directly behind this aperture, the edge of the pupil touching it. Consequently, when the lens is opaque, the ray cannot pass through to reach the retina, or may be so broken up as to produce only a confused image not sufficient for good vision. The greater the opacity, of course the greater the blindness. When there is simply cloudiness of the crystalline lens, the patient will see indistinctly as through smoked glass; but, when the lens is quite opaque, then they will only have perception of light as through ground glass.

Now cataract, as it occurs in children, is apt to affect the central portion of the crystalline lens, leaving the margin clear, through which the rays of light can pass to the retina, and there form a more or less distinct image of the external objects. From optical reasons, the image formed by rays of light thus passing through the outer portion of the lens is never so clear, and consequently vision never so good. In order that the rays of light may pass through the outer clear portion of the lens, the pupil must be somewhat dilated, as will be seen by the accompanying diagram (Fig. 2),

FIG. 2.

where the central rays are

stopped by the cataract, and only the outer ones can pass to converge on the retina, the pupil being dilated. It will be also seen that light may then get into the eye sideways, as it

were, between the edge of the pupil and the opaque portion of the lens.

The stimulus of light contracts the pupil, as we all know; and therefore the little child with cataract, in order to keep the pupils large, seeks to avoid it by turning his back to the window, contracting his brow and partly closing his eyelids, or, in other words, imitating the appearance of a person who is near-sighted. Moreover, in order to obtain larger pictures on his retina, or to get the light sideways, he holds the book close to his eyes, perfectly simulating what a near-sighted person without glasses must do. Meantime the opacity of the crystalline lens may be of such a character, or so far back in the lens, that the pupil can to the unaided eye seem quite black, as it naturally is; and thus even the family physician

may be deceived into believing the child is simply near-sighted, and it is consequently allowed to grow up without the ophthalmic surgeon being consulted. The latter can, by means of his ophthalmoscope, as the instrument is called, and by employing light thrown in sideways, immediately and perfectly detect the very slightest opacity of this crystalline lens.

Now, in order that light may pass to the retina, this partially or wholly opaque lens must be either removed from the eye, or broken up and allowed to dissolve; or, if only the central portion of it is opaque and the margin transparent, and this state is to be stationary, modern science has shown that we may then cut out a piece of the iris, and so make an artificial pupil for the entrance of light, by which the little patient may be able to see very well. Experience and judgment on the part of the ophthalmic surgeon are, of course, necessary to determine this.

The earlier cataracts in children are operated on, the greater the chance of restoring or retaining useful vision. The cataract itself generally continues to change, so as to render it less easily removed from the eye, or liable to complicate an operation. Another point, however, and one not generally understood, is, that when the retina ceases to be impressed by the stimulus of light and the formation of images upon it, the eye-or, if we may choose so to say, the mind loses a proportionate power of vision. Further still, a retina deprived of its proper stimulus ceases, together with the optic nerve, to be properly or fully developed with the rest of the body. Consequently, even if we succeed in clearing the pupil and admitting light freely to the retina, the patient will not then have the power of vision, or the appreciation of objects, which they would have had if they had been operated on earlier. This the ophthalmic surgeon too often sees, and he may even be blamed for not having accomplished what would be a miracle. The operations for cataract in children are comparatively slight, and, in these days of ether, of course not in any way to be dreaded. Again I would repeat, the earlier they are done the better. The trustees of the great eye-hospital at Moorfields in London, in a late annual report, call the special attention of the public to the necessity of bringing children for operation at an early period, instead of

allowing their eyes to be damaged by delay. Physicians and the public have recently been particularly warned, by myself and others, of the necessity of having every eye not perfect, and especially children's, examined by the scientific ophthalmic surgeon, whose advice may save to many useful vision. And I would here again call upon parents and teachers, when they notice the little ones shunning the light, holding the book near to or sideways, and seeming dull in learning their letters and lessons, to remember that cataract, and not simply near-sightedness, may be the cause, although their eyes look perfectly natural to the observer. Whether there is near-sightedness or cataract can only be determined by the ophthalmic surgeon; and the sooner the child is brought to him, the better for its future sight.

MATHEMATICAL TEACHING IN GERMAN SCHOOLS.

