With one unimportant exception (the inversion of the order of two unsuccessful financial periods), this table coincides so closely with Table II. of the former Essay, that the observations which apply to the one apply almost equally to the other. In the case of the customs and excise, as of the net ordinary revenue, the unsuccessful quinquennial periods are periods of higher price than any of the successful financial periods of the same duration. But neither in the quinquennial periods nor in the longer periods of fifteen years, does the price of wheat vary as the degree of the success attending our financial operations; for the two most successful financial periods of five years each, are periods of higher price than the two least successful periods of the same duration; while the most successful of the two periods of fifteen years corresponds to a somewhat higher price than the least successful period of the same length.

Having followed so closely throughout this communication the order of inquiry observed in the Essay on the "Relation of the Price of Wheat to the Revenue," I cannot do better than maintain my consistency to the end, by appending the following summary of the results to which the present inquiry has conducted me. The first proposition will be found to be almost word for word the same as the first proposition in the former Essay:

:-

1. The influence of the price of wheat on the revenue derived from customs' and excise duties is not such as to establish a very close and uniform relation between the one and the other; for equal prices of wheat do not coincide with equal amounts of revenue, nor equal amounts of revenue with equal prices of wheat; while cycles of years of rising and falling prices are found to correspond with diminishing and increasing amounts of revenue indifferently; and even those numerical results which seem to indicate the closest relation between the price of wheat and the yield of customs and excise duties, display exceptions and irregularities which tend to impair the evidence they afford.

2. The influence of the price of wheat on the revenue from customs and excise is much less considerable than the influence of the price of wheat on the net ordinary revenue of which the customs' and excise duties constitute so considerable a part; for while, in five out of six instances, the net ordinary revenue in groups of years of low prices exceeded the net ordinary revenue in similar groups of years of high prices, in no less than four out of the same six instances the yield of the customs and excise duties was higher in the groups of dear years than in the corresponding groups of cheap years. Again, when the years following high and low prices are substituted for the years in which those prices respectively occur, and groups of years following dear years are compared with groups of years following cheap years, though there is uniformly an excess in groups of cheap years over groups of dear years, that excess is always proportionably much less in the case of the customs' and excise duties than in the case of the net ordinary revenue; and other numerical comparisons lead to similar results.

3. When the amount of the revenue derived from customs and excise duties in different years is subjected to the necessary correction of taxes imposed or remitted, and the years of successful and

unsuccessful financial operations are compared with the price of wheat, the results are found to be more in harmony with those obtained in the case of the net ordinary revenue, though the irregularities are such as to confirm the principle just laid down in the first proposition, that there is no close or uniform relation between the price of wheat and the revenue from customs and excise.

4. If the relation proved to exist between the price of wheat and the revenue from customs and excise in the year following may be safely assumed to be the true relation, then the measure of that relation would be, in round numbers, 1,841. to 24,0531. of customs and excise duties for every rise or fall of one shilling in the price of wheat, the relation between the price of wheat and the net ordinary revenue in the year following being measured by the much more considerable amount of from 42,7467. to 114,9437.

In the Essay on the "Relation of the Price of Wheat to the Revenue," I took occasion to make some observations on the light thrown by that inquiry on the real difficulties and alleged fallacies of statistics. Those observations apply with equal force to the results of the present communication. It is true of the revenue derived from customs and excise duties, as it is of the net ordinary revenue of which it forms a part, that the one result-the yield of the revenue year by year is brought about by a vast variety of distinct agencies acting with ever-varying intensity, and in constantly shifting combinations, so that it is most difficult and even impossible to obtain, in respect of any one agency, that separation and isolation which is essential to an estimate of its exact force and value. Again, the yield of customs and excise duties, like the amount of the net ordinary revenue, is subject to great disturbance, not merely from causes beyond the control of statesmen, but from fiscal reforms and revolutions of very frequent occurrence. The natural prices of wheat and of flour, for instance, have been, as already observed, disturbed by no less than seven distinct Acts of Parliament in thirty years; and other articles of prime necessity and general consumption have been subject to the same disturbing cause.

