invited since the course herewith offered is based upon it. The quantitative method aims to bring the student into direct contact, so to speak, with the relations of quantity as well as with those of quality. It most distinctly does not aim to present the systematic methods of quantitative analysis. No more does it propose that the pupil shall prove to his own mind the laws of quantity. Such laws are inductions from a great many observations, and the student should be carefully guarded against the idea that his experiments are to prove them, even to his own conviction. His experimentation is simply to aid him by direct observation and by guided thought to get a clear notion of the content and meaning of the laws. The relations of quantity are absolutely fundamental to the science. No branch of physical science has made any considerable progress until it has been placed on a quantitative basis. Therefore there is the same desirability to illustrate for the student the quantitative aspect of things as there is to illustrate their properties in descriptive experiments. Moreover, it is desirable that quantity shall receive due consideration and illustration at the moment when the logic of the subject calls for the same, and that is early in the course. I believe it also a positive advantage that the careful manipulation which is necessary when attention is given to quantity should come at the outset of the student's experience rather than after he has formed the habit of disregarding quantity. In addition, it may be claimed that the quantitative method, speaking broadly, contributes very considerably to the disciplinary value of any branch of natural science. It is this which gives to the subject of Physics its advantage over other branches. But whatever may be said as to the desirability of these things, the use of the method must be limited by its practicability. Probably the first objection to be urged is the impracticability of providing the necessary equipment. Of this the balance is the essential feature. If it were de manded that this should be a balance capable of weighing to one ten-thousandth of a gram, the impracticability of the thing would be manifest. Not only this, but it would be folly to try to use such a balance if it were provided. One which weighs to the hundredth of a gram is all that is called for, and this is surely within the range of the practicable. The rest of the equipment is hardly more than is provided for the usual courses. The next objection to be expected is that the beginning pupil has not sufficient skill in manipulation to do the work. This may be true, but it is equally true that he can very quickly acquire that skill. No one, not even the most advanced worker, has skill until he acquires it. And the only way to get skill is to do, and of all doing there must be a beginning. The pupil may just as well learn to use the balance by using it the first day in the laboratory, as by deferring its use until he has worked a year, if in the meantime he never touches it. I have in mind, of course, a balance like the one just specified, nothing finer. Another objection is that quantitative experiments take more time than do descriptive experiments. This is true, but before the former are condemned for this reason, it should be duly considered that they are used to lead the student to a clear notion of fundamental laws which are based on broad generalizations, and, if this is gained, it is worth the greater expenditure of time. Suppose the pupil could make a dozen experiments descriptive of some substance or substances in the time needed for the quantitative experiment illustrating multiple proportions, does it follow that the time is spent to better advantage in the former? Indeed, there may be positive gain in the fact. that the student must work slowly and deliberately at the outset, when he is getting the fundamental notions of the subject. This, if not carried to excess, may help to make the laboratory what it should be-a place for thinking as well as for seeing. Nor should it be overlooked that items of description also occur in the quantitative experiments, although description is subordinate to the main idea. Finally, it may be objected that with the limitations of equipment and of manipulative skill already suggested, the quantitative results obtainable are worthless. The truth of this depends on how the results are used. If they are used with any pretense to prove laws, they are worthless for the purpose; but if they suffice to bring to the student's mind the relation of quantities within the limits of his observational accuracy, the point is made. Therefore it is reckoned essential to the satisfactory use of the quantitative method that the limits of accuracy be carefully estimated for each experiment. The teacher is urged to keep this constantly before his pupils. For a concrete example, take the experiments Nos. 41/3 and 41/4 in which the student determines the volume and mass of hydrogen liberated by 2.4 grams of magnesium and 6.5 grams of zinc, as illustration of equivalent proportions. If he makes two determinations of the value for each metal, and finds that the value for zinc does not differ from that for magnesium more than one value for magnesium differs from the other for the same, or one zinc from the other zinc, then the experiment has served its purpose to bring to his observation and to impress upon his mind the relation of equivalency within the limits of his observational accuracy. It should not be forgotten that this careful consideration of the limitations to accuracy is necessary in all experimental results, even in those obtained by the most skillful experimenters and with the most refined apparatus. TIME AND TOPICS One of the first things to which a teacher must reconcile himself is the fact that he can not teach to beginners in a course of one year the whole of the science. Even if he were willing to make information the sole end of his teaching, he could not present all the so-called useful in 1 formation of the subject of chemistry. But training is, after all, a fundamental purpose of education, and it may be reckoned as one of the peculiar advantages of our subject that training and useful information are so effectively combined. In choosing topics, therefore, both these features must be carefully considered as well as the limitations of time. I assume an aggregate time not less than four periods a week through the academic year of thirty-eight or forty weeks; also that the quantitative method in the laboratory is accepted. I also assume a maturity (with no previous chemical instruction, however) on the part of the student, which I estimate is attained by the average pupil in the last year of his high school experience or the first year of college; and I must be permitted to decline sponsorship for the course outside of these conditions. But four periods a week may not always mean the same amount of available time. Sessions limited to one hour or less are very uneconomical of time for laboratory study, and make it almost impracticable. Two, or at least one and a half, hours of uninterrupted time should be provided, and two hours of laboratory time should be reckoned as one of prepared recitation. In my own classes the time assignment is four hours a week, but this is interpreted as allowing eight hours of aggregate time to the subject, either in the class room or in the laboratory. It is an advantage to have the time assigned for class room work continuous with that for the laboratory. This permits of adjustment according to the demands of a particular topic. I therefore have three sessions a week of two and a third hours each, thus taking seven hours and allowing a margin of one hour for work outside of the laboratory and of the class room. If it is necessary to divide a class into sections for laboratory work, there is advantage in having successive days for each section-e. g., Monday and Friday for one, and Tuesday, Wednesday, and Thursday for another—as pupils can thus suspend work on an unfinished experiment with less inconvenience. However, this advantage may be overbalanced by the difficulty of securing such allotment of time. With the arrangement that has been indicated, I allow thirty-five weeks, vacations not included, for completing the course offered in the text. But inasmuch as the amount of work accomplished is likely to vary considerably, even with the same time assignment, it may be helpful if I give more in detail an estimate of the time needed for the several portions of the course : Chapter I, 6 weeks. Chapters III and IV, 2 weeks. Chapter V, Law 1, 3 weeks; Laws 2 and 3, 1 week; Laws 4 and 5, 2 weeks. Chapter VI and VII, 3 weeks. Chapter VIII, 12 weeks. If circumstances make it necessary to curtail the course, the following expedients are suggested: 1. To waive the requirement of two good quantitative results from each student. If this is done, care should be taken to bring before the whole class a sufficient number of the individual results to show the range of variation. 2. Under the law of equivalent proportions, Chapter II, the four parts of the experiment might be assigned to dif.ferent members of the class. Some could be asked to determine the hydrogen with magnesium and the oxygen with zinc; others to determine the hydrogen with zinc and the oxygen with magnesium-some by the first method and some by the second. In a similar manner the problem of determining the vapor-density of carbon dioxide, Chapter V, Law 1, might be divided, the determination of weight being assigned to a part of the class and that of volume to another part. An expedient of this kind is a sacrifice, for it is very desirable that the student's work should be thor |