher the coefficients. It is
evident that here increasing temperatures exert a progressively declin-
ing accelerative effect upon growth.

Mitosis. — Not only is there, in a relatively simple physiological
complex, a decrease in Qio values as the temperature increases, but if
growth, which is most complex physiologically, is measured in terms
of permanent bulk-increase, we find the same phenomenon.

In comparing the values found in the mitosis velocity-measurements
at different levels on the temperature scale with the two types of
velocity-increments which Harvey points out, the striking thing is
that in mitosis all of the stages measured in the present investigation
show a greater velocity-increment for a rise of 10° C. from 10° to 20° C.
than from 20° to 30° C. Thus, unlike the rate of nerve conduction in
Cassiopea, and the increase of length in the root-tips of the seedling
maize along with physiological activity generally, mitosis behaves in
its velocity-increments to temperature-increments like the simpler chem-
ical reactions. This does not mean that mitosis is a ''simple
chemical reaction." Far from it it is a vast complex of physical and
chemical activities. By chance the resultant of the actions and inter-
actions of these processes present, when measured as a whole, an
aspect resembling in this one feature a simple chemical reaction.

Many biological curves are shaped like an elongated and slanting
capital letter S — thus ^y'^ ; for instance, the curve of auto-catalysis,
when time (abscissae) and quantity of product (ordinates) are plotted.
If the temperature at which the onion root-tips of the present study
were sampled had extended beyond the cardinal temperature points
for mitosis in the specimens used, we would have found ultimately
a breaking-point and a decrease in velocity increment in the higher
temperatures, such as Harvey found in the velocity of nerve conduc-
tion in Cassiopea at 28° C. to 38° C, and Lehenbauer in the growing
root-tips of maize at 32° C. to 42° C. The curves for velocity of physio-
logical reactions in response to temperature-changes are the shape of the
upper end of the elongated y^ , while the curves for mitosis and also
for the simpler chemical reactions take the direction of the lower half.
The range of temperature in the mitosis experiment (10° C. to 30° C.)
is somewhat lower on the temperature scale than those used by Harvey
(18° C. to 38° C.) and by Lehenbauer (12° C. to 43° C). In the region
of the medium temperatures this particular contrast between the
velocity-gradients of mitosis and of physiological processes generally
and the closer resemblance of the mitosis-gradient to that of the
simpler chemical reactions is undeniable. We must look for its mean-
ing not in position on the temperature-scale, but in a physiological
(physico-chemical) complex in which the many specific elementary
reactions to temperature-changes give a resultant in which the many
aberrations from the velocity-gradient characteristic of a simple
chemical process are mutually canceled.

44 DURATION OF THE SEVERAL MITOTIC STAGES

(e). THE REACTIONS OF DEFINITE MITOTIC STAGES.

General survey.— The temperatures 10°, 20°, and 30° C. at which the
plants experimented with were grown are medium in the sense in which
the term is used in relation to physiological experiments generally.
At these temperatures, with mitosis as with other physiological pro-
cesses, we find Qio values of the expected magnitude. Here also, as is
usual with both simple chemical and complex physiological processes,
accompanying an arithmetical change in temperature, we find a geo-
metrical change in reaction velocity.

In some stages, such as No. 2, it appears that the activity is chiefly
chemical, or at least diffusional mvolving most minute bodies, for a
high-power microscope reveals few structural changes. If the products
of reaction were immediately removed, if auto-catalysis and other
activating or retarding factors were absent, such a stage might, in its
behavior, be expected more nearly to approach van't Hoff's rule than
would a stage whose changes appear to be mostly physical, such as, for
mstance, stage 6, which seems chiefly a physical shift. This surmise
in reference to stage 2 holds good in the temperature-difference 10° to
20° C, but falls down utterly in the 20° to 30° C. rise. While other
stages— N OS. 4 to 10 — which seem to be characterized chiefly by gross
structural changes, in the 10° to 20° C. change generally respond with
a Qio value less than van't Hoff's expectation, but in the 20° to 30° C.
change are well within the range of such prediction. These differences
indicate an interplay of forces specific for each stage. Doubtless the
non-removal of products, which become thereby factors influencing sub-
sequent activities, constitutes a very great if not the principal cause
of difference between the response of a mitotic stage and a homogene-
ous chemical reaction to temperature-changes.

A cell through a given mitotic stage is apt to be more homogeneous,
i. e. simpler, in its physico-chemical complex than the same cell traced
throughout its whole mitotic cycle; also the activities of a given
mitotic stage may be chiefly chemical or chiefly molar. We should,
therefore, expect to find individual stages presenting velocity-gradients
more elementary {i. e., less composite) than the same gradient char-
acteristic of mitosis as a whole. Examination of the data shows that
for the mitotic cycle as a whole {i. e., the 10 active stages), an increase
of 10° (from 10° to 20° C.) causes a reduction in duration from
unity to 0.8342 (velocity increase of +1.1990), while an increase of
10° C. (from 20° to 30° C), taking 20° as the standard, causes a
reduction in duration for the 10 active stages from unity to 0.7158
(velocity increase of + 1 .3926) . Thus the cumulative effect of increas-
ing temperature upon the velocity of mitosis is, in the present experi-
ments, greater in the higher than in the lower temperatures, in this
respect resembling the simpler chemical reactions. (See pp. 39
and 43.)

IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 45

Further, if we take each of the 10 active stages singly, we find that the
same rule appHcable to the 10 stages as a whole holds good, with the
single exception of stage 3, the spireme stage, in which an increase of
temperature from 10° to 20° C. causes an increase in velocity of 2.9599
times, while from 20° to 30° C. velocity is increased only 2.6404. This
decrease is sUght, but it operates in the direction of general physio-
logical rather than simple chemical expectation. (See pp. 38 and 42.)
Nevertheless the values are so close that, considering stage 3 only, the
fitting to van't Hoff's rule is most striking. Thus, judged by the
van't Hoff rule alone, from its reactions to heat, stage 3 seems to be
a comparatively simple chemical reaction; but, as seen through the
microscope, it is characterized by molar changes also. So it is prob-
able that the close approximation of its Qio value to +3.0 at both the
upper and lower temperature ranges is due to its being the resultant
of a number of conflicting higher and lower values, else all processes
involved were alike in having the same Qio characteristics, which latter
is possible, but not probable.

The movement of chromosomes. — Stages 4 to 7, as designated in this
study, involve the movement of chromosome-bodies within the cell.
Although the chromosomes may be attached by strands, it may be
profitable to make comparison with the action of heat upon the rate of
movement of other bodies in protoplasm. In Davenport's ''Experi-
mental Morphology" a diagram^ shows the relation between tempera-
ture and the rate of movement of the chlorophyll-grains floating in the
protoplasm of the cells of three species of green plants. These curves
show a rapid rise in rate of movement from slightly above 0° C. to from
33° to 39° C, and then a rapid falling off. Before their breaking points
they are essentially the shape of the curves plotted for velocity-reactions
of most of the mitotic stages to temperature-changes. The curve is
specific for each particular species. So, with the specific mitotic stages,
there is a specificity of reactions due, doubtless, as among the different
species and processes above referred to, to a distinctive complex of
physiological {i. e., physico-chemical) properties.

