54
Para. 29
The same equations must apply to all conditions of parasitism, animal
or vegetable.*
The last result is of special interest here ; if a point of toleration is reached
the resistant energy of the host must be exactly equal and opposite to the
morbific energy of the infection.
Again,  from the first two fundamental equations we get, s = vn - h.
At the point of toleration s = o, and we obtain, n = h/v ; that is,  the number
of parasites which can exist at the point of toleration varies inversely as the
virulence of the species of parasite ; which is just the idea suggested by a
comparison of halteridium, proteosoma and human malaria.
The co-efficient r represents the power of the host to inhibit the multipli-
cation of the parasites-that is, the degree of immunity possessed by him.
It is really a very complex quantity depending partly on the duration of the
infection, tending to increase with that duration, and to decrease again after
the infection has passed off. The study of it belongs specially to the new
and important science of Immunity.
It is now necessary to apply these considerations briefly to human palud-
ism. We may suppose that the first parasitic invasion begins with a rush,
before the system has had time to bring its resistant energy into play. As,
however, this energy begins to act, the invasion is repulsed (unless death
occur) and driven back to or below the point of toleration. Perhaps if the
resistance be strong enough, the parasites are exterminated then and there,
and we have spontaneous recovery. If not, the parasites remain in small
numbers ; a few, perhaps the hardiest of them, being able, like other living
things, to struggle on in an unfavourable medium. Presently the energy of
resistance relaxes (as it is known to do in other infections), or is weakened
by chill, fatigue, and so on. The parasites increase again in numbers. A
second severe invasion accompanied by a recrudescence of fever ensues, to
be followed by a second establishment of partial immunity. The history
repeats itself ; several similar attacks follow ; and we obtain the picture of a
typical case of untreated malarial infection.
Now, it is obvious that this state of things cannot continue for ever.
Each attack has a sensibly pernicious effect on the host ; anĉmia, congestions
of the organs are established. The system must make some final effort to
obtain the mastery and to exterminate and not only reduce the invaders.
It is probable that the energy of resistance increases with each successive
attack, and that each attack becomes weaker and weaker in consequence.
Lastly, the parasites can no longer make head ; the medium becomes intoler-
able for them, and they die out altogether.
Such appears to me to be the true history in untreated paludism. The
infection is a continuous one ; the successive conflagrations of fever and
periods of quiescence are due, as it were, to the swinging to and fro of the tide
of conflict between the opposing forces of the host and the invaders ; final
extinction of the invasion occurs when the former gain the victory.
This is somewhat more than hypothesis ; we are compelled to admit that
something of the kind occurs. Otherwise recovery in untreated cases would
never take place.
I have just referred to the fact that sparrows infected with proteosoma
by the bites of mosquitoes threw off the infection much more readily in
December than in July and August. This suggests that their energy of resis-
tance is greater in the cool season. Another experiment made in August last-
suggests that one attack of proteosoma confers some immunity against a second.
Five sparrows, each containing a very few parasites, were subjected to the bites
of some old infected mosquitoes [2] ; after the usual incubation period of five to
eight days, four of these birds showed a new infection characterised by the
presence of numerous young parasites. This new invasion was much more
copious than the original infection, but still it never showed the enormous
numbers of parasites found in all the originally healthy birds infected in this
manner. I bad hoped to repeat this experiment in order to obtain greater
* Note-Of course, these equations are of the roughest ; the correct ones are differential equations, involving
the independent variable time and requiring various integrations. It is scarcely necessary to go into such
detail here.                                                                                                                                                                    *