some of his cases before the onset of the fever. The question
is probably determined partly by the skill and patience of the
observer, partly by the susceptibility of the patient, and partly
by the " virulence " of the parasites. A laborious search may
reveal the parasites when they are comparatively few in
number ; and on the other hand, a patient who has never been
previously infected will probably begin to suffer earlier during
the course of the invasion than one who is partially " immune."
But for a broad general rule we may, I think, accept the
principle (pending more exact researches) that if we cannot
find the parasites after careful search, their number is not
usually sufficient to produce fever. Hence I calculate that they
will not generally be numerous enough to cause illness unless
there is at least one parasite to 100,000 haematids ; that is,
50 parasites in i c.mm. of blood; or 150,000,000 in a man of
10 stone (64 kilograms^ in weight.
(9). The time required to examine blood microscopically. — It
92 THE PARASITIC INVASION IN MAN [Sect.
is very necessary to have clear ideas upon this point. Suppose
that the diameter of a " field " seen by an oil-immersion
Objective and a No. 2 Ocular measures 0*165 mm., or nearly
i/6th of a millimetre. Then by moving the specimen across
this field of vision, searching it as we move it, we shall cover,
after traversing sixty times the diameter, a strip nearly ro
centimetre long, and 0"Oi65 cm. broad. Examining strip
after strip in the same way, when we have examined sixty
strips we shall have covered nearly one square centimetre
of area.
The time required for this will depend upon the care
with which we must examine the successive fields as they
pass under the eye. If we can search at the rate of twenty
fields a minute, we can search a whole strip in three minutes
and a whole square centimetre in three hours. If the object
is large and easily visible we shall be able to move the
specimen faster than this ; if it is small and delicate, the
observer must be fairly expert to search so quickly.
Now suppose that we must examine a thin film of liquid
blood spread under a coverglass. If the average depth of
the film is only 0*00025 mm. (2*5^ or about 1/3 the diameter
of haematid), then i c.mm. of the blood will be spread out
under 4 sq. cm. of area — that is, over the whole area
occupied by a square coverglass of 2 cm. side. To do this
will require twelve hours' continuous work. If the average
depth of the film is 3*3 3/u the c.mm. of blood will cover a space
of 3 sq. cm., requiring nine hours' search ; but in this case we
shall be more liable to overlook small objects, though we
shall more easily find large ones.
With an average depth of 2*5/x, i sq. cm. of film will
normally contain 1,250,000 haematids. One-sixtieth of this,
that is, one strip as defined above, will contain 20,833
haematids ; so that, if we are fairly expert, we should be able
to search 6,944, ^^ ^^Y 7)000 haematids a minute. With an
average depth of 3'S3/m, i sq. cm. of film will contain 1,666,666
i8] TIME REQUIRED FOR SEARCH 93
haematids, which can be searched at the rate of 9,259 haematids
a minute. In the former case a single circular field of the
microscope, 165^ in diameter (area 0*0209 sq. mm.), will
contain an average of about 261 haematids. In the latter
case it will contain about 345 haematids on the average.
There are, of course, more than 3,600 squares of 165^ side
in a square centimetre; and therefore four and three times
this number of squares must be examined to search i c.mm.
of blood in films of 2'5/ji and 3'33^t in depth respectively. If
we could examine the squares at a rate so fast as one a
second, three to four hours would still be required to search i
c.mm. completely. To search the whole of the 3,000,000 c.mm.
of blood contained in a man of about 10 stone in weight would
therefore take, at the quickest rate, more than 1,027 years.
I have just estimated roughly that the parasites will
probably be numerous enough to cause fever if they number
1/100,000 haematids. If it requires twelve hours to search
I c.mm. of blood containing 5,000,000 haematids, 100,000
haematids can be searched in a little less than fifteen
minutes ; so that if the parasites are so few as this we can
expect to find them at the rate of about one every quarter of
an hour. But chance intervenes here : if we are lucky we may
find the first parasite almost at once ; if we are unlucky we
may have to search several hundreds of thousands of haematids
before finding an infected one. There is always the danger of
overlooking a plasmodium even when it should have been seen.
In a dry stained film the blood is spread out over a wider
area, so that there are only about 150-200 haematids in a
circular field of 165/ji. I think therefore that the larger
pigmented parasites are less quickly found in such than in
liquid films ; but on the other hand, the smaller plasmodia,
being characteristically coloured, are detected with much greater
certainty — as Marchoux showed [1897]. On the whole, I think
that the two methods are about equal in diagnostic value.