The peculiar reaction of mitotic stage No. 6. — From the present
experimentation one of the most interesting results is in reference to
mitotic stage No. 6, in which the chromosomes are moving from the
equatorial plate toward the poles. One would naturally suspect that a
rise in temperature would increase the speed of these moving bodies,
as a rise in temperature increased the rate of movement of the
chlorophyll-granules above referred to, but such is not the case.
"WTiereas it is true that a rise in temperature increased the speed of the
whole mitotic process, it actually decreased the speed of this particular
stage. The unexpected response of this stage to temperature-

^ Davenport, Charles B. Experimental Morpholog>-, p. 226, 1899. Data from Velten, W.
Die Einwirkung der Temperatur auf die Protoplasma-bewegung. Flora 59: 177-217, 1876.

46 DURATION OF THE SEVERAL MITOTIC STAGES

increments might indeed be considered as a mistaken interpretation
due to bad statistical methods, or to experimental errors, if we did not
have corroborative evidence. If the temperature-response of stage 6
in cells growing at 20° C. is compared with those growing at 10° C. we
find a slowing-down, both relatively and absolutely, caused by an
increased temperature, and when we take the duration at 10° C. or
that at 20° C. as a basis, we find also that at 30° C. there is a similar
response, namely, a slowing-down relatively to the velocity increments
of the preceding and following stages. This is seen graphically in
Chart No. 18 and is too consistent to have been due to error. The
decrease in the velocity of stage 6 caused by a rise in temperature is
outstanding and real. This brings within range of profitable experi-
mentation work seeking to determine the nature of the forces moving
the chromosomes from the equator toward the poles.

From whatever angle viewed, the problem of the nature of mitotic
forces enters the field of physical chemistry, and consequently a more
refined analysis of its dynamics is being sought with greatest profit in
the realm of this science. Analysis by differential temperature-reac-
tions is only one means of attacking the problem, but its possibilities
are promising. In a supplementary study^ there were brought together,
for the purpose of aiding in the analysis of the mitotic potential, (a) the
facts concerning the velocity-reactions to temperature-differences of
the several mitotic stages of the growing root-tips of the onion as
determined in the present investigation, and (6) data from the experi-
ments recorded in scientific literature on the temperature-coefficients of
a number of elementary and complex physical, chemical, and physio-
logical processes.

SUMMARY.

(1) This study sets forth and demonstrates the mathematical and
biological soundness of a statistical and cytological method of measur-
ing both the relative and absolute durations of the several arbitrarily
delimited progress-stages in cell-division.

(2) The net results of this investigation are given in concise form in
the accompanying table (No. 3) ''Principles and formulas for determin-
ing the relative and absolute durations of the several mitotic stages,"
and in the ''Summary Chart," which constitutes the frontispiece and
which gives in detail the measurements and ratios found by applying
the demonstrated principles to three actual cases, namely, to meas-
uring and comparing the duration of the ten active and one resting
mitotic stages in the dividing root-tip cells of the common onion
{Allium cepa) at 10°, 20°, and 30° C.

'Laughlin, Harry H. The Dynamics of Cell-Division. Pro. Soc. Exp. Med. and Biol.,
XV, 8, No. 179 (1357), pp. 117-122. May 1918.

IN THE DIVIDING ROOT-TIP CELLS OF THE ONION. 47

(3) From the Qio values derived from these comparisons it is found
that each mitotic stage presents characteristic velocity-reactions to
temperature-increments. These reaction-values approximate van't
Hoff's expectations, thus indicating that most probably the repertoire
of activities constituting each such mitotic stage is composed of the
actions and interactions of those much more elementary physical and
chemical forces which measured in more isolated relations have been
shown to react in this same velocity-fashion.

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Bayliss, W. M. Nature of enzyme action. London. 1911

. The mechanism of chemical change in living organisms. Nature 97, 352-353.

1916.
Chamberlain, C. J. Periodicity in mitosis. Bot. Gaz. 61, 242-243. 1916.
Child, M. C. Individuality in organisms. Chicago. 1915.
CoNKLiN, E. G. Cell size and nuclear size. Jour. Exp. Evol. XII. 1912.
. Experimental studies on nuclear and cell division. Jour. Acad. Nat. Sci. Phila.

1912.

. Why polar bodies do not develop. Proc. Nat. Acad. Sci. 1, 491-496. 1915.

. Effects of centrifugal force on the polarity of the eggs of Crepidula. Proc. Nat.

Acad. Sci. 2, 87-90. 1916.
Davenport, C. B. Action of heat upon protoplasm. Experimental Morphology, Ch.

VIII, 219-273.

. On normal growth. Experimental Morphology, Ch. x, 281-292.

. Effects of heat on growth. Experimental Morphology, Ch. xviii, 450-469.

. On scientific and plotting data and the frequency polygon. Statistical Methods,

Ch. II, 10-18.
Green, J. Anatomy of plants. History of Botany (Sachs), 181-182. 1909.
Harvey, E. Newton. Effects of different temperatures on the medusa Cassiopea, with

special reference to the rate of conduction of the nerve impulse. Carnegie Inst.

Wash. Pub. No. 132. 1910.
Heidenhain, M. Die vitale Granulafarbung. Plasma und Zelle, 1, 434-472.
Kanitz, a. Temperatur und Lebensvorgange. Berlin. 1915.
Karsten, G. tjber Embryonales Wachstum und seine Tagesperiode. Zeit Bot., 7, 1-34.

1915.
Kellicott, W. E. The daily periodicity of cell division and elongation in the root of

Allium. Bui. Torr. Club., 31, 529-550. 1904.
Krough, August. On the influence of temperature on the rate of embryonic development.

Zeit. f. All. Physiologie, 16, 163-177; Ibid., 16, 178-190.
Laughlin, Harry H. The dynamics of cell-di vision. Proc. Soc. Exp. Med. and Biol.,

XV, 8, No. 179 (1357), pp. 117-122. May 1918.
Lehenbauer, p. a. Growth of maize seedUngs in relation to temperature. Physiol. Res.,

5, 247-288. 1914.
Levi, G. II ritino e le modaUita della mitosi neUe cellue viventi coltivate in vitro. Arch.

Ital. di. Anat. e di. Embr., 15, 243-264. 1916.
Lewis, W. H., and Margaret, R. The duration of the various phases of mitosis in the

mesenchyme cells of tissue cultures. Anat. Rec, 13, No. 6, 359-367. 1917.
LiLLiE, Ralph S. Mass action in the activation of unfertilized starfish eggs by butyric

acid. Journ. Biol. Chem., 24, 233-247. 1916.
. Physiology of cell division, vi. Rhythmical changes in the resistance of the

dividing sea-urchin egg to hypotonic sea water, and their significance. Journ.

Exp. Zool., 21, 369-402.

48 REFERENCES.

LiLLiE, Ralph, S. Temperature-coefficients in the activation of starfish eggs by butyric

acid. Biol. Bui., 32, 131-158. 1917.
LiNSSER, Carl. Die Period ischen Erscheinungen des Pflanzenlebens in ihrem Verholtniss

zu den Warmeerscheinunzen. Mem. Acad. Sci. St. Petersb., ser. vii, vol. xi, No.

