according to their relations. A scholar can never hold in mind the principles of a science if he is able to look at isolated facts only. But these can be classified in such a way that the contents of a book are comprehended in a few statements; these are sufficient to bring the whole before him. I have of late required my classes to make a comprehensive analysis of each book, in writing, starting with the point, and proceeding not in the book order, but the natural order. Following the point, come the generation of the line and surface, kinds of lines, formation of angles, relations of lines to angles, laws of lines in general as embodied in the theorems, laws of particular kinds of lines, formation of the simplest geometrical figure, kinds of triangles, laws of each kind, properties of triangles in general, etc., thus classifying every theorem and corollary. The mental exercise necessary in making an analysis of this kind, will so fix the subject, that, in the language of many of my scholars, they cannot forget it, if they try.

Many do not fully understand that geometrical figures are so many portions of space. I have found much difficulty in making them comprehend the true province of Geometry, especially if they have started with no more light than the book gives. I have succeeded best in giving clear views of the subject by two or three familiar talks with them, upon space, before opening the book, until they understand that it is a reality, the condition of material existence, that it has certain properties which make it capable of being measured. Then comes the advantage of measuring space, and the connection with the measurement of matter. Then the class employ the imagination in the generation of lines, surfaces and volumes, before being allowed to represent them. In this familiar way, the foundation of the study may be laid, without using the erm Geometry, which is often a bugbear of itself. The class will find such an introduction vastly more interesting than blank and bare definitions. Before giving the proportions, a short exercise upon the different kinds of truth which form the material for reasoning, and the kind of reasoning applicable to each will be found a good preparation. I am aware how meagre a written sketch of a plan of teaching must appear, but in no study is a good method more important than in Geometry, and possibly these brief hints may be useful to beginners.

F. A. R.

HOUSE-KEEPING BY DOUBLE ENTRY.

Last year I lived in a tenement-house in Broadway. It has since been rebuilt, and all its occupants are scattered; so it will do no harm to write about them, as I am going to. There were more than fifty families on the first floor. They were birds in a great salesroom, with claborate cages and other fancy wire-works. "Birds in their little nests agree;" and their agreement, their happiness, their heavenly morning music were the glory of the tenement-house. On the second floor lived a dress-maker and a milliner, the aristocracy of the house. The third floor was rented by representatives of the middle class of tenants, an actor and an actress, who were married to each other, and an insurance agent who was married to somebody else. On the fourth, or "top floor," as our grocer would always call it, was the tiers état, a lady artist with her family, a horse-car conductor with his family, and two poor teachers, Sissy and I. I am going to write something about how we two lived, because I have often been told that I can do good by such a narrative, and because I believe it. There are some women who do not have to economize. I am not writing to them. There are some women who think they ought to receive the same remuneration for everything they do that men would receive in their places. I hope I am not writing for them. And I'll tell you why. A man has to spend more than a woman. If he is married, no matter how poor he is, he usually has to support a servant. If he is single, no matter how poor he is, he has to take ever so many young ladies to ever so many places, and pay for their tickets. Another fact which has more to do with my subject is, that a man can't save as a woman can. If he is invited suddenly to a party, can he run into a store on his way up town, hasten home with a bundle in his hand, and before the party hour, make for himself a new white vest? I should think not. I should think he can't wear anything without a sense of what it cost readymade. Another fact, which has most of all to do with my subject is, that a man can't board himself. A woman can. No; two women can. That is what I mean when I say House-keeping by

Double-entry. There were two of us, and we both entered into it, as follows:

1st. How cheaply we lived. Our rent wasn't much, because the house was old and shabby. Our fuel wasn't much, because the room was small. It was so small that I thought for a while we had no space for any stove but a naphtha stove. So I consulted a veteran oil-striker. He said, "Naphtha is dangerous stuff, and women had better not have anything to do with it." There are some women who would have taken this as an insult to their sex. I shall never write for them. They may experiment with nitro-glycerine and the cyanide of kakodyle, if they want to, just because men do. I thanked the veteran, and went up and down the Sixth Avenue till I found the smallest coal-range you ever saw, with two griddles and an open grate. A naphtha stove would have cost twelve dollars. This one cost only three. It was second-hand; but the soap-stone lining was not burned out. Somebody had evidently sold it because it was too small. It was such a darling that I wanted to take it up in my arms. And I did, to set it on the table, where it stood while I tacked down the matting. We tried to burn coke; but it comes in boulders, and isn't the thing for a very small stove. So we bought a bushel of nut-coal once or twice a month, and had a splendid fire every day after we came home from our schools. In the morning there was no time for a coal-fire, and the blessed little stove was so little as a whole, so minute as to its penetralia within the soap-stone, that one three-cent bundle of kindling-wood cooked steak and coffee, and warmed us and the dish-water. If we wanted to boil potatoes, we used part of another bundle. The food for both of us cost exactly four dollars a week. And so it came to pass that, for four months in the coldest weather of 1865 and 1866, Sissy and I lived in Broadway, at an average expense to each of us of less than three dollars a week for food and fuel and lights and rent. I never lived for that in strawberry time; and, if I know my own heart, I never will. Ants and squirrels lay up for the winter; teachers ought to lay up for the summer.

