there is something in the social state of the locality which requires to be remedied; if in the latter, it is merely a matter for the police, or probably accidental. The informa. tion on these points should form part of the police returns, and should be carefully collected, together with the number of times which the offenders have, in each case, been charged with crimes, whether proceeded against or not; and if not, for what reason. With this view a new Table is proposed, in the form annexed.

To obtain more accurate knowledge as to the criminal classes generally, it might be desirable to adopt the Casiers Judiciaires, which have been established in France since 1851. They are placed in various localities—one of them in each judiciary arrondissement. Notices are there sent and classed, of every sentence of the different tribunals of the empire (soit du continent, soit des colonies), against any individual belonging to any part of a district of which the locality where the casier is established may be considered as the centre. Of these there are 361. If it be wished to ascertain the antecedents of any individual, application is made to the clerk (au greffe du tribunal de première instance), by whom the casier for the district to which the party belongs, is kept; and a notice is returned, stating that he either has, or has not, been reported as a criminal; and if reported, how often and under what circumstances. A central office takes cognizance of foreigners and persons whose birth-place is unknown. The police find in these establishments one of the most valuable and ready modes of obtaining information*; and they appear to be a much more reliable source than the revelations made, as with us, by the criminal himself in his interviews with the governor or chaplain.

It is stated in the Report that the Judicial Statistics, Part I.,' prepared at the Home Office, for 1856, show a continued approach to whatever is most valuable in the best returns which have hitherto been devised: that for still greater improvements we shall find the materials in our police offices and courts of petty-sessions; and that it is principally from these sources, if carefully and faithfully watched, that we can derive a better knowledge of the classes whom we have to punish or reclaim. It is not thought desirable, however, till our arrangements are more perfect, to require complicated returns either from the prison officers or the police. The great object should, in the first instance, be to make them reliably correct.

Proposed New Table, for the Police.

(Taken from the 'Journal of the Statistical Society,' vol. i. (1839), p. 174, with some additions.)

The second division is chiefly applicable to juveniles. A column of Remarks may be added for the remaining information required.

On Equitable Villages in America. By RICHARD H. WALSH. These villages were established on the principle that persons were to sell articles at what they cost without any profit; the sovereignty of every individual; the adaptation of the supply to the demand; and a circulating medium founded on the cost of labour. A paper had been read before the meeting of the Association in Glasgow, in which these villages were stated to have produced a successful result. The author had however corresponded with parties in America and found that they had failed, and that very unsettled notions of family relations prevailed in them. He considered that the principles upon which they had been founded were unsound and mischievous in practice,

*Compte rendu de la deuxièmeSession (1855) du Congrès International de Statistique, p. 86.

On Statistics of Crime in Ireland, 1842 to 1856. By JAMES MONCRIEFF WILSON, Actuary, Manager of the Patriotic Assurance Company of Ireland.

The state of crime in Ireland, for the period extending from the beginning of 1842 to the end of 1856, was analysed so far as to show the classes of crime most prevalent during their course, a course made up partly of years of prosperity, but chiefly of years of adversity; and a more complete analysis was made of the state of crime for the year 1851, showing the effect of age, sex, locality, education, general occupation, intemperance and low-class house accommodation upon the amount of crime during that year.

The following are some of the general conclusions derived from the facts established in the paper:

1. That the best measure of crime at present available is the computation of the persons committed or held to bail for trial at the assizes and quarter sessions.

2. That when a person is thus committed or held to bail, the probabilities in favour of his being convicted are about fifty-six to forty-four.

3. That no inquiry into criminal statistics can be of service unless the proportion of crime to population is taken into account.

4. That although it is impossible to state the exact population of Ireland for each year from 1841 to 1856, that still approximations not very wide of the truth may be made; and that in Table A are given about as accurate approximations to the real population in the different years referred to as could well be arrived at.

5. That want and privation are fruitful multipliers of all classes of crime, and that to such a parentage we may safely look first, when we find a general and marked increase in the crime of a country.

6. That although during the years of distress the tendency to every class of crime was greatly increased, it was chiefly offences against property, committed without violence, which swelled the criminal calendar of Ireland.

7. That in the year 1856, the tendency to crime in Ireland was certainly not greater, and perhaps less than the tendency to crime in England and Wales.

8. That the criminal returns for Ireland are susceptible of very considerable improvements, which if made, would greatly add to their value for practical purposes. 9. That among males the maximum tendency to crime for Ireland generally, and for each province separately, except Connaught, is at the period of life twenty-one and above sixteen, and for Connaught at the stage thirty and above twenty-one; and among females, for Ireland generally, and for each province separately, at the period thirty and above twenty-one; and that in both cases the minimum tendency is at the period twelve and under.

10. That the tendency to crime generally among males is only about two-fifth times the like tendency among females; but that were the petty offences against property committed without violence to be dropped, the tendency to all other classes of crime among males would be between four and five times the like tendency among females.