7, p. 35. 1867.
Livingston, B. E. Physiological temperature-indices for the study of plant growth in

relation to climatic conditions. Physiol. Res., 1, No. 8, 399-420. 1916.
. A single index to represent both moisture and temperature conditions as related

to plant growth. Physiol. Res., 1, No. 9, 421-440. 1916.
LoEB, Jaques. The Organism as a Whole. New York. 1916.
LoEB and Chamberlain. An attempt at physico-chemical explanation of certain groups

of fluctuating variations. Exp. Zool. vol. 19, No. 4. 1915.
MacDougal, D. T. The auxothermal integration of cUmatic complexes. Amer. Jour.

Bot., 1, 186-193. 1914.
MacMillan, C. On the growth-periodicity of the potato-tuber. Amer. Nat., 25, 462-

469. 1891.
Mathews, A. P. General properties of living matter. Physiol. Chem., Ch. 1, 3-15.
McClendon, J. F. Physical chemistry of vital phenomena. Princeton. 1917.
Pearl, R. On the frequency constant of a variable, z=f (xiXj). Biom., 9, 437-438. 1909,
Pearson, K. On the probable error of frequency constants. Biom., 2, 273-281. 1902.
Philip, J. C. Velocity of chemical reaction. Physical Chem., ch. xiii, 276-306.
Reed, G. B. Some modern conceptions of spontaneous generation. Sci. Am. Sup. No.

2133 (Queen's Quarterly). 1916.
Riddle, Oscar. The rate of digestion in cold-blooded vertebrates. The influence of

season and temperature. Amer. Jour. Physiol., 24, 447-458. 1909.
Richards, A. Mitosis in the root-tip cells of Podoplyllum peltatum. Univ. Kans. Sci. Bui.,

vol. 5, No. 6, 87-99. 1909.
Sabline, V. L'lnfluence des agents externes sur la division des noyaux dans les racines

de Vicia faba. Rev. Gen. Bot., 15, 481-497. 1903.
Sachs, Ferdinand Gustav Julius von. Tiber die obere Temperaturgrenze der Vegetation.

Flora, 5. 1864.
. Uber den Einfluss des TagesUchtes auf Neubildung u. Enfaltung verschildener.

Pflanza-organe, Bot. Zeitg. sup. 1863.
Snyder, Charles D. A comparative study of the temperature-coefficients of the velocities

of various physiological actions. Amer. Jour. Physiol., 22, 309-334. 1908.
. On the meaning of variation in the magnitude of temperature-coefficients of

physiological processes. Amer. Jour. Physiol., 28, 167-175. 1911.
. An interpolation formula used in calculating temperature-coefficients for velocity

of vital activities. Science, 34, 414-416. 1911.
Strasburger, E. Zellbildung und Zelltheildung. 3 Aufl. 171. 1880.
Tashiro, Shiro. a chemical sign of life. Chicago. 1917.

van't Hopp, J. H. Vorlesungen iiber theoretische und physikalische Chemie, 1898.
Ward, H. M. On the biologv of Bacillus ramosus (Fraenkel), a schizomycete of the River

Thames. Pro. Roy. Soc, 58, 26.5-468. 1895.
Wilson, E. B. Cell-division. The Cell, Ch. ii, 65-121.

Woodruff, L. L., and G. A. Baitseli<. The temperature-coefficient of the rate of repro-
duction of Paramoecium aurelia. Amer. Jour. Physiol., 29, 147-155. 1911.

I. ^Method Chart.

a Hypothetical Case ir> v.

iM^

i^W-

m

mc attempt by connecting high
pmnu in Procession Index (P. I.) Com-
plete corrections made for dilTorences in
(n) size of &amplo and (b) variatione in
Mitotic Indices and (o) vuri.

2.— Properties of four

condition-cc

miplexes in reference to mitotic indices and stage durations.

Type,

Condition-
complex.

Relative stage

frequency (i. e.

S.l.)inaselected

observation.

E S.I. for
a given stage
through 8Ur-

observations.

P, I.

Use of P. I. in determining the A. A. D.

Possibility of
determining
the A. A. D,
by S. I. or
P. I.

I.
II".

III.

IV'.

Stage durations

equal. M. I.

constant.
Stage durations

equal. M. I.

varying.

Stage durationa
unequal.

M. I, constant.

Stage durationa

unequal.

M. I. varying.

ocA. R. D

Not ocA. R. D.

ocA. R.D

NotocA. R.D.

ocA. R. D.
ccA. R. D..

ccA. R. D. . .
ccA. R. D..

Constant for all
stages and obser-
vations.

Not constant, but
bearing a con-
stant relation to
its concomitant
S. I. of the same
stage through
successive obser-
vations.

Constaut for all
stages and obser-
vations.

Not constant, but
bearing a con-
stant relation to
its concomitant
S. I. of the same
stage through
successive obser-
vations.

None

Impossible.

Possible by
either S. 1.
or P. I.

Impossible.

Possible by
P. I. only.

Superfluous; S. 1. and P. I. coincide. Orderly pro-
cession of S. I. in relation to successive mitotic
stages and successive observation-intervals is
adequate to determining the absolute duration
of a definite portion of the entire mitotic cycle.

Essential. In complex cases the P. I. restores the
recognizable and orderly procession of the S. 1. in
relation to successive mitotic stages and succes-
sive observation-intervals, thus making it possible
to measure the absolute duration of a definite
portion of the entire mitotic cycle.

n The key situation into which the
situation b, that actually found in mitosis
in onion root-tip cells, tends to be corrected
by means of the P. I. The condition-com-
plex of Type IV is the one analyzed in the
method chart (Chart No. 1) because of this
direct appUcabiiity to the case in hand.

For meaning of formulas see table No, 3,
"Principles and Formulas."

stage-d urations)

Notes:

1. Only when M. I. is constant (but regardless of variation i
S. I. of a given stage in a given observation ocA. R. D. in a single sample.

2. £ S. I. for the same stages is always cc A. R. D., regardless of variation i
stage duration or constancy in M. I.

3. Jamming is the confusion of the orderly processions of S. I. which results when one fluc-
tuation in M. I. follows another so closely that a considerable percentage of cells beginning
mitosis in the first fluctuation have finished so small a portion of the cycle that the same
stage in both the first and second waves is recorded in the same time interval. The shortening
of observation -intervals tends to diminish, but can not totally correct, this difficulty.

4. The amount of fluctuations in M. I. is not essential (however, the greater and more sudden
the fluctuation the easier the determination) to determining absolute duration by the P. I . method,
but the time intervening between pulsations (i. e., changes in M. I.) is very important — relatively
long intervals simplifying, relatively short intervals complicating, the determination.

3. — Principles and formulas for determining the relative and the absolute
durations of the several mitotic stages.

PRINCIPLES.

1. The duration of a mitotic stage is directly proportional to the summation
of its percent-frequencies (^. e., stage indices [S, I.]) observed at successive
intervals, in accordance with the principles of sampling, during the mitotic
process.

