better then than now would be inferred from the apologetic tone adopted by Jacob when questioned by Pharaoh as to his age: The days of the years of my pilgrimage are a hundred and thirty years; few and evil have the days of the years of my life been, and have not attained unto the days of the years of the life of my fathers in the days of their pilgrimage.' David, to whom, before the advent of the modern statistician, we owe the idea that seventy years is to be regarded as the normal period of life,30 is himself merely stated to have died in a good old age.' The periods recorded for the Kings show a considerable fallingoff as compared with the Patriarchs; but not a few were cut off by violent deaths, and many lived lives which were not ideal. Amongst eminent Greeks and Romans few very long lives are recorded, and the same is true of historical persons in medieval and modern history. It is a long life that lasts much beyond eighty; three such linked together carry us far back into history. Mankind is in this respect more favoured than most mammals, although a few of these surpass the period of man's existence. 31 Strange that the brevity of human life should be a favourite theme of preacher and poet when the actual term of his 'erring pilgrimage' is greater than that of most of his fellow-creatures! The end of life. The modern applications of the principles of preventive medicine and hygiene are no doubt operating to lengthen the average life. But even if the ravages of disease could be altogether eliminated, it is certain that at any rate the fixed cells of our body must eventually grow old and ultimately cease to function; when this happens to cells which are essential to the life of the organism, general death must result. This will always remain the universal law, from which there is no escape. 'All that lives must die, passing through nature to eternity.' Such natural death unaccelerated by disease—is not death by disease as unnatural as death by accident?-should be a quiet, painless phenomenon, unattended by violent change. As Dastre expresses it, The need of death should appear at the end of life, just as the need of sleep appears at the end of the day.' The change has been led gradually up to by an orderly succession of phases, and is itself the last manifestation of life. Were we all certain of a quiet passing-were we sure that there would be no moaning of the bar when we go out to sea '—we could anticipate the coming of death after a ripe old age without apprehension. And if ever the time shall arrive when man will have learned to regard this change as a simple physiological process, as natural as 30 The expectation of life of a healthy man of fifty is still reckoned at about twenty years. Hominis ævum cæterorum animalium omnium superat præter admodum paucorum.'-Francis Bacon, Historia vitæ et mortis, 1637. the oncoming of sleep, the approach of the fatal shears will be as generally welcomed as it is now abhorred. Such a day is still distant; we can hardly say that its dawning is visible. Let us at least hope that, in the manner depicted by Dürer in his well-known etching, the sunshine which science irradiates may eventually put to flight the melancholy which hovers, bat-like, over the termination of our lives, and which even the anticipation of a future happier existence has not hitherto succeeded in dispersing. REPORTS ON THE STATE OF SCIENCE. The further Tabulation of Bessel and other Functions.-Report of the Committee, consisting of Professor M. J. M. HILL (Chairman), Dr. J. W. NICHOLSON (Secretary), Professor ALFRED LODGE, Professor L. N. G. FILON, Sir GEORGE GREENHILL, and Mr. J. R. AIREY. PART I.-Elliptic Functions. THE calculations of the Committee have proceeded steadily during the year, and the results are given in four sheets of tables for four modular angles. Sir George Greenhill has prepared the following statement for the explanation of the notation, and of the mode of use of the Tables for the various applications which may arise : The Notation and Use of the Elliptic Function Table. The Elliptic Integral which arises in a physical problem of Dynamics or Electro-magnetism requires to be carried out to a numerical result, and with as little delay as possible; but so far Table IX. in Legendre's Fonctions elliptiques' is the only source available for reducing the labour of the calculation. This Table IX. of Legendre gives F(p), the First Elliptic Integral, and E() the Second Elliptic Integral, for every degree of p, and for every degree of the modular angle ; these are defined by Legendre has shown that F() and E(p), together with the complete functions F(T) and E(T), denoted by K and E, are sufficient for the numerical calculation of the Third Elliptic Integral, when complete; as required, for instance, for 2, the conical angle subtended by a circular or elliptic disc, which gives the magnetic potential for uniform normal magnetisation, or the apsidal angle of a spinning-top. But for the general incomplete Elliptic Integral of the Third Kind (E. I. III.) the Theta and Eta function of Jacobi is required, and these are given in the Table by the function |