Finishing his school education at the age of fifteen, he now began his own education of himself. In 1795 he was apprenticed to a surgeon and apothecary (afterwards a physician), in Penzance, with whom he learned the elements of medical science; but his time during the years which he spent under Mr. Borlase was much occupied in shooting, fishing, searching for minerals and geological specimens, composing poetry, and pursuing metaphysical speculations. He was now, as through life, an enthusiastic lover of Nature; his mind was extremely active, ranging over the most diverse subjects; he was full of imagination, and seemed certain to distinguish himself in any pursuit to which he should turn his attention. During the next three or four years Davy indulged freely in speculations in all manner of subjects; he started, as people generally do when young, from general principles and followed these out to many conclusions. Even in his study of physiology and other branches of science, he appears at this time to have adopted the speculative rather than the experimental method; but unlike most youthful metaphysicians he was ready to give up an opinion whenever it appeared to him incorrect. By the time he reached the age of twenty he had discarded this method of seeking for truth, and was ever afterwards distinguished by his careful working out of facts as the foundation for all his brilliant theories.

Davy appears to have begun the study of chemistry about 1798 by reading Lavoisier's "Elements of Chemistry," the teachings of which he freely criticized. About this time Mr. Gregory Watt came to live at Penzance as a lodger with Davy's mother, and with him the young philosopher had much talk on chemical and other scientific subjects. He also became acquainted with Mr. Davies Gilbert—who was destined to succeed Davy as President of the Royal Society—and from him he borrowed books and received assistance of various kinds in his studies.

It was during these years that Davy made experiments on heat, which were published some years later, and which are now regarded as laying the foundations of the modern theory according to which heat is due to the motions of the small parts of bodies. He arranged two brass plates so that one should carry a block of ice which might be caused to revolve in contact with the other plate; the plates were covered by a glass jar, from which he exhausted the air by means of a simple syringe of his own contrivance; the machine being placed on blocks of ice the plates were caused to revolve. The ice inside the jar soon melted; Davy concluded that the heat required to melt this ice could only be produced by the friction of the ice and brass, and that therefore heat could not be any form of ponderable matter.

In the year 1798 Davy was asked to go to Bristol as superintendent of the laboratory of a new Pneumatic Institution started by Dr. Beddoes for the application of gases to the treatment of diseases. Davy had corresponded with Beddoes before this time regarding his experiments on heat, and the latter seems to have been struck with his great abilities and to have been anxious to secure him as experimenter for his institution. Davy was released from his engagements with Mr. Borlase, and, now about twenty years of age, set out for his new home, having made as he says all the experiments he could at Penzance, and eagerly looking forward to the better appliances and incitements to research which he hoped to find at Bristol.

The Pneumatic Institution was supported by subscriptions, for the most part from scientific men. It was started on a scientific basis. Researches were to be made on gases of various kinds with the view of applying these as remedies in the alleviation of disease. An hospital for patients, a laboratory for experimental research, and a lecture theatre were provided.

At this time many men of literary and intellectual eminence resided in Bristol; among these were Coleridge and Southey. Most of these men were visitors at the house of Dr. Beddoes, and many distinguished men came from various parts of the county to visit the institution. Davy thus entered on a sphere of labour eminently suited for the development of his genius. With ample mechanical appliances for research, with plenty of time at his disposal, surrounded by an atmosphere of inquiry and by men who would welcome any additions he could make to the knowledge of Nature, and being at the same time not without poetic and imaginative surroundings, by which he was ever spurred onwards in the pursuit of truth—placed in these circumstances, such an enthusiastic and diligent student of science as Davy could not but obtain results of value to his fellows. The state of chemical science at this time was evidently such as to incite the youthful worker. The chains with which Stahl and his successors had so long bound the limbs of the young science had been broken by Lavoisier; and although the French school of chemistry was at this time dominant, and not disinclined to treat as ignorant any persons who might differ from its teaching, yet there was plenty of life in the cultivators of chemistry. The controversy between Berthollet and Proust was about to begin; the Lavoisierian views regarding acids and salts were not altogether accepted by Gay-Lussac, Thenard and others; and from the laboratory of Berzelius there was soon to issue the first of those numerous researches which drew the attention of every chemist to the capital of Sweden. The voltaic battery had been discovered, and had opened up a region of possibilities in chemistry.

Davy began his researches at the institution by experiments with nitrous oxide, a gas supposed by some people at that time to be capable of producing most harmful effects on the animal system. He had to make many experiments before he found a method for preparing the pure gas, and in the course of these experiments he added much to the stock of chemical knowledge regarding the compounds of nitrogen and oxygen. Having obtained fairly pure nitrous oxide, he breathed it from a silk bag; he experienced a "sensation analogous to gentle pressure on all the muscles;... the objects around me became dazzling and my hearing more acute;... at last an irresistible propensity to action was indulged in.... I recollect but indistinctly what followed; I know that my motions were various and violent." Southey and Coleridge breathed the gas; the poets only laughed a little. Encouraged by the results of these experiments, Davy proceeded to prepare and breathe nitric oxide—whereby he was rendered very ill—and then carburetted hydrogen—which nearly killed him.

In his chemical note-book about this time, Davy says, "The perfection of chemical philosophy, or the laws of corpuscular motion, must depend on the knowledge of all the simple substances, their mutual attractions, and the ratio in which the attractions increase or diminish with increase or diminution of temperature.... The first step towards these laws will be the decomposition of those bodies which are at present undecompounded." And in the same note-book he suggests methods which he thinks might effect the decomposition of muriatic and boric acids, the alkalis and earths. Here are the germs of his future work.

After about eight months' work at Bristol he published a volume of "Researches," which contained a great many new facts, and was characterized by vigour and novelty of conception. These researches had been carried out with intense application; each was struck off at a red heat. His mind during this time was filled with vast scientific conceptions, and he began also to think of fame. "An active mind, a deep ideal feeling of good, and a look towards future greatness," he tells us, sustained him.

Count Rumford, the founder of the Royal Institution in London, was anxious to obtain a lecturer on chemistry for the Institution. Davy was strongly recommended, and after a little arrangement—concerning which Davy says in a letter, "I will accept of no appointment except on the sacred terms of independence"—he was appointed Assistant Lecturer on Chemistry and Director of the Laboratory. About a year later his official designation was changed to Professor of Chemistry. This appointment opened up a great sphere of research; "the sole and uncontrolled use of the apparatus of the institution for private experiments" was to be granted him, and he was promised "any apparatus he might need for new experiments."