In my "thick-film" process [1903], i c.mm. of blood
94 THE PARASITIC INVASION IN MAN [Sect.
occupies only about i/Sth of a sq. cm. of area, or less, so that
there should be twenty to thirty times more haematids and
parasites per field. But the latter require more skill for
detection (section 65).
Such calculations demonstrate the absurdity of supposing
that there are no plasmodia present in a person because we
fail in finding one after a few minutes' search. As a matter
of fact, even if as many as 150,000,000 plasmodia are present
in an average man, the chances are that ten to fifteen minutes'
search will be required for each plasmodium found ; while if
we are careless or unfortunate we may have to look much
longer.
(10). TJie period of incubation. — To resume our study of
the invasion — we saw in subsection 6 that, in the case of P.
vivax, 1,000 protospores should produce 100,000,000 parasites
in ten days and 1,000,000,000 in twelve days. The former
number would probably be insufficient to produce fever in the
patient, and the latter would be more than sufficient. Hence
the illness would probably begin on the twelfth day after
inoculation.
It is usually thought that the incubation period must
depend exactly upon the number of organisms injected either
by the mosquito or by the experimenter ; but this is not
always correct. The proliferation of P. vivax at the rate
of ten spores at each generation every second day, starting
with various initial numbers, should be as follows : —
No. of days 028 10
{1,000 i 0,000 10,000,000 100,000,000
2,000 20,000 20,000,000 200,000,000
3,000 30,000 30,000,000 300,000,000
10,000 100,000 100,000,000 1,000,000,000
15,000 150,000 150,000,000 1,500,000,000
Thus, starting with 1,000 protospores, the number of
parasites required to produce fever, namely 150,000,000, will
not be attained until the twelfth day. Starting with 2,000
protospores, this number will, it is true, be attained on the
i8]
INCUBATION PERIOD
95
tenth day, two days earlier; but after this point we shall have
to increase the number of protospores originally injected up
to 15,000 before we can reduce the incubation period by
another two days. In other words, if we estimate correctly,
2,000 protospores should give as long an incubation period
as 14,000 protospores, or seven times as many, would give.
That is, it makes little difference to the patient whether he
is bitten by one or by seven mosquitos, each of which injects
2,000 protospores. I suppose that even two or three protospores,
if they survive, would set up infection.
I have assumed that P. vivax increases tenfold at every
generation, but this is a mere guess. The following table
gives the first seven powers of some natural numbers and
also the proliferation of a single plasmodium according to
various rates, from fivefold to twentyfold. The party-line
shows where the numbers, if multiplied by 1,000, would reach
the fever-point.
Powers of Natural Numbers.
5
6
7
25
36
49
64
81
100
121
144
169
196
225
400
125
216
343
512
729
1,000
1,331
1,728
2,197
2,744
3,375
8,000 I
625
1,296
2,401
4,096
6,561
10,000
14,641
20,736
28,561
38,416
50,625
160,000
3,125
8,776
16,807
32,768
59,049
100,000
15,625
46,656
117,649
8
9
10
262,144
531,441
1,000,000
II
12
13
14
15
20
161,051
248,832
371,293
537,824
659,375
3,200,000
1,771,561
2,985,984
4,826,809
7,529,536
11,390,625
64,000,000 ]
78,125 I
279,936
823,543
2,697,152
4,782,969
10,000,000
19,487,171
33,831,808
52,748,517
105,413,504
170,859,375
1,280,000,000
This table may prove useful for estimating the average
rate of increase of the various parasites, exact experiments
upon which are much needed. I think it possible that more
spores may be produced early in the infection than later;
and also that there is likely to be a much smaller mortality
among the spores at first than there is later, when the
germicidal powers of the host become (hypothetically) stronger
96
THE PARASITIC INVASION IN MAN
[Sect.
The following table gives the incubation periods actually
found in the fundamental inoculation experiments described
in sections 14 and 16, omitting the doubtful results. The
cases are numbered as in those sections.
I. P. MALARIAE: Blood Inoculations.
Case
10
13
14
16
23
Quantity of blood c.cm.
3
?
I
I
4
How injected
ven.
ven.
cut.
cut.
ven
Incubation (days)
12
IS
17
12
II
Case
29
30
35
36
37
Quantity of blood
2
2
4
4
4
How injected
cut.
cut.
cut.
cut.
cut
Incubation ....
16
II
25
25
25
{No JHOsquito inoculations.)
