sequently determined. At the recent Portland meeting there was an attendance of 1,714 members. The association authorized the publication of a medical directory of the country and the purchase as the basis for it of the 'Standard Directory.' This national medical directory is to contain an abbreviated biography of all physicians of the United States. Among other topics taken up by the house of delegates was the exclusion of advertisements of nostrums from the journal of the association and the question of incorporation by congress. The American Medical Association has a large budget, especially in connection with its weekly journal, the publication expenses last year amounting to $181,298.

A MEETING was held at Toronto, on July 13, for the purpose of extending a formal invitation to the British Medical Association to meet in Toronto in 1906, indorsing the action of the Canadian Medical Association. Mr. I. H. Cameron was delegated to present this invitation at the approaching meeting of the association.

(b)

THE fourteenth International Congress of Americanists will be held at Quebec from September 10 to 15, 1906. Dr. Robert Bell, director of the Geological Survey of Canada, is president, and Dr. N. E. Dionne, librarian. of the Legislative Assembly, Quebec, is secretary. The work of the congress will have reference to: (a) The native races of America, their origin, geographical distribution, history, physical characters, languages, civilization, mythology, religions, morals and habits. The indigenous monuments and the archeology of America. (c) The history of the discovery and European occupancy of the New World. The meetings of the congress will take place in the legislative building. Details pertaining to receptions, entertainments and excursions will be given in a later announcement. It is probable, however, that after the close of the sessions of the congress, an excursion to Lake St. John, including a visit to a camp of Montagnais Indians of the region, will be organized. Excursions in the neighborhood of Quebec will be made during the week of the congress.

A PRELIMINARY program has been issued for the next International Medical Congress that will be held at Lisbon from April 19 to 26, 1906.

The Experiment Station Record states that an act recently passed by the state legislature of Massachusetts makes provision for the appointment of a superintendent for suppressing the gypsy and brown-tail moths, and outlines the duties of cities and towns in that connection and the conditions under which they may be reimbursed in part for the expense of suppression. The bill appropriates $300,000, of which $75,000 may be expended during the calendar year 1905, $150,000 during 1906, and the remaining $75,000, with any unexpended balances, up to May 1, 1907. An additional sum of $10,000 in each of the three years may be expended for experiments with parasites or natural enemies for destroying these moths. A. H. Kirkland, a graduate of the Massachusetts Agricultural College, and formerly connected with the gypsy-moth work of the state, has been appointed superintendent at a salary of $5,000 a year.

ACCORDING to an abstract in the Geographical Magazine the report for 1903-4 of the New Zealand Lands and Survey Department shows satisfactory progress in the way of mapping and defining areas and of the appropriation of the land. There were, in 1903-4, 2,813 new selections comprising over 1 million areas, an increase of 35,279 on the area of land selected in 1902-3; 432 of the selections were less than 1 acre each, and 166 reached 1,000 acres and upwards, the average selection measuring 577 acres. Under the Village Settlement system there were, on March 31, 1904, 2,014 settlers holding 43,146 acres, an average of 211 acres each. In view of the great shrinkage of land inviting settlement and other drawbacks, the record of land operations must be accounted satisfactory. The gross total of milling timber on Crown lands is estimated at 21,000 million superficial feet, Nelson district. heading the list with a volume of about 6,000 million superficial feet of all varieties, closely followed in order by Westland and Wellington. The Crown kauri timber in Auckland is found

million trees were and plantations in million in 1902-3.