2ndly. How neatly we lived. They told me that such a stove as ours would be a dreadful one to manage, because we should have to pick out all the coal with our fingers, and they would blacken,

crack and bleed, and be a pretty sight in the school room, especially at the time for using chalk, when a teacher's hand is like a city set on a hill. Not so. An iron spoon costs twenty cents. The handle don't hurt anybody's hand, and the bowl does the best of service in digging out the cinders. (Other papers will please copy.) We found that we didn't need to split kindling-wood if we only had plenty of shavings. There was a carpenter's shop one block above us, the other side of Broadway. Once or twice a week one of us would put on her shawl, hat and gloves, and carry a goodlooking carpet-bag to the shop. The carpenters treated us as if we were queens. They wouldn't take any money for the shavings. They wouldn't let us fill the bag. And, after they had filled it, they carefully brushed the shaving-dust off the outside. Then we locked it, and carried it leisurely home, as if it contained some brittle treasure that we wouldn't trust to an expressman. I have never apologized for carrying my own bundle since the day when I went down town with Mrs. Alexander Exact. Something made me in such a hurry that I couldn't wait to have my purchases sent. So I told my friend that if she was ashamed of my bundle, we would take separate stages. She said, "Why should I be ashamed of your bundle? My husband's debts are paid." On our table, against the wall, stood a new cupboard, with panel doors. The shelves inside held our silver, glassware and crockery. When the cupboard doors were open, and the table-cloth spread, how easy it was to take our seats, and help ourselves to anything on the shelves or the stove. We did not keep food in our room. Outside of it, in a ventilated packing-room, there was a shelf, and a clean wooden box, with a lock and key. The coal-box was out there too, and the shaving-bag, and the brooms and pails. So, when our cupboard was shut, you wouldn't have known it from a book-case, and to us the room seemed more like a parlor than some rooms that go by that name. The little grate gave a cheerful glow. An English ivy grew in a beautiful sea-shell hanging between the window and its thin white curtain. The walnut bracket made our gift-books look their best. pictures looked well enough in passe-partouts. hyacinth, or pansy, or some other bright flower

And our giftA green-house bloomed in an

earthen pot on the bureau for a few weeks, and then faded, to be replaced by another. How sorry I was to leave that room when the time came for the whole block to be rebuilt!

3rdly. How well we lived. In the first place, we were well all the time. We should not have been if we had used a naphtha stove, a kerosene stove, a gas stove, or any other that did not communicate with out-door air. We didn't have influenza nor diphtheria nor neuralgia nor dyspepsia nor cold feet. And we didn't practise gymnastics, fashionably so called. An English physician once prescribed for a wealthy dyspeptic, "Live on sixpence a day, and earn it." Live on two dollars a week, and cook it, might be a good prescription for more than one invalide. In the next place, we fared well. You don't see how any one can on two dollars a week? Why, as Prof. Blot says about making lobster salad, "That's easy! It's nothing but work." The secret is in buying the raw material; also, in buying seldom the raw material known as porter-house steak. We had a breakfast worthy to precede a day of faithful teaching, a dry lunch, with some kind of fruit, and a milk supper with variations that is, toast, mush, hominy, samp, rice, corn-cakes, or crackers. Once we tried wheaten grits, and only once "farina cocido." We always had enough of what always tasted good. Who can say more of the costliest fare?

Meanwhile, the Deaconess was paying seven dollars a week for board in a house which my dressmaker left because the table was so poor. Couldn't the Deaconess board herself? Yes; she used to keep house for her father in the country. Her efficiency would have made it a happy privilege for any other woman to live with her. But it would have taken time which the Deaconess spent at No. 1 Bond Street, waiting among the offensive crowd there daily assembled till her turn should come to intercede for some freezing, starving wretch unable to go there for help; time which she spent in a sewing-school, teaching poor little girls to make bed-quilts for themselves out of rag-bag bits of calico; time which she spent reading the Bible aloud in parts of the city where cholera is expected. If there is a record anywhere of self-denying services, prompted by the highest love, it is written therein that for Christ's sake the Deaconess stooped to be a boarder.-" Rosa Palmer" in the N. Y. Independent.