2. The absolute duration of a succession of mitotic stages is measured by
the time intei-val between two points in a recognizable procession through
time intervals and mitotic stages of the procession indices [P. L], marking,
respectively, the first and last stages in the selected succession.

FORMULAS.

1. Mitotic index.

M I = No. cells dividing. ^ ^^^^ /p. ct. PpXPi

Total number of cells (both ' a/ ^

resting and dividing) ob-
served in the same fields.

2. Stage index.

g J No. cells in a given mitotic stage.

Total number of mitotically active cells (i. e., excluding the resting
cells) observed in the same fields.

3. Average relative duration of the active cycle.

A. R. D. of C. = l when "resting" is not included as a stage; = 1— A. R.D.
of R. when "resting" is included as a stage.

4- Average relative duration of a given mitotic stage.

S S. I. of the given stage in all S S. I. of the given stage in all
A T> Tk ^f a observations. observations.

A. K. D. 01 b. = ^ r^ ^ ;; — Ti — : : \ — ; — r Or

2 S. I. of aZZ stages included No. of observation-instants,
in the cycle, in all obser-
vations.
= also the average stage index of the given stage.

5. Procession index.

S.I.

P. I.=

A. R. D.of S.

6. Average absolute duration of the entire active mitotic cycle.

Time periods elapsing between
two points in a recognizable
procession of P. I.

A.A.D.ofC.=

No. of stages covered.

X No. stages in cycle.

' No. P. I. waves followed.

7. Average absolute duration of a given mitotic stage.

A. A. D. of S. = A. A. D. of C.XA. R. D. of S.

Note: An observation consists of 1,000 cells from the same root-tip selected by counting
all cells withm a sufficient number of microscopic fields selected at random within two root-
diameters of the extreme tip.

4 —

Stage

index table.

{Preliminary study.)

Sta^e 1

\0^ 00"
a.m.

\0^ 10""
a.m.

10" 20"
a.m.

lO*" 30"'
a.m.

a.m.

\0^ 50"
a.m.

ll^'OO"'
a.m.

,,h jo-n

a.m.

l|h 20"'

a.m.

Ijh SO-"
a.m.

a.m.

l|h 50""
a.m.

12*' 00-"
noon

X Count '
2S.I.

tive Duration
(A.O.R.)

Rest-
ing

I^ount

682

668

696

744

795

846

684

789

530

507

wn

505

653

8,596

<f

S.I.

1

Count

193

189

ZOO

133

114

82

111

82

115

141

158

232

107

1,857

S.I.

.6069

.5692

.6578

.5195

.5560

.5324

.3512

.3886

.2446

.2860

.3021

.4686

.3083

5.7912

.4473

2

Count

53

59

27-

5ih_

38

_35.

.--9r

'"'wi

146

121

148

130

85

1,029

5.1.

.1666

.1596

.0838

_.2-ie9'

'.Tels

.2272

"72B79~-H^3iL.

.3106

.2454

.2829

.2626

.1449

2.8717

.2218

3

Count

22

15

— F —

113

17

16

18

37

22

69

36

53

53

49

420

S.I.

.0691

.045!