11. That the tendency to the class of crime termed "Offences against the person," attains its minimum among both sexes at the period of life thirty and above twentyone; that the tendency to the classes "Offences against property committed with and without violence," reaches its maximum among females at the same period, but among males at the earlier stage twenty-one and above sixteen; that the tendency to the class "Malicious offences against property," is at its maximum among both sexes at the stage twenty-one and above sixteen; and that the tendency to the classes Forgery and offences against the currency," and "Offences other than those before enumerated," is at its maximum also among both sexes at the period thirty and above twenty-one.

66

12. That among both sexes the tendency to each separate class of crime is at its minimum at the period of life twelve and under.

13. That popular education singly, but especially when combined with occupation, tends powerfully towards the diminution of crime.

14. That the good effects of education and occupation upon crime are very seriously marred by the abuse of intoxicating drinks.

15. That low-class house accommodation tends towards the increase of crime.

16. That popular education, as a means of diminishing the tendency to crime, although most useful in so far as both sexes are concerned, has yet much greater effect among females than among males; and that is emphatically the case in regard to four classes of crime, "Offences against the person;""Offences against property, committed without violence;' "Malicious offences against property;" and "General offences," class No. 6.

17. That ignorance among the masses operates injuriously among the educated and half-educated classes; and that, therefore, to educate the ignorant will tend not only to lessen crime among them, but also among the better classes thus influenced.

18. That were intoxicating drinks less freely used, education as a means of reducing crime, would become more powerful.

19. That the average tendency to the class of crime "Offences against property committed without violence," is rather more than one-half the average tendency to crime generally.

20. That, as without doubt, a large proportion of the serious crimes are committed by those who in early life may be said to have served an apprenticeship to theft; and that as this (No. 3) class of offences, at the period of life sixteen and above twelve among males, amounts to three-fourths of the whole male crime, and among females to five-sixths of the whole female crime, it follows that by getting reduced at this period of life such offences, the more serious crimes at later stages of life will also necessarily be diminished.

21. That increasing efforts should be made to educate all classes of the youth of both sexes; and that instructors ought not to rest satisfied with merely teaching to read and write; but that in all our schools industrious habits should be constantly taught, cleanliness and morality daily enforced, and the danger of indulging to excess in the use of intoxicating drinks frequently pointed out.

On Deferred Annuities. By CADOGAN WILLIAMS.

On Annuities on Lives. By CHARLES M. WILLich.

On a Formula for ascertaining the Expectation of Life.
By CHARLES M. WILLICH.

On the Application of the Decimal Scale in the Construction of Maps. By JAMES YATES, M.A., F.R.S.

Since the commencement of the present century the various continental nations have to a great extent adopted the principle of constructing their maps upon a decimal scale. I will briefly notice some of the most remarkable examples that have come to my knowledge.

In France, the adoption of this principle is an obvious and even necessary result of the introduction of the metre as the unit of length. Millimetres, centimetres and decimetres are, as a matter of course, made to correspond in maps to kilometres, or other decimal multiples of themselves, on the surface of the earth.

Hence one of the results of the annexation of Algeria to France has been the production of excellent plans of cities and maps of the whole country, all decimally projected, and consequently either identical in their scale, or related to one another by clear and simple proportions*.

In Belgium this important task has been taken out of the hands of the Government and admirably executed by M. Van der Maelen, proprietor of the celebrated Geographical Institute. He has published a general map of Belgium, the scale of which is 1 to 200,000; and another, the scale of which is 1 to 20,000 (Brussels, 1846), consequently ten times the dimensions of the preceding.

Sardinia is most honourably prominent in labours of this class. Its Government

'Environs de Blida,' 1838.

*Carte de la Province d'Alger,' 1838. Scale 1 to 400,000. Scale 1 to 20,000. Plan d'Alger et de ses Environs,' 1832. Scale 1 to 2500.

1

1

1

1

1

1

has published beautiful maps, both of the island of Sardinia and of the continental territories, on the following scales, 2,000,000, 800,000, 500,000, 250,000, 50,000, 25,000. Germany has adopted the same method, although it has not yet obtained the full advantage of using the metrical system for commerce and other ordinary transactions. The kingdoms of Bavaria and Wurtemburg and the Electorate of Hesse Cassel, together with some of the neighbouring duchies, employ the General Staff of each country in executing maps on the same scale, which is that of 1 to 50,000. Thus the maps of these several governments fit one another like the dissected maps of our English counties. There is also a Topographical Atlas of Bavaria, the scale of which is 1 published in 1843.

800,000'

Spain and Portugal have decreed that the metrical system shall after a few years be exclusively employed for weights and measures in those countries; so that it must ere long be employed for the government maps, if it has not been adopted already.

It thus appears that the whole of the west of the continent will shortly be described and delineated in maps and plans adjusted to one another and capable of easy comparison, in consequence of being all projected with dimensions decimally related to the surface of the land.

