positive need consideration; and while experiments are made in digestion of proteids with pepsin and acid together, it is well to test whether either pepsin or acid alone would produce the same effect, and whether pepsin will digest other foods than proteids; or whether starch digests equally well at all temperatures.

For the study of cell structures and functions several days may be profitably spent on the paramoecium or amoeba, and the most important functions of the animal may be considered in the following order:

(1) Locomotion; (2) taking in of food; (3) digestion; (4) circulation; (5) assimilation; (6) taking in of oxygen; (7) oxidation of metabolism; (8) excretion; (9) sensation; (10) reproduction.

It is thought this will help in fixing the idea that physiology deals with units in action, each influencing the other. The cir culation of the blood, for example, is not a fixed state,

to be

memorized, but is, at any given moment, an equilibrium resulting from the interaction of many shifting factors. Such factors must be severally known and the result of their interaction reasoned out. If the factors have not been acquired largely by personal observation, the mind will not grasp them with sufficient clearness to make possible their subsequent combination. For most part physiology cannot be memorized but must be under

stood.

the

This part of the work often brings questions about bacteria and it is an easy way of introducing a little elementary bacteriology. A few test tubes if one has no Petri dishes, and any good nutrient medium, and it is easy to demonstrate the bacteria of dust, water, air, ice, milk, etc. This of course enters upon

the

field of diseases caused by bacteria, and the laboratory work is followed by a set of questions for which references are given, and their range, including the use of feather dusters; susceptibility which are finally talked over in class. These are rather wide in and immunity in disease; antitoxine; vaccination; flies and typhoid; mosquitoes and malaria; and special emphasis is placed

upon tuberculosis, its prevention, and cure. Last spring

this

came at the time of the Anti-tuberculosis Society's exhibition in our city and we spent one class period in a very profitable study

of that exhibit.

The remainder of the work follows more nearly the beaten

track

so far as the study of circulation, respiration, and excretion are

concerned. As we study the lungs we make records of the vital statistics of each pupil, finding age; height; weight; chest measurement in inspiration and expiration; lung capacity with a simple form of spirometer; relation of chest average to height; and of height and weight. Students take pride in a good lung record and often take pains to increase it, taking occasional measurements during the semester.

Before we begin the study of the nervous system this semester, the class will be given an illustration of reflex action in a brainless frog. We shall also see the nervous system and get some notion of nerves and ganglia and their functions. A dissected model is a great help in teaching the structure and functions of the brain.

It is quite possible that muscles and bones will form the last subjects we may touch upon. A very few laboratory periods spent on these subjects when the pupils are really desirous of knowing, and have got over their fussy notions, will settle their structure. As to muscular action, why should it be learned from a book when, as Huxley said long ago, "There is a very convenient and handy animal which everybody has at hand, and that is himself." A little experimental study of his biceps will tell a boy more than any book, and for that matter he has probably learned it without any book; and has only, to quote Huxley again, to realize that "Science is only trained and organized commonsense." The Harvard joint apparatus will interest him in a calculation of how much force he expends in his various motions.

Bones are more interesting to boys and girls if studied from the standpoint of comparative anatomy, and the study of the human body offers a fine chance to develop this side of the subject. If you can send them to a museum with a set of questions applicable to the bones of any vertebrate, you are likely to be furnished with subject matter for some time. It is usually possible to have a collection of skulls in the school, and teeth are vastly more interesting if compared in man, and in horse, cow, dog, and rat or squirrel.

I have left the subject of the teaching of alcohol and narcotics. until the last, partly because I hesitate to take it up-my students come to me with a distaste for the whole subject of physiology, which I often find is acquired as the result of a grammar school experience of the subject, dealing with it only from the standpoint of temperance teaching. Perhaps the most successful

way in which we have ever dealt with this included the collection of a large set of statistics from the police courts of our city showing the total number of arrests, the proportion of those arrested for drunkenness and disorderly conduct, the whole cost of our police department; and the part of this expense due to drunkenness. In the same way we calculated the cost of caring for paupers, criminals, and insane due to drink; and finally the amount it cost each citizen because of this. It happened that the class was composed of pupils who had studied domestic science and shop work in the grades, but could not continue their study in the High School, because of lack of funds to establish and maintain a manual training addition. They made a few very startling applications of their own as to possible disposals of such a sum of money.

Everywhere and always, throughout the semester of physiology in laboratory and class room we try to demonstrate the connection of right living and health; the need of knowing what right living is, and under what conditions it is attained, and the danger of ignorance, not only to the individual, but to the family and the community. People who treat their bodies as they please, and transgress rules of personal hygiene of which they should have a definite understanding, are physical sinners, and unfortunately the results of the crime do not always visit them alone.