2.
P. VIVAX:
Blood Inoculations
Case
8
9
18
19
20
21
Quantity of blood c.cm.
?
15
2
2
2
2
How injected
ven.
ven.
?
?
?
?
Incubation .
■
II
II
12
12
10
10
Case
. .
22
34
41
42-
Quantity of blood
3
0-2
3
2
How injected
ven.
cut.
ven.
ven.
Incubation .
6
21
3
5
3. p. VIVAX: Mosquito Inoculations.
Case
No. of mosquitos
Incubation .
9
ID
II
24
25
27
?
I
?
?
?
6
21
15
25
17
17
15
4. /*. FALCIPARUM : Blood Inoculations.
Case
Quantity of blood
How injected
Incubation .
15
I '5
cut.
15
17
cut.
18
24
0*25
cut.
12
25
2
?
26
5
?
27
07s
i8]
INCUBATION PERIOD
97
4. P. FALCIPARUM : Blood Inoculations.
Case
.
28
31
32
33
38
39
Quantity of blood
02
2
?
?
15
1-5
How injected
?
cut.
cut.
cut.
cut.
cut
Incubation .
4
15
6
10
30
6
Case
40
43
44
45
46
47
48
Quantity of blood
1-5
I •5-4-0
I •5-4-0
I •5-4-0
r5-4-o
I •5-4-0
1-5
How injected
cut.
ven.
?
?
?
?
ven
Incubation .
17
2-5
4
7
4
3
5
5. p. FALCIPARUM: Mosquito Inoculations.
Case
No. of mosquitos
Incubation .
26
30
31
33
34
35
?
6
7
2
I
2
15
6
10
12
14
II
From these figures we collect the following extremes and
averages for the incubation period in days per case.
Lowest
Average
Highest
Quartan, blood inoculation .
II
17
25
Tertian, blood inoculation .
3
ID
21
„ mosquito inoculation
15
18
25
Malignant, blood inoculation
2-5
8
30
„ mosquito inoculation
6
II
15
As we might expect, P. malai'iae gives the highest average
incubation period, P. falciparum gives the lowest, and the
mosquito inoculations have distinctly longer periods than the
blood inoculations.
The short periods given by some of the blood inoculations
may be easily explained. When discoverable in ordinary thin-
film preparations, the parasites may number anything from
50 per c.mm., or less, to 200,000 per c.mm., or more. In the
latter case there will be 200,000,000 parasites per c.cm., so
that if I c.cm. or more of such blood is injected, the subject
should receive enough parasites to produce fever at once (by
98 THE PARASITIC INVASION IN MAN [Sect.
hypothesis) in a non-immune person ; and this has almost
occurred in some of the cases. But, besides the number of
parasites contained in the inoculated blood, there is another
question requiring consideration ; that is, whether many of
them are not killed in the syringe. In spite of the experi-
ments of Bein and Sacharoff (18-21 and 24), I think that this
is possible, or even likely. The experiments of Celli and
Santori (35-40), in which various sera were mixed with the
inoculated blood, generally show long incubation periods,
probably due to such destruction of the parasites. It is un-
fortunate that the inoculated parasites have not been counted
in a single one of these experiments.
We need not refer here to incubation periods determined
by observation of natural infections.
19. The Further Progrress of the Invasion. — We now
endeavour to trace the progress of the invasion after the
commencement of the fever.
(i). Increase of the parasites. — In assuming that about fifty
Plasmodia per c.mm. are required to produce the first illness,
we must remember that this applies only to a single set of
parasites. If the patient contains several sets, each sporulating
on different days, the total number of plasmodia should by
hypothesis be several times larger. Moreover, it does not
follow, if fifty Plasmodia per c.mm. are sufficient to produce
the first attack, that they will suffice to cause subsequent
ones after the patient has become (hypothetically) habituated
to their poison. Lastly, the various species may vary in
" virulence."
As I have said, this number, which may be called the
pyrogenous limit, is merely a rough estimate of mine. Long
researches are required to obtain a more exact figure from
observation, but it may be useful to give a few of the first
counts made by D. Thomson and myself in cases in Liverpool,
that is, not in fresh infections : —
19]
PROGRESS OF THE INVASION
99
Case.
Date.
I.
Quartan
24.1. 1910
M
25.I.1910
5)
26.1. 1910
27.1. 1910
3,
Malignant
10.I.1910
3-
Malignant
1 1.1.1910
4-
Malignant
II.I.1910
5-
Malignant
13.I.1910
Temperature.