to be below former estimates, and as there are about thirty-six kauri mills clearing 144 million superficial feet per annum, in eight years the colony's supply of kauri would be exhausted. However, the timber of the rimu, matai and totara forests in the north is now found far in excess of previous computations. The output of all the mills in the colony is estimated at 372 million superficial feet per annum, a rate which would clear away all the colony's timber in seventy years. On the other hand, over 6 raised in the nurseries 1903-4 as against 4 The total number of trees raised between 1896 and 1904, on an area now measuring 1,040 acres, was 18,293,682. The prisonlabor applied to tree-planting has proved every way profitable, notably in a moral sense, to the prisoners. The weight allowed to the claims of natural beauty may be gathered from the assignment of ample areas as scenic reserves. More particularly, in the highly picturesque south land it is proposed to preserve in native immunity no less than 2,772,440 acres, including the Sounds National Park of 2,500,000 acres. During 1903-4 triangulation continued more or less in abeyance owing to settlement requirements, but the surveyor-general urges the resumption of triangulation on a large scale. A full report of the magnetic work of the year is furnished by Mr. Skey. Particularly interesting is the reference to the joint work of the Hagley Park observatory and the Antarctic Expedition. Eight photographs of the most marked seismograms of the year are appended. In the northern part of the South Island magnetic work has been suspended since February, 1904. A further three months' work by one officer is all that is now needed to complete the magnetic survey of the colony, the results of which would be of so great value as well to navigation as to pure science. The comprehensive report deals also with temperature, rainfall, sanctuaries for animals and birds, etc. Besides maps and plans, there are numerous illustrations of scenery, flora, fauna, etc. The report of the minister

of railways shows the railway mileage of New Zealand as 2,328.

UNIVERSITY AND EDUCATIONAL NEWS. THE Cornerstone has been laid of the new engineering building of the University of Iowa, which is to be erected at a cost of $600,000.

THE Contract has been awarded for a new bacteriological building at the University of Minnesota. It will be built at once and will cost $100,000.

MR. SIMON GUGGENHEIM has given $75,000 to the Colorado School of Mines at Denver. It will be used for the erection of an administration building.

THE university benefaction fund for Cambridge University now amounts to about $400,000. The largest gift during the past year is one of $25,000 from Lord Rayleigh.

THE Bates College corporation will ask from the Maine legislature a repeal of the charter which provides that the president of Bates College and a majority of the board of fellows and of the board of overseers shall be members of some church in the Free Baptist denomination. It is understood that this action is taken in order that the college may take advantage of the pensions of the Carnegie Foundation.

Two new fellowships have been created in the department of chemistry, Ohio State University, Columbus, Ohio. The holders of the fellowships will receive free tuition and $300. Applicants should apply at once to Professor William McPherson, Columbus, Ohio.

THE council of the University of Liverpool has instituted a lectureship in experimental psychology. The work in psychology will, for the present, be carried on in the physiological laboratory.

PROFESSOR H. S. WHITE, of Northwestern University, has been appointed professor of mathematics at Vassar College.

MR. W. H. WATKINSON, of the Glasgow and West of Scotland Technical College, has been appointed professor of engineering at the University of Liverpool.

Now the latest of the great sciences is biology, and it could be so widely interpreted as to include many of the others, for example, physiology, psychology, sociology; but chiefly it takes for itself the broad general beginnings.

These older sciences were really engaged upon narrow domains, narrow ramifications in the universe of biology; and the general has helped the preexistent special by giving the broader conceptions connoted by comparative physiology, comparative psychology, comparative sociology.

Since Wöhler, the distinction between organic and inorganic matter has become merely schematic; but the line drawn at life has resisted obliteration.

It is true that my friend Professor Herrera has said:

I conceive the human organism as a machine containing some five or six liters of blood employed in appropriating to itself the nutritious principles of food, absorbing oxygen, and carrying it to the nerve to make it vibrate by discharges of carbon dioxide.

Life is now to be defined as the result of the physicochemical action of protoplasmic currents, the cause of such currents being diffusion, heat and some other secondary factors.

But until some one sees such currents set up in some way differing from the natural transmission of preexistent life, a thing which no one at present even hopes for, the old boundary remains undisturbed.

If any benefit is obtainable from a physico-chemical nomenclature and notation, science will not object to their use.

Suppose, then, we put it in the boldest form, that biology is now engaged in the creation of an available representation of the activities and laws of activity of these wonderful protoplasmic currents.

The definition then would be something like this: Biology is the science created to give understanding and mastery of the protoplasmic activities on this earth; to make easy the explanation and description

of such activities and the transmission of this mastery.