These observations apply rather to the difficulties than to the fallacies which beset the path of statistical research. The results of the present inquiry are at least equally instructive with those of the Essay so often referred to as to the true nature of some alleged statistical fallacies. In the case of the customs and excise duties as of the ordinary revenue, the curious and unexpected results obtained by comparing the price of wheat with the yield of the revenue in cycles of years of rising and falling prices, throw light upon one of the most common of statistical fallacies. By comparing the prices of wheat during every cycle of either class with the revenue in the first and last years embraced in the cycles, that uncertain response which, coinciding with the conflicting results of other comparisons, represents the whole truth, would have been converted into a response in favour of or against the prevalent opinion by the accidental or intentional selection of certain cycles to the exclusion of the rest. If such a selection was made in good faith, error would have honestly crept in-if in bad faith, the proverb "that anything may be proved by figures," would have received an apt illustration.

But the results arrived at in the present communication are suggestive of other reflections not less instructive in a statistical point of view. There is reason to believe that the great majority of statists shared the opinion of the late Mr. Porter, that the price of wheat has so constant and close a relation to the revenue as to be at all times the chief cause of the fluctuations to which the revenue is subject. The Essay on the "Relation of the Price of Wheat to the Revenue," while it showed that that opinion was not tenable, at least in the decided and dogmatic form in which it has been so often expressed, did not merely modify the strength of this preconception, but suggested to many persons a ready explanation of the result so unexpectedly obtained. It was alleged that though the price of wheat might not exercise that decided influence on the yield of the entire revenue which had been attributed to it, the prevalent opinion would be fully borne out if the inquiry were limited to those branches of the revenue which are dependent on the consumption of articles of prime necessity, and of luxuries in great demand among the mass of the population-in other words, the articles charged with customs and excise duties. There can be no doubt that this modified opinion was at least as strongly entertained as the more comprehensive dogma which it had served to replace; nor is it to be denied that the opinion which attributes to the price of wheat a great influence on the consumption and yield of articles charged with customs and excise duties is among the most general and most seemingly natural of all the articles of popular belief. Nevertheless, this opinion, general as it is, and reasonable as it seems, is not borne out by facts. It is even less able to bear the test of statistical investigation than the error which it has replaced, for the yield of the customs and excise duties is even less affected by fluctuations in the price of wheat than is the ordinary revenue itself. Does not this fact, then, teach us a useful lesson on the necessity of not taking even the most probable and popular opinions for granted? Does it not give us good grounds for believing that in all the sciences of observation -in medicine, in hygiène, in agriculture, in political economy-there are many received opinions which would be entirely changed or greatly modified if submitted to the ordeal of statistical inquiry? In the case of the question now under consideration it is obvious that it is not the statistical method which is to blame for having led to fallacious conclusions; but statists whose opinions were entitled to consideration have fallen into error and exaggeration, because, being statists, they had not taken the precaution of submitting their opinions to the necessary test of their own method.

This inquiry into the relation of the price of wheat to the revenue will not be complete till it has been made to embrace not merely the effect produced by fluctuations in the price of wheat on the net ordinary revenue, and on that part of it which arises from customs' and excise duties, but also on special articles of consumption subject to those duties, such as tea, sugar, wine, and spirits. As this is one of those questions that ought not to be left subject to any doubt which a little labour properly bestowed can remove, I hope to be able, on some future occasion, to address myself to it.

Old and New Bills of Mortality; Movement of the Population; Deaths and Fatal Diseases in London during the last Fourteen Years. By JOHN ANGUS, Esq., General Register Office.

[Read before the Statistical Society of London, Monday, 10th April, 1854.] To the plague the public of London owed their bills of christenings and burials; to the acknowledged value of such records in connexion with the property of individuals, and only in a second degree to the knowledge of their importance in political arithmetic, we are indebted for the present system of registration of births, deaths, and marriages. This is another illustration of a natural law, by which contrivances, to which men are led by fear, love of property, or other powerful impulses of the mind, become fertile in new suggestions, and subserve innumerable uses, which enrich the storehouse of knowledge and dispense incalculable benefit to mankind. If it could be imagined that England should cease among nations, that her institutions should perish and her cities crumble to the dust, and that the records of the births, deaths, and marriages of her people had survived the wreck, with collateral proof of the social purposes to which they had been applied, these records would furnish evidence, and evidence of a most satisfactory kind, that she had made some progress in civilization. Within the range of philosophical inquiry there is nothing more attractive in its character, or more important in relation to practical medicine, sanitary police, and the economy of wealth, than the laws of vitality, and the influence of age, sex, occupation, condition in life, situation, climate, change of seasons, and institutions, in promoting health or planting the seeds of disease.