1

.0^27

.0664

.0780

.1168

.1163

.1042

.14

68

.0730

.1013

.1070

.1412

1.2079

.0933

4

Count

18

6

6

6

~~~3~

:z^=-^--

rrT?r

5

21

21

14

6

II

123

S.I.

.056fi_

-.0180-

-ruTaT'

.0234

.0146

.0194

.0125

.0236

.0446

70-4 2-3-

tOZ62.

.0121

.0317

.3454

.0266

5

Count

2

"^^3^

3

4

1

0

0

1

_6,

_- -5'

' ^ "3

6

5

38

S.I.

.0062

.0090

.009§^

-0156

.0047

.0000.

..froeo'

70047

.0127

.0101

.0057

.0101

.0144

.1000

.0077

6

Count

1

2

6

X 5

2

d
1

5

1

6

9

3

2

2

44

S.I.

.0031

.0060

.019^

.0195

.0096

.ooo'o

.0157

.0047

.0127

.0182

.0057

.0040

.0057

.1246

.0096

7

Count

2

6

7

5

\-

-4^

5

2

3

11

4

1

4

51

S.I.

.0062

.0180

.0023

.0195

.0048

1
.oopo

.0157

"^009?^

~:0063-

_^23

.0076

.0020

.0115

.1163

,0089

8

Count

3

14

IS

II

7

t

1

3

27

/22

7

5

10

127

S.I.

.0094

.0421

.0493

.0429

.0341

.0129

.6q31

.0142

.0|,7<

.0446

.0134

.0121

.0288

.3643

.0Z8I

9

Count

6

12

11

12

5

3

9

~~S~

-3X

42

20

5

14

175

S.I.

.0188

.0361

.0361

.0468

.0243

.0194

.0284

.0236

.0659

^0^5?

"0^62-

.0121

.0403

. .4751

.0367

10

Count

,a

26

16

9

18

II

53

48,

,^e^

-^'-65-

113

56

60

559

S.I.

.0566

.0783

.0526

.0351

*- —

^08-76-

TOT 14'

.1677

.2274-

.0978

.1724

.2160

.1128

.1729

1.5488

.1196

2 Count
1-10

318

332

304

256

205

154

316

Zll

470

493

523

495

347

4,424
12.3453

2 Count
R + l-IO

1,000

1,000

1,000

1.000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

13,000

Mitotic
Index
(M.I.)

.318

.332

.304

256

205

.154

.316

.211

.470

.493

523

.495

.347

» If the resting stage had been included in the cycle considered,
. . No- cells in a given mitotic stage ^^^ ^^^ ^^^^,.^^ ^^ ,^^ ,0 ^^j,^^ 3,3^^3 ^.^ ,^,3 ,g3,i,g ^^^^^

bage n ex ^b. .) ^^ ^^ ^ mitotically active cells (i. e., excepting the rated at unity, A. R. D. of the resting stage=.6612 and A. R. D. of

resting cells) observed in the same fields. all 10 active stages =.3388.

There is no systematic procession of a recognizable S. I. through the succes-
sive mitotic stages during the definite time periods.

If there were fair constancy of duration of the several mitotic stages, and If
there were a rhythmic fluctuation in the Mitotic Index^then the Stage Index
procession would be quite pronounced; provided the duration of the several
stafres were equal. Hence the necessity of converting the several Stage
Indices into indices which would have appeared had all stages been of equal
duration. The Procession Index (P. I.) does this.

• ■ Connects highest S. I. of each stage.
■ Connects lowest -S. I. of each stage.

5. — Graphs shovnng mitotic and stage indices. (Preliminary study.)

lO^'OO"' lo''10'" lo''20"' lo''30'" 10''40'" lo'' 50" tl^'OO'" ll^'IO"' ll''JO"' ll''30'" ll''40" n''50"' I2''00"

= = = Mitotic Index. Based on entire number o( cells observed.
Stage Indices based on cells showing mitotic activity.

-.-.-. = Stage One = Stage Six

= Stage Two = Stage Seven

==— = Stage Three = Stage Eight

= Stage Four = Stage Nine

-'— = Stage Five = Stage Ten

6. — Procession index table. {Preliminary study.)

Stage

A.RO.

I

2

3

4

5

6

7

8

9

10

11

12

13

10^' 00""

am.

lO*' 10"
am.

10^' 20"

a,m-

a.m.

a.m.

lO** 50"

am.

ll*>00"
am.

||h lom
a,m.

,|h 20"
am.

lli^SO"
am.

||h 40"
am.

ll^50'"

a.m.

12*' 00"
noon

1

4473

S. 1.

.6069

.5692

.6578

5195

5560

5324

.3512

3886

2446

2860

,3021

4686

3083

P.I.

1.3628

1.2524

197^

1.1614

1,2430

1,1902

785!

8685

5468

6393

6753

1,0476

6892

2

.2218

&I.

1666

1596

0888

2103

■~-|053-

__;2272

2879

1390

3106

2454

2823

.2626

.2449

P.I.

751!

7195

.4003

.9508

,8354

1.0243

1.3016

■~:8972--

04013

1.1064

1,2754

1,1839

1,1041

3

0933

&I.

.0631

04S1

.0427

0664

0780

1168

1163

1042

14 68

.0730

1013

1070

1412

P. 1.

7406

.4333

4576

.7116

,8360

1 2518

1.2465

I.II17

1.5734

7824

1,0851

1.1463

1,5133

4

.0266

&I.

0566

.0180

.0197

.0234

.0146

.0194

.0125

0236

044by

0425

0267

.0121

0317

P.I.

2,278

.6766

7406

.8796

5488

.7293

,4639

.8872

1.6766

'V^gz

1,0037

4548

1.1917

5

0077

S. 1.

.0062

"~oTi3e-

...^0093

0156

.0047

.0000

.0000

.0047

.0127

0101

^0057_^

.0101

.0144

P.I.

.8051

1.1688

1.2727'

■2«.^59

.6103

.0000

.0000

.6103

1.6433

.6346

7402

1^3?!?^

04701

6

.0096

S. 1.

.0031

.0060

.0197

^tfl95

.0096

.0000

.0157

.0047

.0127

.0182

,0057

.0041

.0057

P.I.

.3229

.6250

l.OS^d

2.0312

1.0000

.0000

1.6354

4895

1.3229

1.8958

,5937

.4166

.5937

1

.0089

S. 1.

.0062

.0180

.0023^

0195

.0048

.0000

.0157

.0094

.0063

.0223

0076

.0020

.0115

P.l.

.6966

2.0224

X

.2584

2>aj^

.5393

.0000

1.7640

1.0561

7078

2.5056

,8534

2247

1.2921

8

.0231

S. 1.

.0094

.0421

.0493

.0429

"".m^t-

>..0I2_9

.0031

.0142

,0574

.0446

,0134

.0121

.0288

p.l.

.3345

1.4932

1.7544

1.5266

1.2131

.4590

.1103

"5053-

-2.0427

1.5871

4768

.4306

1.0249

9

.0367

S. 1.

.0183

.0361

.0361^

.0468

.0243

.0194

.0284

.0236

.0659\

.0851

.0382

.0121

.0403

p. 1.

.5122

.9336

.9836

l.'2v.52

.6621

.5286

.7738

.6430

1.7356

2^^88

1,0408

.3297

1.0980

10

.1196

S. 1.

.0556

.0783

.0526

.0351

"'.5B7&-

...^0714

.1677

.2274

.0978

1724

.2160

.1128

.1729

p. 1.

.4732

.6546

.4937

.2934

,7341

.5963

l,40"Zi^

.1^093

.8177

1.4414

1.8060

.9431

1.4456

«

Calculating the Absolute Duration of the Mitotic Cycle.

= The movement of a recognizable Procession Index 'through 5 stages of equal duration in 100 minutes

= The movement of a recognizable Procession Index through 6 stages of equal duration in 90 minutes

= The movement of a recognizable Procession Index through 3 stages of equal duration in 50 minutes