The association, the suggestion, is immediate:

Beyond the microtome, the microscope, the statistics of observation, of experiment. of what instrument of world-conquest must the new science avail herself? The answer is patent: of mathematics, that giant pincers of scientific logic which showed Newton the moon as simply a bigger apple trying to fall straight down on his head, flashed out in the mind of Adams the unseen planet Neptune, told Rayleigh that the chemists had always been breathing vast quantities of argon without knowing it, pointed to Mendelieev the places of unknown chemical elements, and through Helmholtz and his pupil Hertz has given us the Lenard rays, the Roentgen rays, radium itself, and wireless telegraphy based on Hertzian waves.

In mathematics, the part which is being recognized as pure deductive logic is ever greater. The residuum takes from biological advance itself new form and new statement.

After the questions, what are facts? what is reality? questions not to be answered either by biology or mathematics, there come, if we decide to retain as rough working hypotheses the expressions, fact, reality, subsequent questions, such as what then is a geometric fact, a geometric reality?

These latter questions involve a wrestling with primitive origins in physiological psychology, now entangled with metaphysical constructions, all being studied at present with help of the biologically given hypothesis of evolution.

To note the essential interrelation of biology and mathematics it is only needful to recall that evolution postulates a world independent of man, preceding man, and

teaches the production of man from lower biologic forms by wholly natural causes.

If this be so, then skipping the fundamental puzzle as to how a living thing gets any conscious knowledge, any subjective representation of that independent world, it remains of the very essence of the doctrine of evolution that man's knowledge of this independent world, having come by gradual betterment, trial, experiment, adaptation, and through imperfect instruments, for example, the eye, can not be metrically exact.

In the easiest measurements it is said we can not even with the best microscopes go beyond one one millionth of a meter; that is, we are limited to seven significant figures at most. What is the meaning then of the mathematics which, as in the case of the evaluation of π, has gone to seven hundred places of significant figures?

If then we are to hold to evolution, science must be a construction of the animal and human mind; for example, geometry is a system of theorems deduced in pure logical way from certain unprovable assumptions precreated by auto-active animal and human minds.

So also is biology. But here the assumptions are more fluctuating, and many of them are still on trial.

Since every science strives to characterize as to size, number, and, where possible, spatial relations, the phenomena of its domain, each has need of the ideas and methods of mathematics. One of the fundamental ideas of mathematics is the idea of variation, the variable, qualitative and quantitative variability.

When related quantities vary, one may vary arbitrarily. This is called the independent variable. Others may vary in dependence upon the first. Such are called dependent variables or functions of the independent variable. The change of the variables may be continuous or discontin

uous. The blind prejudice for the assumption of continuity is so profound as to be unconscious.

But if biologists did but know it, the characteristics, peculiarities and methods of investigation for continuous functions dif fer essentially from those for discontinuous functions.

Our calculus assumed continuity in all its functions, and also that differentiability was a necessary consequence of this continuity.

Lobachevski, the creator of the nonEuclidean geometry, emphasized the distinction between continuity and differentiability, therein also being half a century in advance of his contemporaries.

The mathematicians of the eighteenth century did not touch the question of the relation between continuity and differentiability, presuming silently that every continuous function is eo ipso a function having a derivative.

Ampère tried to prove this position, but his proof lacked cogency. The question about the relation between continuity and differentiability awoke general attention between 1870 and 1880, when Weierstrass gave an example of a function continuous within a certain interval and at the same time having no definite derivative within this interval (non-differentiable).

Meanwhile, Lobachevski, already in the thirties, showed the necessity of distinguishing the 'changing gradually' (in our terminology, continuity) of a function and its 'unbrokenness' (now, differentiability).

With especial precision did he formulate this difference in his Russian memoir of 1835: A Method for Ascertaining the Convergence,' etc.

A function changes gradually when its increment diminishes to zero together with the increment of the independent variable. A function is unbroken if the ratio of these two increments, as they diminish, goes over insensibly into a new