To express this truth mathematically is not difficult.  Thus, when a represents the amount of blood of the whole body, b the amount of the remedy, e the amount of atmospheric compression, and x the pharmaco-dynamic potentiality which we are seeking, we shall then have the simple formula: 

b x e
x =   -----
a

A definite conception of the truth of this proposition will, I think, be more readily attained by the presentation of the steps which led me to its discovery.

Let me begin, then, by stating that my attention was attracted several years ago by that unique complex of symptoms known as the “caisson or tunnel disease.”  As most physicians are aware, the caisson disease is an affection of the spinal cord, due to a sudden transition from a relatively high atmospheric pressure to one much lower.  Hence, those who work in caissons, or submerged tunnels, under an external pressure of two atmospheres or even more, are liable to be attacked by the disease shortly after leaving the tunnel.  The seizure never, however, occurs while the subject is in the caisson, or in other words, while he remains under pressure.  Moreover, when the transition from the condensed atmosphere to that of ordinary density is gradually accomplished, which may be done by letting the air escape from the lock very slowly, the caisson disease is rarely if ever set up.  It is the systematic disregard of this principle by those who work in compressed air that is responsible, or largely responsible, for the occurrence of the disease.

The chief clinical features of the caisson disease are pain, which may be relatively mild, as when confined to a circumscribed area of one extremity, or of frightful intensity, as when it appears in the ears, knees, back, or abdomen; anaesthesia and paralysis, usually of paraplegic type; bladder symptoms, assuming the form of retention or incontinence; and, more rarely, rectal disturbances (usually incontinence).

These phenomena, or rather some of them, appear some time within half an hour after the subject has left the compressed atmosphere.  It was while investigating this most interesting affection as it occurred in the course of the construction of the Hudson River tunnel, that I was able, at the same time, to study the effects of compressed air upon the organism, and especially upon the nervous system, as exhibited in a large number of persons.

The results of these studies I now submit without hesitation, and in all candor, to the judgment of the profession, believing, as I certainly do, that their practical significance from a neuro-therapeutic standpoint is assured.  Without anticipating, however, let me state that the first thing which impressed me about compressed air was its extraordinary effect upon cerebral and cerebro-spinal function.

Those who remain for a certain length of time, not too long, however, in the condensed atmosphere, exhibit a most striking exacerbation of mental and physical vigor.  They go up and down ladders, lift heavy weights, are more or less exhilarated, and, in short, behave as though under the influence of a stimulant.