htocessbn Index

Time

Average Time
per Stage

5 stages 100 min.

6 " 90 " 15
3 " 50 " 16.66 "

Giving equal weight to each procession 3)51.66 min.
Average Duration of 1 step, i. e., ■'fo the

cycle = n.22 "

'.'The Average Duration of the entire

active mitotic cycle = 172.2

The Average Duration of the resting

stage =33&06 "

The Average Duration of the entire

cycle including the resting stage = 508.26

20 min Average Absolute Duration of/. . p, rp^^
the Entire Active Mitotic Cycle ^^'^- '^•° ^'

Time elapsing between 2

, points in a recognizable

S procession.ofa definite P. I.

No. of stages covered

No. P. I. followed

Naof
X stages
\n cycle

Average Absolute Duration of..,-, rc\ «Ar-. r^ »r^r^ re
a given Mitotic Stage ^^- *" °- °^ S.) = A. A. D. of C. x A. R. 0. of S.

.*. In this onion root-tip experiment the Average Absolute Duration of the succes-
sive mitotic stages is as follows:
Stage Stage Stage Stage Stage Stage Stage Stage' Stage Stage

123456789 10

77.02 38.19 16.05 4.58 1.32 1.65 1.53 4.83 &31 20.59

min. min. min. min. min. min, min. mia min. min.

7. — Graphs showing orderly succession of procession indices. {Preliminary study.)

= Lines connecting highest points of procession indices in successive stage and time order.

■*^ Procession Indices of Stage One = Procession Indices of Stage Six

": ," I I " Two = Seven

, „ Three " " " " Qght

„ „ , ^°'" = ' Nine

Five = " " " " Tor,

8. — Mitosis I

n onion

rooUip cells at 10° C.

Stage index table, and calculation of average relative duration of the several mitotic stages.

Mitotic

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

IS

17

18

19

2 Count.
2 S. I.

Average

Btage index.

= also

average relative

duration (A.R.D.)

2S. I.

A. R. D.

when R "reat-

Bidered a
Btage.

lOi'OO-

10M0»

10»20»

10''30"

101.40"

10'50"

ll'OO"

ll'lO"

llt20»
a. m.

lli'30"

11>40"

11150"

12>0O"

12M0"
p.m.

121.20"
p.m.

12'30"
p.m.

12I.40"
p.m.

12'60"
p.m.

I'OO"
p. m.

Rest-
ing.

Count.

785

722

773

760

742

780

660

641

745

735

781

776

705

606

792

547

639

739

647

13,575

.7144

Count.
S. I.

136
.6325

166
.5971

117
.5154

136
.5666

129
.5000

131
.5954

171

.6029

228
.6350

78
.3058

160
.6037

173
.7899

119
.6312

187
.6338

202
.5126

82
.3942

183
.4039

122
.3379

186
.7126

141
,3994

2,847
10.1699

.5364

10.1699

.1498

2

Count.
S I.

Count.
S. I,

38
.1767

36
.1294

43
.1894

67
.2791

66
.2558

24
.0930

56
.2545

107
.3147

67
.1866

69
.2705

50
.1886

37
.1689

45
.2008

54

.1830

84
.2131

65
.2644

124
.2737

105
.2908

47
.1800

100
.2832

1,250
4.3034

.2265

4.3034

0657

3
4

17
.0790

44
.1582

25
.1101

18
.0750

22
.1000

28
.0823

25
.0696

32
.1254

30
.1132

7
.0319

25
.1116

25
.0847

38
.0964

25
.1201

39
.0860

47
.1301

12
.0459

28
,0793

511
1.7918

.0943

1.7918

.0268

Count.
S. I.

11
.0511

31
.1115

25
.1101

11
.0458

22
.0852

6
.0272

10
.0294

9
.0250

14
.0549

10
.0377

1
.0045

11
.0491

.0101

18
.0456

18
.0865

20
.0441

16
.0415

1
.0038

19
.0638

255
,9169

.0482

.9169

.0134

5

Count.
S. I.

0
.0000

0
.0000

4
.0176

2
.0083

5
.0193

2
.0090

9
.0264

7
.0194

7
.0274

3
.0113

0
.0000

3
0133

.0033

8
.0203

11
.0528

7
.0154

7
.0193

0
.0000

3
.0084

79
.2715

0142

.2715

.0041

6

Count.
S. I.

1
.0046

0
.0000

0

.0000

3

.0126

3

.0116

1
.0045

1

.0029

5
.0139

3

.0117

2

.0076

0
.0000

3
.0133

.0033

.0025

1
.0048

8
.0176

4
.0110

0
.0000

2
.0066

39
.1273

.0067

.1273

.0020

7

Count.
S. I.

1
.0046

0
.0000

4
.0176

2
.0083

5
.0193

0
.0000

1
.0029

5
.0139

5
.0196

3
.0113

0
.0000

2
.0089

.0033

4
.0101

2
.0096

4
.0088

1
.0027

0
.0000

0
.0000

40
.1409

.0074

.1409

.0021

8

Count.
S.I.

4
.0186

0
.0000

8
.0352

1
.0041

2
.0077

2

.0090

5
.0147

4
.0111

15
.0588

5
.0188

0
.0000

5
.0223

6
.0203

12
.0304

2
.0096

20
.0441

10
.0277

1
.0038

8
.0226

no

.3588

.0188

.3588

.0057

9

Count.
S.I.

2
.0093

0
.0000

0
.GOOD

0
.0000

1
.0038

0
.0000

6
.0176

5
.0139

14
.0649

1

.0037

0
.0000

5
.0223

8
.0271

9
.0228

5
.0240

33
.0728

20
.0554

2
.0076

22
.0623

133
.3975

.0209

.3975

0070

10

Count.
S. I.

5
.0232

.0035

1

.0044

0
.0000

1
.0038

0
.0000

2

.0058

4
.0111

18
.0706

1
.0037

1

.0045

6
.0267

9
.0305

18
.0456

7
.0336

15
.0331

30
.0831

12
.0459

30
.0849

101
.5139

.0270

.5139

.0068

2 Count
1 to 10.

215

278

227

240

258

220

340

359

255

265

219

224

295

394

208

453

361

261

353

6,425

2 A. R. D.
.9994

22 S. I.
18.9919

2 10 active
.2834

2 Count
R+1 to 10.

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1.000

1,000

1,000

1,000

22 Count
19,000

2R+10 active
.9978

Mitotic
Index (M. I.).

.215

.278

.227

.240

.258

.220

.340

.359

.265

.265

.219

.224

.295

.394

.208

.453

.361

.261

.353

2 M. I. 5.425

Average
M.I. .2865

9.-

—Mitosis in or

ion root-tip cells at 20° C. Stage index table

and ca

'culation of average relative duration of ike several mitotic stages.

Mitotic
stage^

1

2

3

4

5

6

7

8

9

10

u

12

13

14

15

16

17

IS

19

S Count.
I S. I.

.\verage

stage index

= also

average relative

duration (A.R.D.)

22 8. I.

A. R. D.
when R "rest-
ing" ia con-
sidered a
stage.

lO'DO"

lO'lO"

10'20»

lO'SO"

lOMO"

10''50"

n'OO"

U'lO-

1H20"'

11>30"

IIHO"

U'SO"

12i'00»

12110"
p.m.

12>'20"'
p. m.

12''30"
p.m.

12M0"
p. m.

12i'50»
p.m.

I'OO"
p.m.

Rest-

Count.

665

758

751

770

795

686

717

035

469

603

605

680

720

750

620

647

557

485

11,919

.6621

1

Count.
S. I.

253
.7552

192
.7933

188
.7469

140
.6517

138
.6731

194
.6178

222
.7844

281
.7698

433
.8154

267
.6725

297
.7518

215
.6718

203
.7250

145
.5800

290
.7631

271
.7677

356
,8036

389
.7653

4,478
13,0984

,7280