397 C. = 27 P.i
slight rigor (? temp.)
37-40. slight rigor = 4 P.
normal = P.
396 C. = 26 P,
4ro C. = 4o P.
38oC. = io P.
3870. = 17 P.
Parasites per c.mm.
1,500, mature
83, mature
150, mature
36, mature
58,000, young forms
300,000, young forms
15,000, young forms
55,000, young forms
In the malignant cases, the young forms, being merely the
offspring of the mature parasites which caused the corresponding
forms and which were at the time in the inner organs, do not
give the number of the parent forms ; but we may form a
rough estimate of the latter by dividing the number of young
forms by ten. The quartan case (triple) gives some justifica-
tion for the figure which I have tentatively selected as the
pyrogenous limit (addendum i).
From this point, to judge from the experimental inoculations
and also from general clinical experience, the progress of an
untreated case is generally that the parasites continue to
increase in numbers till they may reach the figure of several
hundred thousands per c.mm.
No accurate computations of the increase of the parasites
seem to have been attempted even where their numbers are
large enough for easy enumeration. If they increase by 10
at each generation, they should multiply from 50 to 5,000 in four
days for tertian parasites, but there is reason to suppose that
the increase now begins to be considerably checked.
(2). The viaxinmin number of parasites. — I do not consider
that 200,000 young malignant parasites per c.mm. is exception-
ally high. In Mauritius we found in a fatal case 12/100 of the
haematids infected. Several authors record 30/100, and Rogers
^ Here P. stands for the Pyretic Scale which I propose for pathological work. It
is merely the Centigrade Scale between 37° and 47° divided into 100 parts. Thus : —
0° P. =37° C. =98 '6° F. =29 '6° R. = normal human blood temperature
30° P. =40° C. = 104° F. =32° R. =high fever.
loo THE PARASITIC INVASION IN MAN [Sect.
[1908, p. 222] mentions a fatal case " with more parasites than
corpuscles." Three or four parasites are frequently found in
one haematid. Similar copious infections are the rule in genus
Haemoproteiis {Halteridium) of birds.
There are innumerable references to this part of the subject
in the literature, but none of them are exact. Many authors
give the proportion of their cases in which they have detected
the Plasmodia in a single thin-film specimen — that is, I suppose,
in numbers over about 50 per c.mm. Rogers states that out
of his successful cases they were detected in a minute or two in
78% and in over five minutes in 10% [1908, p. 220] ; but he
failed to find any parasites in 10-20% of undoubted malaria
cases. Other observers have had still more failures. In Liver-
pool we nearly always succeed if fever is present, but the
blood is generally distributed to a class. It is obviously a
question not only of the number of parasites, but of skill ; and
I should add that not all of those who write on the subject are
as expert as may be imagined.
According to the classical theorem of Marchiafava, Celli and
Bio-nami, the sporids of P. falciparum tend to retire to the inner
organs after reaching a certain size. I remember a case where
I undertook to demonstrate the plasmodia to a sceptic, and
found for the purpose a case swarming with young malignant
parasites. A few hours later, however, when the sceptic saw
the case, they had all vanished ! Nevertheless, I think that
this theorem requires to be better verified by strict numerical
work, as it is possible that much of this supposed disappearance
from the peripheral circulation is due to the death of the
organisms (addendum i).
(3). Limiiatien -of the invasion. — Clearly, if the parasites
can continue to multiply for ever "aT the original rate, every
untreated case would infallibly die. We are therefore obliged
to admit that something happens to check the invasion. The
subject belongs to the pathology of malaria, but we should note
the following points.
19] PROGRESS OF THE INVASION loi
The arrest of the invasion may be due to one or both of two
causes. Either the parasites themselves begin to lose their
power of reproduction, or else they or the body produce some-
thing which opposes them. I doubt the former hypothesis,
because the same number of spores appear still to be formed ;
because the parasites do continue to reproduce in smaller
numbers for months, or even years ; and because in some cases
they actually do continue multiplying until they kill the patient.
Whether they are destroyed by their own toxins, or by some
germicidal substance produced by the host, is a question which
deserves much more attention than it has received. The idea
that they are destroyed solely by the phagocytes is no longer
generally accepted.
Whatever it is, the germicidal substance appears usually to
increase in power with the number of the parasites, and there-
fore to check the invasion at its height. On the other hand,
the failure of many inoculation experiments suggests that some
persons possess such a substance from the first — unless the
failures have been due to some unseen error. Out of six
birds which escaped infection in my mosquito inoculations,
one (the only survivor) was infected on a second trial ; and
the same thing happened in some of the human experiments.