Public hygiene may be enforced but personal and domestic hygiene must be taught. No law can compel citizens in time of epidemic of typhoid to boil their drinking water, and cleanse food to be eaten without cooking, but persistent teaching will do much toward it. A grade teacher of my acquaintance found not long ago, as the result of an accidental question that only one child in her entire roomful ever had an open window in his bedroom at night.

General sanitary improvement is dependent upon the intelligence of the community, as well as upon efficient health officers, and one of the important duties of the physiology teacher is to disseminate more widely knowledge concerning public, domestic and personal hygiene.

Personal hygiene is applied physiology, and knowledge of the normal functions of the body and the simple methods of keeping them in healthy action, is the one thing no educated person should be excused from possessing. Yet most children reach maturity without sufficient parental or scholastic instruction in many essen

tial matters of health. Men and women who would be greatly chagrined to be corrected in the pronunciation of a popular foreign proper name, or who would resent any suggestion as to their lack of general culture or learning, show not the slightest embarrassment at their ignorance of the common physiologic functions.

Said an exasperated physician on this point, "Not to know what each one owns would, in commercial life, be considered as either idiotic, or criminal negligence; and yet not one in ten can tell on which side of the body the liver is placed, while the vast majority complacently clasp their hands over some thirty feet of intestines when asked to locate the stomach, and of its structure, use, and care, they know even less."

Persons of intelligence continually furnish thoughtless recommendations of purely "quack" remedies, and unscientific instruments and apparatus, and allow their names and pictures to appear in periodicals-like those "eminent" clergymen who recommend "Peruna" with its 28.5 per cent by volume of alcohol; and its kindred spirits! A list of the common patent medicines. with their percentages of alcohol is a good thing to put up for a class to read, and a discussion of their ingredients and the effects of them on the human body is a good thing for the pupils and indirectly for the parents.

We approach the subject of physiology by two paths; the direct, which I have outlined above; and the indirect in connection with the year's work in Zoology. This has its advantage in the fact that pupils are often wearied of the subject of Physiology in the elementary schools, and this gives an entirely new approach. There is also an advantage in that erroneous impressions gained from the elementary work are more likely to be corrected when the facts of human structure and function are, approached from the animal standpoint, instead of from the familiar human aspect of elementary school physiology. The study of animals and plants gives the proper perspective for the biological study of man, making this vastly more interesting and intelligible. In this connection of course the comparative view prevails, emphasis is placed upon resemblances in structure and function between man and animals, resemblances to all living things; similarities to all vertebrates; resemblances and differences of man and other mammals.

Incidental references to human structure come up in connec

tion with many lessons, but the formal comparative study is best taken up at the end of the course in Zoology, which will then have prepared for an intelligent appreciation of human physiology. This course is handicapped with us because Zoology precedes instead of follows Chemistry, whereas the reverse should be true. So long as any science which deals with living matter precedes Chemistry it must be hampered; for the study of life constitutes the Chemistry and physics of living matter

PERSONAL OBSERVATIONS OF THE TEACHING OF MATHEMATICS IN PRUSSIA.*

BY HERBERT E. COBB,

Professor of Mathematics, Lewis Institute, Chicago. When one speaks of Germany or of the German schools he has in mind usually Prussia or the Prussian schools. The reason for this is apparent when we compare Prussia with the other German states. The German empire has a population of 56,000,000. Prussia, 34.000,000; Bavaria, 6,000,000; Saxony, 4,000,oco; while the other twenty-three states form only a small part of the empire. Prussia is the leader in the rapid advance along all lines in the empire.

To say that certain things are true of German schools is in many cases not an exact statement, since there are differences in the schools, not only between the several states but also between the different parts of the same state. There is no Minister of Education for the empire; though the general character and aims of the schools, and the training and duties of the teachers are the same throughout Germany. Another cause of difference in the schools is that while some of the states are largely Protestant others are largely Catholic; in Prussia the number of Protestants is to the number of Catholics as eleven to six, while in Bavaria the ratio is four to eleven. The greatest differences exist in the common school system. In Bavaria, for example, the common schools are the preparatory schools for all the higher schools, while in Prussia they are the schools for the lower classes, cut off entirely from the higher schools which have preparatory schools of their own. In 1902-3 the number of laborers' sons in the ten Prussian universities was

*From a paper read before the Mathematical Section of the Central Association of Science and Mathematics Teachers on Nov. 30, 1906, at the University of Chicago.