WHATEVER the Germans do, they do heartily. This is quite as evident in the charming pictures of German home-life drawn by Minnie Myrtle as in the impassioned verses of Schiller and Goëthe. Work, with them, never becomes drudgery, for it never overcomes the worker." This quality, admirable enough in itself, may sometimes give undue brilliancy to their system of public instruction; for it is very certain that that system would fail if transplanted bodily to America, for instance. Still this quality of heartiness is essential to the success of any system. That quality wanting, there is a grain of truth in the assertion that we can learn nothing about education by going to Germany. With this concession, it must be roundly asserted that a man who cannot learn anything of fundamental importance to the science of education, by going to Europe, should, by all means, stay at home. The school-system of Germany is the growth of centuries. It is the product of the direct and absorbing study of her greatest men. It is one of the most pronounced expressions of the national character.

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It is not necessary to recount its prominent characteristics, — graded schools, educated, professional teachers, effective and responsible supervision, and thorough examinations. The topic of

professional teaching may be discussed in future. Now it concerns us to inquire into the machinery of the schools, so to speak, the means by which the surprising results of teaching are marked, especially in the department of mathematics.

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The sense of form and proportion is first trained. It is amazing that so few have noticed that children build block-houses in good proportions before they can count. It is here more than anywhere else that the philosophy of German methods shows itself. Children are exercised in drawing, in the production of geometrical figures by colored strips of paper, or by the ingenious methods of the Pestalozzian Ausstech-schule, in the construction of solids from blocks, and in various other ways, before they hear of figures. The combinations of numbers are there taught by means of large movable figures on the blackboard, the children meanwhile repeating every process on their slates. Elementary Arithmetics, even the wonder-working Colburn, are quite unknown. By patience and heartiness of teaching, the pupils are thus easily and thoroughly taught the fundamental operations of arithmetic. Everything comes from the teacher first, is placed on the board, then the pupil repeats it on his slate. Every day he goes over the lessons of four or five preceding days, and then adds a little. So the dreary and disheartening desert of impossible pages of rules and examples to be learned in some gloomy future is entirely avoided. The pupil knows only what he has learned. He knows nothing of what is to

come.

When the groundwork is well done, the pupil gets a small book, about the size of the Massachusetts Teacher, consisting entirely of problems, arranged according to a regular plan; that is, several problems based on the same general principle, but varied in detail and method of solution, are placed in a paragraph. The use of this book is obvious. The general principle is explained and fully illustrated on the blackboard, the pupils meanwhile repeating every step on their slates. At the following lesson, the class must be able to solve and explain every problem given in the book which is based on that principle. This is the only text-book used in arithmetic; but the rapidity, accuracy and elegance of the solution of problems in these grammar classes is astonishing. In fact, I think

it is almost unattainable in our system, which groans under the incubus of "Series of text-books." One is almost tempted to believe that the wholesale use of arithmetics in our common schools is a concession either to the indolence or the incompetence of instructors.

What has been said refers, of course, to the best schools. No doubt there are pedants in Saxony, and no doubt many schools far behind the times; but the percentage of poor schools is very small.

The observations and experiments of the more thoughtful educators in our country are steadily leading them to one conclusion: text-books in arithmetic must be mainly abandoned before any thorough and lasting reform is effected in the methods of teaching the subject. The time is certainly coming when the order, Arithmetic, Algebra, Geometry, will be reversed. If Dr. Hill would repeat the experiment he tried in Waltham some years ago, in this direction, he would find more cordial supporters.

C. O. T.

A MOTHER'S VISIT TO A PRIMARY SCHOOL.

MESSRS. EDITORS,— I often find allusion made, in the Reports of School Committees and other educational papers, to a want of interest manifested by parents in the schools their children attend. I suppose this is so, or it would not be said; but I am also sure that many fathers and mothers are not remiss in this particular duty. If you think it will be worth publishing, you are welcome to use the following account of a visit to our Primary School, No. 7, in S., where I have a little boy of eight years and a girl of six, to whom I attempt to do a mother's duty.

We live about sixty rods from the school-house, which is situated on a quiet cross street, and has a plain, well-gravelled, and dry yard of about a quarter of an acre in extent. The house has two rooms in it, one for the older and the other for the younger classes, where the alphabet is taught. Miss Fuller is the teacher of the latter, and Miss Meagher of the former. I am pretty well acquainted with the ladies, and like them; and they sometimes come