He first went to Braintree school, where, as he used often to say himself, he soon learned all that they could teach him.

Founded in 1807 by non-conformists, our original mission was to offer an excellent education to young people irrespective of their background, and to do so close to London but away from the pressures of the inner-city.

He held no college office except during the last two years of his residence, when he took part in the college examinations. The vacations he spent with pupils in the Isle of Wight, Wales, and the English Lakes, once also visiting France.

On 24 October 1834, Ellis and his father arrived at Papworth Everard, the village some 13 miles outside Cambridge where Challis was Rector:

"We stopped - & got out - & a fussy little man introduced himself as Mr Challis - & two, to my eyes, yahoos as his pupils - However we walked all five about half a mile to his house which is pleasantly situated - & I underwent an introduction to madame, & in an hour I was alone. ... We dined at five & began to brighten up - Crowfoot & Barrett are the two beside myself - both gentlemanly."

Ellis's initial reaction to his fellow pupils was hardly favourable - "yahoos" then as now is not exactly a term of endearment. But this occasion would have been one of his first opportunities to see students of his own age with Cambridge aspirations and presumably he expected them to exhibit a similar demeanour to himself.

As far as mathematics was concerned, Challis' teaching plan was to 'begin at the beginning', a plan which Ellis thought not altogether bad, despite the fact that his mathematical preparation was far ahead of that required. Nevertheless, shortly after arrival he was somewhat surprised to find himself having to study Bonnycastle's 'Arithmetic', an elementary textbook, first published in 1780 and designed for use in schools.

Despite plans to the contrary, Ellis's stay with Challis lasted only six weeks, the ill health which had dogged him throughout his childhood forced an early return to Bath. ... in the summer of 1835, Ellis did express regret at not being able to return to Papworth Everard. By then he was not only missing the mathematical stimulus from Challis and from being in the company of other students, he also wanted to be away from Bath.

In the Report on the Analytical Theory of Hydrostatics and Hydrodynamics which is printed in the second volume of the Transactions of the British Association, I have ventured, under a persuasion that the cause of scientific truth might be benefited, to express some doubt of the accuracy in principle of the received method of determining the nature of transmitted motion. The question will be allowed to be an important one by all who have turned their attention to this part of the application of analysis; but as it is somewhat of an abstruse nature, I fear that what is there said may not be perfectly understood without further illustration. For this reason I propose in the present communication to adduce a simple instance, which may serve to exhibit both the received method, and that which, as I conceive, ought to be substituted in the place of it.

He is best remembered for his missed opportunity to discover the planet Neptune in 1846.

Unfortunately the use of the Northumberland telescope meant Challis's direction of operations. It may be admitted that Challis was a man of no imagination. The Athenaeum, in one of its comments on the event, speaks of "the wise men who never believe until the thing is done, the sober men to whom everything that is to be is a figment in the brain of a visionary, the practical men who are not quite sure there is a future until it runs by them in the shape of time present." Challis was one of them. The search had no attraction for him. One might suppose he did not want to discover the planet, for when his eye lighted actually upon it in the course of his sweeps, and he made the note "appears to have a disc," he was not sufficiently interested to verify it on the first opportunity. We may agree he did not deserve to find it.

Challis would now be as forgotten as his peculiar ideas had not the events surrounding the discovery of Neptune in 1845 given him a genuine opportunity for scientific immortality. But he fumbled it.

I beg distinctly to say that I had no intention of putting in any claim to discovery, either for Mr Adams or myself. The facts I stated were, as I thought, sufficient to show that no such claim could be made. I certainly was desirous of proving, for the credit of English science, that Mr Adams's researches were spontaneous and independent: but I am unable to see that the fact of their being so at all diminishes M Le Verrier's merits, or that the making of the fact public implies an intention of taking in any degree from the honour of the discovery. The very natural wish to show that the University of Cambridge could produce a mathematician capable of handling a problem of so high an order ...

Challis was trying to do his university teaching, maintain an ambitious meridian programme with mural and transit circles, use the recently completed Northumberland telescope - the largest refractor in England - and employ a smaller equatorial for extrameridian work, all with one senior and one junior assistant. For most of 1846 Challis was also fully occupied with the reduction of comet observations.

You know that I attach importance to the examination of that part of the heavens in which there is a possible shadow of reason for suspecting the existence of a planet exterior to Uranus. I have thought about the way of making such examination, but I am convinced that ... there is no prospect whatever of this being made with any chance of success, except with the Northumberland telescope.

Courteous in manner, kindly in disposition, simple and unassuming in character, Challis was nevertheless thrown into a position of intellectual antagonism to many of his most distinguished contemporaries by the peculiarity of his scientific views. A striking proof of the amiability of his disposition is afforded by the fact that he never lost consideration for an opponent, or allowed disagreement to degenerate into hostility. For some slight acerbity in the mode of carrying on a controversy with Mr Adams in 1854 on points connected with the lunar theory, he, fifteen years later, publicly expressed regret, while acknowledging the justice of the criticism he had then repudiated.

His aim was a lofty one. It was nothing less than the co-ordination of all the known facts of science under one general theory of physical action. Certain hydrodynamical theorems, which he believed himself to have demonstrated, admitted, in his firm conviction, of application to the observed laws of light, heat, gravity, molecular attraction, and electricity. The conclusion pointed to was that the physical forces are mutually related, because all are modes of pressure of the same ethereal medium.

After repeated efforts to prosecute this undertaking, I was compelled by the pressure of my occupations at the Cambridge Observatory, to desist from it in 1859, when 112 pages had been printed. I had not, however, the least intention of abandoning it. ... When, according to the best judgment I could form respecting the applications which the results of my hydrodynamical researches were capable of, I seemed to see that no one was as well able as myself to undertake this necessary part in science, I gave up (in 1861) my position at the Observatory, under the conviction, which I expressed at the time, that I could do more for the honour of my University and the advancement of science by devoting myself to theoretical investigations, than by continuing to take and reduce astronomical observations after having been thus occupied during twenty-five years.

By calculations made on the hypothesis that the force of gravity acts according to the law of the inverse square, Newton gave dynamical reasons for Kepler's laws, which may also be called causative reasons, in-as-much as whatever causes is force, or power, as we know from personal experience and consciousness. The principle which is thus applied to physical astronomy I have extended in a subsequent part of this work to all quantitative laws whatever. I have maintained that all such laws, as discovered by observation and experiment, are so many propositions, which admit of à priori demonstration by calculations of the effects of force, founded on appropriate hypotheses. This, in short, is Theory.

... gave in detail the reasons of his disapproval of the new theorems. These reasons, I now willingly admit, proved that I had no right to conclude from my arguments that ...

... while my views were in a transition state, and then, as I received from none of my mathematical contemporaries any expression of assent to them, I was desirous of giving the opportunity for discussion which is afforded by publication in that Journal.

I have argued that the superstructure of physical science is raised by two essentially different means, by experiment and by mathematical reasoning, and that for making it complete, it is absolutely necessary to employ them in combination.

... I feel a desire to be released from the more immediate duties of my Professorship, in order that I might have complete leisure for preparing a new edition of the portion of this work that embraces Physics, with the view of producing a 'Treatise on the Theoretical Principles of Experimental Philosophy' as exact in point of reasoning, and as free from defects, as in the existing state of physical science may be possible.