The old bills of mortality* for London were commenced in 1592, but in December, 1595, on the cessation of the plague, were discontinued. They were resumed on the 29th of December, 1603, the first year of the reign of King James the First, on the recurrence of the plague, and have been continued since that time to the present without intermission, except during the great fire, when the deaths of two or three weeks were given in one bill. On the 18th of July, 1625, the parish-clerks set up a printing-press in their hall, for which they had obtained a decree under the seal of the High Commission Court; and from that date the number of burials was printed against each parish.

The returns profess to include 97 parishes within the walls, 17 without the walls, 24 out-parishes in Middlesex and Surrey; also Westminster (which was added in 1626,) containing 10 parishes. When a person died, the tolling of a bell, or an order given to the sexton for a grave, announced the event to the searchers,women-searchers," as Graunt calls them, the accuracy of whose

"old

* The invention of "bills of mortality" is not so modern as has been generally supposed, for their proper designation may be found in the language of ancient Rome. Libitina was the goddess of funerals; her officers were the Libitinarii, our undertakers; her temple in which all business connected with the last rites was transacted, and in which the account of deaths-ratio Libitina-was kept, served the purpose of a Register Office.

reports on the cause of death was sometimes damaged by "the mist of a cup of ale or the bribe of a two-groat fee," instead of one groat, which was their usual honorarium. Each parish-clerk made his report on Tuesday night; the general account was made up and printed on Wednesday, and was published on Thursday. The price of the bills was 48. a-year. In the modern bills prepared by the RegistrarGeneral the report of each registrar shows the births and deaths registered by him in the week up to Saturday night; it is transmitted to the central office early on Monday; the return is made up on that day, printed on Tuesday, and published on Wednesday. A day is therefore lost in the preparation, in consequence of the intervention of Sunday. But the Registrar-General (Major Graham) makes no charge for his returns, though he might plead for that course a venerable precedent. He distributes them gratuitously to individuals, learned bodies, and newspapers,-to those who apply for them, who take an interest in them, and are likely to turn them to useful account.

Captain John Graunt, a citizen of London, and F.R.S., who lived in Birchin Lane, published his "Natural and Political Observations on the Bills of Mortality," in 1662. He reckoned that there had been 399,910 deaths in thirty-three years (1629-1661), and by a process which he has described, he estimated the population at 403,000* in the last of those years. Hence it would be inferred that the annual rate of mortality did not much exceed 3 per cent., an estimate which may be conjectured to be considerably under the mark for those days of terrible visitation. While the annual deaths were, on an average, 12,119, the births were only 8,201; and this defect of births, as compared with deaths, pervades the bills even in healthy years, a dispensation of which we, in the present returns, happily witness the reversal. In another place Graunt computes the burials in 40 years (1604-43) to be 363,935, and the christenings 330,747 in 123 parishes, (Westminster and other 6 parishes not being included,) giving for the former an annual excess of only 830. He refers the excess to other causes besides a high rate of mortality. The registered christenings were deficient because (1), theological opinions were entertained by some, unfavourable to the baptismal rite; (2). there were occasionally religious scruples on the part of Christian ministers regarding the worthiness of parents to have their children baptized; and (3) what probably formed the chief difficulty, there was a small fee for registration.

But still more grievous causes of debilitation prevailed, and time, which destroyed the people of London, gradually destroyed also the bills of the "Worshipful Company of Parish Clerks" which recorded the births and deaths of that people. In the lapse of years they have suffered severe dilapidation; the number of their baptisms and burials has dwindled to the smallest proportions. Parishes neglected to make their returns; parish clerks were idle or contumacious, and could not be prevailed on to do their duty. It may be noticed here that a defect had been inherent in the organization from the beginning, arising from the circumstance that it belonged to a church which did not embrace the whole population; for all Roman Catholics

* In another place he calculated the population at 384,000, or about that of the city of Glasgow at present.