The literature contains many references to the sudden
disappearance of a whole generation of plasmodia — not in
consequence of quinine, but frequently following rest in bed,
good food or shelter from heat. In the quartan case mentioned
in subsection (i), a large brood followed the sporulation of
24th January, but of these, without quinine, only about 36
per c.mm. reached maturity three days later. Many observers
describe the appearance of death — loss or change of staining
capacity, and so on — among the parasites on such occasions.
(4). TJie illness is due to a toxin. — This point also belongs to
the pathological side of the subject. Omitting reference to the
older hypotheses, it is now almost certain that the patient's
fever is connected with the discharge of some toxic substance
I02 THE PARASITIC INVASION IN MAN [Sect.
from each mature sporid at the moment when its spores are
scattered in the serum. Some of the older inoculation experi-
ments made with blood taken from a source in the state of
rigor — that is, at the moment when the sporids are breaking
up — were followed by an immediate slight reaction, suggesting
that that blood contained a toxin as well as parasites. These
results are, however, scarcely definite enough to prove the point,
especially as the inoculation of healthy blood is sometimes
followed by such a reaction. But the following excellent
experiments of Rosenau, Parker, Francis and Beyer [1905] were
much more decisive.
Case I. At Vera Cruz, Mexico, at noon on 27th October
1903, 100 c.cm. of blood were drawn from F. Martinez, suffer-
ing from a declining paroxysm of P. falciparum ; temperature
38"2° C. (=12 P.); parasites, young sporids and also gametids.
The serum of this blood was separated, diluted with an equal
part of salt solution, passed through a Chamberland B. filter
(tested), and injected (20 c.cm.) into J. Ojeira, and (equivalent)
into L. Peredo. Neither subject showed any symptom.
Case 2. At the same place, at 12.30 on 6th November 1903,
A. Mendez was suffering from a severe benign-tertian rigor
(double infection) ; temperature 39*1° C. (21 P.), rising to 40*2° C.
(32 P.). At that moment 125 c.cm. of his blood were drawn
and defibrinated. To 25 c.cm. the same quantity of salt
solution was added, and the mixture was passed through the
same filter. The filtrate had no figured elements, but showed
a red tinge, and 9 c.cm. of it were injected at 1.40 r.M. into
the right basilic vein of L. Peredo. Thirty-five minutes later
the subject " began having chilly sensations and headaches,
and presently went to bed covering himself with his blanket
(2.25 P.M.), Five minutes later (2.30) he was having a violent
chill, his teeth chattering so that we could not trust the
thermometer in his mouth." Patient was pale and vomited.
Chill lasted to 3.15 p.m.; vomited again at 3.30; fever rose
19] PROGRESS OF THE INVASION 103
rapidly to 387° C. (17 P.) at 4 p.m., nearly normal at 10.30 P.M.
Authors put the duration of the paroxysm at about eight hours.
Case 3. At same place and date, at 2 P.M., 2 c.cm. of the
same blood of A. Mendez, mixed with an equal volume of salt
solution, but unfiltered, were injected intravenously into J.
Ojeira. Subject " reacted within an hour, with a slight rise
of temperature and nausea, and four days afterwards developed
a typical malarial paroxysm, with many tertian parasites in
his peripheral blood." Typical fever (double infection) with
a few parasites at 7 A.M. on loth November. (Case 51 of
section 14.) In this case the preliminary rise of temperature,
which began within an hour after injection, reached 37'9° C.
(9 P.) and lasted five hours.
Thus, both the subjects inoculated with the blood of Mendez
taken during rigor had attacks of fever similar to that of the
source ; but the first subject inoculated with filtered blood did
not become infected, while the second subject inoculated with
unfiltered blood became infected with the same parasites as in
the source.
Unfortunately, no estimate is given of the number of parasites
in the inoculated blood. The infection of Mendez was, however,
said to be "heavy" — let us suppose 10,000 parasites per c.mm.
We may thus calculate : —
The toxin of 45,000,000 benign tertian parasites in 4*5 c.cm.
of blood caused eight hours' fever, reaching to 387'' C. (17 P.)
in Peredo.
The toxin of 20,000,000 of the same parasites in 2 c.cm. of
blood caused five hours' fever, reaching to 37*9° C. (9 P.) in Ojeira.