13.0984

.2487

=

Count.
■S. I.

2S
.0S35

21
,0867

31
.1244

30
1607

24
,1170

43
.1369

25
.0883

30
.0821

37
.0696

46
.1158

21
.0531

36
.1125

25
.0892

44
.1760

28
.0736

26
,0736

35
,0790

51
.0990

587
1,8210

,1012

1.8210

.0326

3

Count.

S. I.

6
.0179

10
,0413

7
.0281

7
.0312

9
,0439

17
.0541

17
.0800

9
,0246

19
.0357

13
.0327

16
.0405

10
.0312

12
.0428

23
.0920

14
.0368

13
,0368

9
.0203

9
0174

220
.6873

0382

.6873

.0122

4

Count,
.S.I.

4
,0119

7
.0289

8
.0321

15
.0669

10
,0487

15
.0477

5
.0176

11
,0301

10

.0188

17
.0428

32
.0810

i

23
.0718

14
.0600

15
.0600

9
.0236

8
.0226

22
.0496

24
.0466

249
.7507

,0417

.7507

.0138

5

Count.
S. I.

0
,0000

1
,0041

2
OOSO

1
.0044

1
,0048

6
,0191

1
.0035

8
.0219

6
.0112

4
.0100

8
.0202

9
.0281

2
.0071

9
.0360

4
.0105

6
.0169

4
.0090

2
.0038

74
.2186

.0121

.2186

.0041

6

Count,
S, I,

3

,O0S9

0
.0000

I
.0040

3
.0133

,0097

5
,0159

1
.0035

4
.0109

4
.0075

4
.0100

3
.0075

s

7
.0218

2
.0071

6
.0200

3
.0078

4
.0113

0
.0000

6
.0116

57
.1708

0094

.1708

,0031

7

Count.
S. I.

2
,0059

1
.0041

2
.0080

3
.0133

3

,0146

7
,0222

0
.0000

4
.0109

4
.0075

5
.0125

2
.0050

1

2
.0062

2
.0071

2
.0080

1
.0026

2
.0056

0
.0000

3
.0058

45
.1393

.0077

.1393

,0025

8

Count.
S. I.

4
,0119

1
.0041

4
.0160

6
.0267

3
.0146

9
.0286

4
.0141

6
.0164

8
.0160

12
.0302

4
.0101

.1
s

2
.0062

1
.0035

2
.0080

7
.0184

1

.0028

2

.0045

9

.0174

85
.2485

.0138

.2485

0047

9

Count.
S.I.

12
,0358

2
.0082

5
.0200

4

.0178

5
.0243

7
.0222

3

.0106

5
.0136

3
.0056

10
.0251

6
.0151

7
.0218

6
.0214

3
.0120

12
.0316

7
.0198

2
.0045

15
.0291

114
.3384

.0188

.3384

.0063

10

Count.
S, I.

23
,0686

7
.0289

3
.0120

3
.0133

10
.0487

11
.0350

5
.0176

7
.0191

7
.0131

19
.0478

6
.0151

9
.0281

13
.0464

2
.0080

12
.0315

15
.0424

13
.0293

7
.0135

172
.5184

.0288

.6184

.0095

S Count
1 to 10,

335

242

249

224

205

314

283

365

531

397

395

320

280

250

380

353

443

516

6,081

S A. R. D.

.9997

22 S. I.
17 9914

£ 10 active
.3375

r Cunt
R+1 to 10.

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

21 Count
18,000

2R+10 active
.9996

Mitotic
Index (M. I.).

,335

,242

.249

.224

.205

.314

.283

.365

.531

.397

.395

.320

.280

.250

.380

.353

.443

.515

2 M. I. 6,081

Average
M. I. .3378

10. — Mitosis in onion root-tip

cells at

SO°C.

Stage index ta

)le, and calculation of

average

relative

duration of the

several mitotic stages

Mitotic
stage.

1

2

3

4

5

6

7

8

9

ID

11

12

13

14

IS

16

17

18

19

2 count
Z S. I.

Average

stage index

= also

average relative

duration (A.R.D.)

22 S. I.

A. K. D.
when R "rest-
ing" is con-
sidered a
stage.

lO'OO-

lOMO"

10'20»

lO'SO"

lOMO"

lO'SO"

ll'OO"

ll'lO"

11'20"

U'SO-

UI.40'"

11'50»

12W

i2no'°

p.m.

12i'20»
p.m.

12i'30«
p. m.

12H0"
p.m.

12''50»
p.m.

I'OO"
p.m.

Kest-
1115.

Count.

369

466

431

531

536

499

477

439

364

325

393

231

373

201

234

82

306

282

6,639

.3632

1

Coimt.
S. I.

547
.8668

454
.8501

469
.8242

370
.7889

389
.8389

429
.8562

467
.8929

476
.8484

563
.8852

675
.8518

482
.7940

715
.9297

583
.9298

747
.9349

716
.9347

885
.9640

653
,9409

673
.9373

10,193
16.8687

.8819

15,8687

,5662

2

Count.
S. 1.

29
.0459

15
.0280

28
.0492

22
.0469

27
.0581

13
.0259

8
.0152

9
.0160

21
.0331

18
.0266

29
.0477

13
.0169

13
.0207

13
.0162

12
.0156

8
.0087

23
.0331

9
.0125

310
.5163

.0286

.6163

.0172

3

Count.
.S.I.

7
.0110

12
.0224

9

.0158

8
.0170

15
.0323

27
.0538

12
.0229

10
.0178

9
.0141

16
.0237

21
.0346

18
.0234

10
.0159

12
.0160

11
.0143

9
.0098

6
.0086

9
.0125

221
.3648

0202

.3648

.0122

4

Count,
S I.

,0348

24
.0449

18
.0316

25
.0533

8
.0172

18
.0359

4
.0076

14
.0249

10
.0157

21
.0311

10
.0164

6
,0078

10
.0159

5
.0062

7
.0091

7
.0076

2
.0028

13
.0181

224
.3809

,0211

.3809

0124

5
6

Count.
.S. I.

Count,
S. I.

4
.0063

3

.0047

_|_

3

.0056

6
.0105

4
,0085

5
.0107

2
.0039

5
.0096

5
.0089

3
.0047

8
.0118

8
.0131

3
.0039

1
.0015

0
.0000

0
.0000

1
-0010

0
.0000

0
.0000

58
.0999

0055

.0999

.0032

1
.0018

9
.0168

3
.0063

1

.0021

4
.0079

3
.0057

3
.0063

3
.0047

8
,0118

9
.0148

1
.0013

2

.0031

3
.0037

5
.0066

3
.0032

1
.0014

1
.0013

63
.1014

,0056

.1014

.0035

7

Count,
S. I.

1
.0015

1

1
.0018

6
.0105

3

.0063

3

.0064

1
.0019

4
.0076

6
.0089

1
.0015

5
.0074

5
.0082

0
.0000

1
.0015

0
.0000

3

.0039

0
.0000

1
.0014

2
.0027

42
.0716

.0039

.0715

.0023

8

Count,
S, I.

3
.0047

6
.0112

4
.0070

5
.0106

5
.0107

2
.0039

7
.0133

5
.0089

6
.0078

7
.0103

11
.0181

4
.0052

.0031

4
.0050

4
.0052

0
.0000

3
.0043

4
,0055

81
.1348

,0074

.1348

.0046

9

Count,
S.I.

12
.0190

8
.0149

14
.0246

14
.0298

4
.0086

4
.0079

6
.0114

15
.0267

4
.0062

10
.0148

16
.0263

3
.0039

0
.0000

7
.0087

4
.0062

3
.0032

1
.0014

5
.0069

130
.2195

.0121

,2195

.0072

10

Count.
S.I.

3

.0047

10
.0187

6
.0106

15
.0319

7
.0150

1
.0019

7
.0133

19
.0338

17
.0267

7
.0103

16
.0263

6
.0078

6
.0079

8
.0100

4
.0052

2
.0021

4
,0057

.0027

139
.2345

.0130

,2346

.0077

I Count
1 to 10.

631

534

569

469

464

501

523

561

636

676

607

769

627

799

766

918

694

718

11,461

2 A. R. D.
.9993

22 S, I.
17.9923

2 10 active
.6364

S Count
R+1 to 10.

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

1,000

22 count
18,000

2R-H0 active
.9996

Mitotic

In.lfxlM. I),

631

..534

569

.469

.464

.501

,523

.561

.636

.675

.607

.769

,627

.799

.766

.918

,694

.718

2 M. I. 11.461

Average
M. I. .6367

11. — Graphs showing mitotic indices at 10° C, 20° C. and 30° C.

