relationship been still closer. Greatly there, fore on every account must he have lamented his loss. His father had already paid the debt to nature; there was now therefore no one left, to whose friendly advice and assistance he could have recourse; for the future he was to be dependent on himself alone, his own guide, and his own counsellor.

Shortly after his removal to Yarmouth he commenced his work on the conic-sections. The design of this undertaking suggested itself to him on reading the universal arithmetic of Sir Isaac Newton. From the 24th Prop. of that book he was persuaded, that the elements of all the properties of the three conic sections might be unfolded with more ease and elegance, than had been obtained by any other method. Though the property of the generating circle was an immediate consequence of the primary proposition, yet it was for some time hid from his view. By means of this he was conducted with order and facility to every prin

cipal property of the conic sections. He soon observed, that all these sections have more connexion with the circle than with the cone; nor is it at all wonderful, that it should be so, since the circle is the principal element, from which the cone itself is generated. The circle being therefore the common genesis of the three sections, the properties which are common to them all are deduced from the common source in one common demonstration to a much greater extent, than in any treatise which deduces the section from the cone; while the discrimination of each of the sections, being a simple variation of the common genesis, not only suggests the discriminating properties, but gratifies the understanding with the immediate perception of the operating cause of them. Indeed the affinity to and dependence of the sections upon the circle is so immediate, that the demonstrator has often little more to do, than to transfer the various properties of the circle to the corresponding properties of the section. These observa

tions are here introduced as explanatory of the nature and design of a work, which for many subsequent years furnished a constant source of agreeable occupation to his leisure hours.

2

The same intemperate application to these and his other pursuits still characterized his habits of life; and a variety of consequent complaints compelled him to occasional intermissions of his studies. It is probable, that from the commencement of his taste for mathematics may be dated that want of œconomy in the distribution of his time, which led him to appropriate to the prosecution of his studies so many of those hours, that, with his infirm state of health, would have been more wisely given to sleep, and the restoration of exhausted nature. For months together has he retired to rest with the rising of the sun, and, till within a few years of his death, when his strength was not equal to such arduous exertions, it was his usual custom to prolong his studies to an advanced hour of the morning. He

seems

seems at all times to have considered his body as the mere slave to his mind, and to pay no other attention to it, than what it's necessities absolutely required. Experience however sufficiently demonstrates the injudiciousness of such a system, and it's tendency to defeat the very object, that it has in view. The powers of the mind require to be renewed by occasional interruptions of ease and relaxation; and all extraordinary efforts are calculated only to impair it's vigour, and to induce a premature decay of it's faculties. Though he was happily exempt from the misfortune of experiencing the latter effect, yet there is no doubt, but that his intemperance of application was attended with serious injury to his health and strength; and most of those bodily complaints, under which at various periods he suffered, were the result of his sedentary life. Yet we must not condemn this imprudence with too much severity, lest we include in our censure many of the wisest and the best of men, who have done honour

to

to human nature. The mere man of the world, occupied in the common concern of business or amusement, may prescribe to himself such a stated regulation of his time, as is best adapted to the nature of his pursuits; nor is there any thing in them, that forbids a practical adherence to it; but the student, who is buried in the profound contemplations of his closet, is abstracted from the world and all it's forms, he is not to be broken in upon by the ordinary calls of life; absorbed in his abstruse speculations, he is wholly inattentive to the lapse of time; nor does he cease from his intellectual exertions, until the powers of his mind, exhausted by intense application, require to be invigorated by an intermission of it's labours. These observations apply with peculiar force to the mathematical student. When the truth to be evolved is dependent upon a long connected series of deduction, where in regular progression it is to be elicited step by step, any sudden diversion of the mind breaks at once the train of it's