Of the scales employed in our own Ordnance Surveys, 1 inch to a mile and 6 inches to a mile, the former is the 63,360th part of the actual linear distance, the latter is the 10,560th part. It is very difficult and inconvenient to calculate by either of these numbers. On the contrary, the decimal method will be found easy in its application to this as well as all other purposes. Either a metre, or any other measure of length, which is decimally divided, may be applied to the map, and will show the real distance from one place to another with the greatest facility. Thus, if the scale be 1 in 10,000, a decimetre on the map will represent a kilometre on the surface of the ground; and if it be 4th less, or 1 in 50,000, as is the case in many of the maps which have been mentioned, a kilometre on the surface of the ground will correspond to two centimetres on the map.

If the decimal scale has advantages as regards the maps of the British Isles, considered by themselves, still greater benefit will arise when they are to be compared with maps of the neighbouring territories on the continent. We have already advanced so far towards uniformity as to sanction one scale for all England and another for all Ireland, and some persons think it would be well to apply the same scale to the whole of the British Isles. But why should not the principle of uniformity be carried further? If the decimal scale has great intrinsic advantages, it must be an additional reason for its application, that it would bring our maps into coincidence with those of our continental neighbours.

In England the decimal principle has scarcely been applied at all to the construction of maps. There is, however, an exception to the universality of this remark in the case of Mr. W. Hughes, F.R.G.S., whose 'Geological Map of the British Islands' is projected on a decimal scale, every line and every distance upon it being to the corresponding distance in nature, as 1 to 2,500,000. Its proportions are consequently th of the proportions adopted in the national maps of Germanyt.

* Gran Carta degli Stati Sardi in terra ferma divisa in fogli 91, alla scala di

1

1852.

50,000'

2,000,000'

† A Report, which was presented by Dr. Farr to the International Statistical Congress at Vienna, in August 1857, contains the following information :

"Conformément aux recommandations du Congrès de Bruxelles, le Gouvernement de sa Majesté Britannique s'est determiné à faire dresser des cartes générales à l'échelle de 10002500, et des cartes des villes à l'échelle de 100-500. Déjà les cartes de plusieurs comtés et de plusieurs villes ont été dressées sur ces échelles. Ce travail a été malheureusement suspendu. Les avantages qu'offrirait une carte de l'Europe à une échelle uniforme sont évidents: ils ont été démontrés à la Chambre par le Vicomte Palmerston; et nous croyons qu'ils seront appréciés par la commission royale qui est chargée de l'examen de la question,"

On the Use of Prime Numbers in English Measures, Weights, and Coinage. By JAMES YATES, M.A., F.R.S.

On examining the Tables of the measures, weights, and coins used throughout England, it is found that the prime numbers used in their composition and of the most frequent occurrence are 2, 3, and 5. Of these, 2 occurs as a factor by far the most frequently, indeed twice or thrice as often as either 3 or 5.

Seven makes its appearance in the following weights and measures :

7000 grains
14 lbs.
28 lbs.

42 gallons

63 gallons

= 1 lb.
=1 stone.
=1 quarter.

=1 tierce.
=1 hogshead.

Eleven is used in one case only, but that is an important one, viz. :—

Long Measure.

or 5 yards=1 rod or pole, from which is deduced 4 poles, or 22 yards=1 chain. The furlong, the mile, and the acre are also multiples of this fundamental number. Thirteen also comes in once as a factor, viz. in

13 or 63 tods

Wool Weight.

=1 wey.

Wool weight is curiously compounded. No less than four primes, 2, 3, 7, 13, are used as factors, producing only six denominations, which are as follows:

1 clove
1 stone

1 tod

1 wey 1 sack 1 last

=7lbs. avoirdupois.
=2 cloves.

=2 stones.

=6 tods or 13 stones.
=2 weys.

= 12 sacks.

Only one other prime number requires notice, and that is found in a very conspicuous position, and where, perhaps, it was little to be expected, viz. in a recent Act of Parliament. The law now in force and known as the Weights and Measures Act, fixes the number of grains in the lb. avoirdupois by the use of the number 7, and goes on to determine the relation of the pound troy to the standard linear measure by declaring, that a cubic inch of distilled water is equal to 252 grains and 458 thousandth parts of a grain." If this number (252458) be divided by 2, it will be found that a cubic inch of water weighs 126-229 five hundredth parts of a grain, the numerator of this fraction, being a prime number.

126.229
500

1000

As the result of this analysis, it appears that the primes used in the English measures, weights, and coins are the following:

2, 3, 5, 7, 11, 13, and 126-229.

I propose to offer a few remarks respecting the aptitude of these numbers for the functions which they are appointed to perform.

The adoption of them does not appear to have been determined, in any case, so far as we can judge, by reason or principle, but to have arisen from accidental and arbitrary causes. There is no apparent benefit in connecting our highest coins by 2 and 5, the intermediate by 2 and 3, and the lowest by 2 only. No advantage arises from measuring land by elevens, and weighing wool by sevens and thirteens. No reason can be assigned why seven should be brought into avoirdupois weight and excluded from troy weight; or why 3 should be excluded from avoirdupois weight, whilst it plays an important part in troy weight and apothecaries' weight. In short, all our Tables present the appearance of an entire want of principle in their construction. The introduction of an additional prime has the effect of making our weights and