I 2 3 ^ 5 6 7 8 9 10 II 12 13 1*1- 15 16 n 18 19

10*' 00" 10^ 10"" 10*' 20"'|o''30"'IO''m'"IO*'50'"Ii''00'"|I*' I0"'1I*' ZO'"m*'30"'11*'40'"i|'' so" IZ*" 00"" IZ*" I0"'i2''20'"i2''30'"i2*'«)'"i2'' 50" l*" 00"
I^Q a.m. a.m. a.m. a.m. a.m. a.m. a.m. a.m. a.m. a.m. a.m. a.m. m. p.m. p.m. p m. p.m. p.m. p.m.

M.I. at lO'C.
20°C.,and 30°C.
M.I. at ZO°C

."flit-Av.M.l.at lO'C,
20°C.,and 30°C.

root-tip ceUs at lO^C. Procession index table, and calculation of average absolute duration of the several mitotic stages.

CaJailation of A mage Absolute Duration lA.A.D)

Wnvc
No.

No. of stages
passed through

Minutes.

Av. stage duration =
No. of min.-J- No. of stages.

1
2
3
4
5
6

7
9
9
9
9
9

60
80
100
90
90
90

8.571
8.888
11.111
10 000
10 000
10.000

Total , ..58 570

10 active stages+R = 100.00 per cent of entire duration = 292,52 r

13. — Mitosis in onion root-lip celts 20" C. Procession index table, and calculation of average absolute duration of the several milotiic stages.

Calnitalion of Average Abssluie Duration tA.A.D.).

Wave

No. of BtaRes

Minutes.

Av. stage duration =

No.

passed through-

No. of min.-^No. of stages.

1

9

50

.I.SSS

2

9

60

6 666

3

9

70

7.777

4

9

90

10,000

5

9

80

8.888

6

8

£0

10 000

Total. ...48.886

Average duration of the entire mitotic cycle when the resting

period is considered a stage.
, resting 8tage)= 66.21 per cent of entire duration = 159,57 r
10 active 8tage8= 33,78 per cent of entire duration = 81.40e
live st3gC3 + R= 100 00 per cent of entire duration = 24 0.97 r

U.-Milosi, in onion root-tip celh SO' C.Procesmn index hbU. a,ui cakMion of average absolute duration of the several mitctic stages.

Wove

No. o[ fitagea

Minutes.

Av.

stage duration =

No.

pas.'^d through.

No. of

min.-r- No. of stages.

g

40

4.444

2

9
9

60
40

6,666
4.444

40

4.444

5

9

40

80

4,444
8,888

7

8

00

7 500

Total -

40 830

= Average absolute duration of stages.

= Average absolute duration of mitotic cycle.

Average duration of Ike ejitirc mitotic cycle when the resting
period is considered a stage.

R (i. e., resting stage) = 36.32 per cent of entire duration = 33.26 r
10 active stagea= G3.67 per cent of entire duration = 58.30 t

10 active 9tage3XR = 100.00 per cent of entire duration = 91.56 i

15

— Mitosis

in onion

Toot-lip cells. Summary and comparison by stages and temperatures.

10° C.

20°C,

30° C,

Mitotic

A. R. D.

A. A. D.

A. R. D.

A. A. D.

A. R. D.

A. A, D.

Per cent

Minutes

Per cent

Compared
with same
at 10° C.

Minutes

Compared
with same
at 10° C.

Per cent

Compared
with same
at 10° 0.

Compared
with same
at 20° C.

Minutes

Compared
with same
at 10° C.

Compared
with same
at 20° C.

!•

,5354

62.2550

,7280

1.3697

69,2592

1.1340

.8819

1.6471

1.2114

61 ,4147

,9839

,8676

2*

.2265

22,1064

,1012

.4467

8,2376

.3726

,0286

.1262

.2826

1.6673

.0754

,2024

3*

.0943

9,2030

,0382

.4050

3,1094

.3378

,0202

.2142

.5286

1.1776

.1279

,3787

4*

.0482

4.7043

,0417

.8651

3,3943

.7216

,0211

.4377

.5069

1.2301

.2614

,3624

5*

,0142

1.3859

,0121

.8621

,9849

.7106

.0055

.3873

.4546

.3212

.2317

,3261

6-

.0067

.6539

.0094

1.4029

.7651

1 , 1700

.0056

.8358

.5957

.3264

.4991

,4266

7*

.0074

.7222

.0077

1.0405

.6267

,8679

.0039

.5270

.5064

.2273

.3147

,3626

8'

.0188

1.8348

.0138

.7340

1.1233

,6122

.0074

.3936

.5362

.4314

.2351

.3840

9*

,0209

2.0398

.0188

.8995

1.6303

.7602

.0121

.5789

.6436

.7054

.3458

.4609

10'

,0270

2.6352

.0288

1 0666

2.3443

.8896

0130

.4814

.4513

.7679

.2876

.3232

Cycle 10 active
stages.'

1,0000

97.60 min.

1.0000

1.0000

81.40 min.

.8342

1.0000

l.OOOO

1.0000

68.30 min.

.5971

,7158

RegtiDg stage. ••

.7147

194.92 min.

.6621

.9264

169.67 min.

.8186

.3632

.5081

.6486

32.26 min.

.1655

.2021

Entire cycle 10 ac-
tive stages and R.**

1.0000

292,62 min.

1.0000

1.0000

240.97 min.

.8237

1.0000

1.0000

1.0000

91. 56 min.

.3130

.3799

Stages 1 to 10 in-
clusive.**

.2855

97. 60 min.

.3378

1.1831

81.40 min.

.8340

.6367

2.2301

1.8848

68.30 min.

.6973

.7162

Stage 1.'

.6364

62,2550

,7280

1.3697

59.2692

1.1340

.8819

1.6471

1.12114

51.4147

.9839

.8676

Stages 2 to 10,
inclusive.*

,4640

45,2861

.2717

.5855

22.1159

.4883

.1174

.2530

.4321

6,8446

.1511

.3094

Average M. T.

At 10°C.= .286

At20°C. = .337

Compared with av. M.l. at 10° C. =1.1824

At 30° C. =.636

Compared with av. M. 1. at 20° C. = 1 .8872
Compared withav.M.r. at 10°C. =2.2315

16. — Comparison at lO'C, SCfC. and SO'C. of the average relative duration of the several mitotic stages.

■ k1, ,^0!IJ!«A«Z"%

,.'-''' /'' /'' ,^'i^tit

/\^^^,. (\^.-,. ( { {{ L,-^

J 999*f% 10 acl.ve stag.s- 28-55%

17. — Comparison at !0°C., 20°C. and 30°C. of the average absolute duration of the several mitotic stages.

"■"'^^-.;.»'*-""%^^^f^^'^i^;-

IS.— Graphs showing comparative measures at 10° C, 20° C, and 30° C. of the average absolute

durations of the ten active mitotic stages.

Base Line

A. A. D. at 20° C. compared with A. A. D.

at 10° C. as a base.
A. A. D. at 20° C. of all 10 active stages

as a whole compared with same at

10° C. as a base.
Average A. A. D. at 20° C. compared with

A. A, D. at 10° C. as a base.
A. A. D. at 30° C. of all 10 active stages

as a whole compared with same at

20° C. as a base.

A. A. D. at 30° C. of all 10 active stages

as a whole compared with same at
10° C. as a base.

■Average A. A. D. at 30 C. compared with

A.A. D.at 20° C. as a base.
Average A. A. D. at 30° C. compared with

A. A. D. at 10° C. as a base.
A. A. D. at 30° C. compared with A. A. D.

at 20° C. as a base.
■A. A. D. at 30° 0. compared with A. A, 0.

at 10° C. as a base.

Data from Table 15.

Mill WllOl 1 IHUAKV

lilH IfiKR J

:'d'l

^^^

'-■S;?*.^Kr