that 1000 head-masters received each less than $375 per annum, and 3684 less than $500, head-mistresses faring even worse. Outside of the chief cities assistant teachers have little to hope for. In the prosperous borough of Salford the maximum salary for an assistant master is $400 per annum, and for assistant mistresses $270. These salaries cover a full year's work, and upon them the teacher is expected to maintain a respectable appearance and provide for the day when the "keepers of the house shall tremble"; for under present circumstances most assistants must remain in that capacity to the end of the chapter. Mr. Collins noted that the lowest class of government clerks fare much better, and that college graduates entering the metropolitan police force, as some have done, have better chances for a comfortable living than the rank and file of teachers. Even a dustman, employed by the Works and General Purposes Committee of a London parish, received higher compensation than the average wages paid assistant teachers in the borough cited above. With these cases in mind it is easy to understand why it is that salaries and pensions have become burning questions in England. This is the more significant to us since English teachers resemble our own in their love of independence and in their opposition to fixed and invidious class distinctions. On the other hand, the English teachers have less of that careless optimism which takes the chances of a better to-morrow and give themselves more earnestly to organized effort for the improvement of their condition. The passage of a pension bill is one of the measures for which they have long contended and which they have at last the satisfaction of seeing presented to Parliament.

Two superannuation bills have in fact been introduced, one by Sir Richard Temple, member of the London School Board, drawn up in the interests of the metropolitan teachers, and the other a general measure for all teachers. A select committee has been appointed to consider the proposals and the success of the general measure appears to be a foregone conclusion. It is in accordance with the recommendations of the

Commissioners appointed to investigate the operations of the Education Act. It is also supported very generally by the press, and will have able advocacy when it comes up for public discussion. The provisions of the bill are substantially the same as those of the Prussian regulations. The pension is to be available for certificated masters at 60 years of age, for mistresses at 55 years of age, and also for teachers who become incapacitated for duty after ten years of service. Teachers are to pay an annual premium of 4 per cent. of their salaries into the pension fund. An ordinary pension is to be reckoned at of the annual salary at the date of retirement for each completed year of service. The measure does not extend to Scotland or to Ireland, buti ts passage is quite certain to be followed by similar legislation in their behalf.

The outcome of the agitation in England seems to be the strongest possible evidence of the necessity of a pension policy for teachers. Without a measure of this kind the most faithful and competent, teachers are in danger of coming to want in their old age, or must often be retained in active service long after the time when they are able to discharge its duties effectively. If anything could add force to the English demand it would be the fact that Ontario, whose system of education bears in every feature the stamp of the master-mind of Mr. Ryerson, maintains a superannuation fund.

The British colonies, as a rule, have not yet evolved this provision. In the Australian colonies salaries average well. Moreover, as in parts of our own country, occupations are easily changed, and teaching is for the most part a stepping-stone to something more lucrative. This is, however, a condition which necessarily passes away as population increases, social conditions assume a fixed state and business competition becomes more keen. A ripple of the movement which has been traced above is already noticeable in the newly federated Australian States. Meanwhile liberal pensions are granted in special cases. Thus in 1885 twelve teachers in South Australia received retiring allowances averaging $815 each. In New South Wales a teacher of music in one of the

Training Colleges received $4170 on withdrawing from the work.

The survey above presented discloses a universal drift toward the pension policy which is certainly not accidental. It is all but universally admitted that the education of the young is a public duty. Even Tolstoï, who scouts all accepted systems of education, does not deny the necessity of the thing itself. The theory that the rates of compensation for teaching can be left to the action of ordinary business principles is thoroughly exploded. It is a matter to be regulated by the State, and the State cannot afford to keep its teachers on starvation salaries.

BUREAU OF EDUCATION,

WASHINGTON, D. C.

A. TOLMAN SMITH.

IV.

TWELVE VERSUS TEN.

To the solid ground

Of Nature trusts the mind that builds for aye.

WORDSWORTH.

In any developed system of numeration there must be a turning-point, at which the notation is folded back upon itself, and from which point on the higher numbers are to be expressed by additive and multiplicative processes through the lower. The number that forms thus at once a point of rest and a point of departure may be called the base or radix of the system. The rising powers of this base are set in order leftward, and the falling powers rightward, of the initial or unit's position. Any natural number other than unity may be taken as this radix, and, in fact, various integers, as two, five, ten, twelve, twenty, sixty, have been taken. Among all of these, however, ten has attained by far the widest and most complete recognition, and within the present century the metric decimal system has established itself firmly in western and central Continental Europe, as well as among men of science everywhere. Nor can there be any doubt of its immense superiority as a labor-saving device over every rival, so long as ten is made the turning-point in our notation. In fact, the thorough-going adoption of it or of its equivalent must follow in time as a natural logical outgrowth of a reversion of our notation back upon itself at the ten-point.

This preference for ten as radix does not, however, rest upon any natural or spiritual basis, upon any inherent fitness of ten itself to discharge this supreme function in arithmetic, but solely upon a physical peculiarity of the counting animal, man. He is a pentadactyl, he has ten fingers. Inasmuch as elementary reckoning is almost always done on the fingers in its first stages and by the young, whether in individual or

educational or national life, it was almost inevitable that ten should be taken as the point of reflection. If only one hand be used, then five presents itself as radix, or if both hands and feet, then twenty, and both of these numbers have indeed served as radices.

But none of these related integers has any intrinsic fitness for the office in question. To be sure, ten is resolvable into the factors two and five, and the first of these is important— the operation of taking the half is so frequently necessary; but not so with five-we have comparatively little use for fifth parts, while on the other hand we meet with thirds and fourths at every turn and in every department of life. But ten is not divisible by either three or four and stands in no simple relation to either six or eight, two other important numbers. These are very serious defects in ten as a radix, and they encumber very gravely all reckoning and especially practical calculation in the denary system or with decimals. Thus, the constantly recurrent fraction is expressible only through an interminate decimal, requires two figures, is interminate as a decimal, requires three figures for its expression. These are very weighty burdens, which the general and final adoption of the decimal system will bind upon the back of humanity forever. Neither will any conceivable development of human intelligence lighten them in the least, for they inhere in the unalterable nature of the number ten.

But there is an altogether simple and easy deliverance lying ready at hand. It is the rejection of the unsuitable radix ten and the adoption of twelve, which is fitted perfectly and in every particular. It may be divided by two, by three, by four, by six; it is related simply to eight and nine. It is this superior divisibility that marks it out among all numbers as pre-eminently the natural radix, a divisibility shared with its own multiples only, as 24, 36, etc. It is the contention of this article that a change from the denary to the duodenary notation would be a great and much-needed simplification, above all to the practical man, and that it is entirely feasible. Let us examine the matter in detail.