This granted, if we conceive that the arcs a and y are described from the points P and c as centres, with a ray equal to a unity, and if from the point P we describe the arc dA with the ray PA, we have the proportions

assuming APP, CA'R, and replacing the arc ad by the arc A 1, which is obviously equal. On the other surface of the lens, if we suppose, again, the arcs 6 and 8 described with a ray equal to unity, the arc an described with the ray making A R′ and A'r' = p', we have likewise d

R

of domestic life, or that tend to its elevation and refinement. This state of things cannot last. The time is not far distant when many social tendencies must at length necessitate a cheap, efficient, and systematic education of the people. Till such is based upon system, and that of an enlarged and unsectarian character, no effectual power will be brought to bear upon much of the ignorance, and many of the social demoralisations, which are justly complained of. For considered in its noblest and most essential principles, in all that constitutes a foundation for what is enlarged and progressive in the individual, enlightened education will recognise no difference of sects or social position. It will give principles and afford enlightenment-leaving the individual to advance therefrom in such social direction of duty as shall best suit his position and aptitude.

In the meanwhile young women, of the classes referred to, might do much for themselves. Presuming an ability to read, or at least the wish to learn, an incalculable power of self-imP'A',provement lies open before them. They want, I think, but to AI understand the immense amount of social good that depends upon their individual culture, of the refinement that is its contingent, of the enlightenment and morality they may be producers of, of the lofty principles they may infuse into the generation to come, to be at once aware of their great individual duty, and to prepare for it by self-culture and discipline. In thus speaking, I do not refer to book-knowledge only, or to any special class amongst the great industrial masses, but to woman generally, however poor and lowly, and to every act and duty which can improve her in person, in manners, in behaviour, and in the conduct of her home. These matters, trivial as they may seem, are amongst the greatest needs of the age; and whilst men are so immensely progressing as they are, and showing the sterling character of this progress by their thirst for science, it will shame woman if she be behindhand in the improvement of her mind, the culture of her person, her better knowledge of domestic duties, and the adornment of her

If we admit that the arcs AE and AI are equal, which is nearer to the truth in proportion as the rays of incidence escape less from the axis, we may suppress the common factor, which gives

1

(n 1

(3). 1 ( + 1 ) = // +

R

R

Such is the formula of bi-convave lenses. If we make pd, home. For let it be recollected that refinement is but a thing ve find

1

p'

= (n − 1) (— + ;; ), p' then designating the

women may be as much gentlewomen in habits, manners, and principal focal distance. Representing this by f, there is duties, as in the proudest homes of the land. Granting that they have to work for daily bread-so much the better; the

When the image is virtual, p changes the sign, and the on cooking, household-work, needlework, the moral manageformula (5) takes the form,

1

1

(6). f

ment and education of infancy, and other relative subjects, exist in abundance; but it is to these subjects as allied, and to their effects in educating woman, that I shall direct my attention, as well as to what relates to the decoration and management

In bi-concave lenses, p' and f'preserve the same sign, but of homes-the latter a somewhat novel feature, as refinement that of p changes; formula (5) then becomes

1

p

1

(7).

in alliance with narrow means has been little understood, or even considered, by our most advanced thinkers.

So much has been done by Mr. Cassell for the self-education of the masses, in his admirable series of the POPULAR EDUCATOR,

As to the rest, the formula (7) is obtained by the same that it will be only necessary for me to refer to some few points reasoning as the above.

FEMALE EDUCATION. - No. I.

BY SILVERPEN.

MUCH as has been done for general education in this country by schools, institutions, and cheap literature, there is yet a great want of it, and its best effects, amongst women of the middle and operative classes. Men, through association, a wider range of labour, the chance of meeting with those more intelligent and educated than themselves, have many means of improvement, even where illiterate; but woman's advantages are fewer. Unless in some degree educated, or surrounded by extremely favouring circumstances, the chances are ten to one that she drag on a life of monotonous domestic duty, and rear a family in the same ignorance of all that constitute the graces

connected therewith. The first important one is that of perseverance. Patient endeavour will win a victory over the hardest educational difficulties; and let what is done, be done well. Scholarship, even when relating to merely rudimentary matters, admits of nothing which is slovenly. Another thing of importance is, that when the power of reading is acquired, and there exists a taste for it, let what is low and trashy in periodical literature or books be passed by, as unworthy the countenance of any young woman who aspires towards some degree of selfcultivation and improvement. Tales relating to seductions, murders, improbable marriages, and profligate courses of life, ought to have no charms for her. The eye, and ear, and mind of woman, of whatever degree, cannot be kept too pure and unsophisticated; and all publications which refer to these subjects ought to be avoided as so much moral poison. Their reign is but for a day-once educate the great industrial masses, give them the noble training which geometry and mathematics, grammar & ad geography, languages and history will afford,

|tion with current events, such as emigration, colonisation, or
the existing war, the value is really great of knowing some-
thing objectively of such places as Melbourne, Canada, or
Sebastopol. With knowledge of this kind, vague generalities
become valuable facts, that in many cases may serve to

and all these corrupt and sensual excrescences of a cheap press
will be heard of no more, simply for the reason that there will
be no market for them. Not but what fiction, in its best kinds,
performs a noble educative duty, besides affording healthy and
innocent amusement. Perhaps, as far as woman is concerned,
even when all classes shall be generally and efficiently edu-influence all the future incidents of individual life.
cated, fiction will always preponderate as the section of litera-
ture most favoured; but this much may be observed, because
a thing worth remembrance, that proportionately as the mental
faculties become strengthened by study and thought, and as
soon as education gives discipline to the mind, the taste for
fiction diminishes. For the period of youth it will always
have a charm, and in many senses an educative effect-just as
nations in their first beginning are amused and instructed by
ballads and legends. Of those branches of fiction destined to
instruct and delight, the novels of Sir Walter Scott will always
stand pre-eminent. Exquisitely pure in their moral tendency,
picturesque as Creswick's and Gainsborough's landscapes in
their delineation of scenery, fresh and spirited in depicting
character, they are destined to enchant unborn millions, and
the broadest sign of mental advance and moral purity will be
on those days when they pass from hand to hand as readily
amidst the masses, as they do at present amongst the pro-
visionally educated. One thing has alone to be guarded against
in their perusal. They underrate, and in some senses ridicule,
the Puritanism of the seventeenth century. But this defect
the popular knowledge of history begot by education will
rectify; for the time will come when English men and women
will look back with as much pride on this phase of their
national history, as educated Americans to their War of Inde-
pendence and Washington. Dickens, too, and Thackeray, are
eminently moral teachers; and there is yet another class of
fiction worthy of all attention, though but in its germ: that
which gives vitality to many abstract questions, and to points
of social and industrial reform, painting pictures, as it were, of
life under better and approaching aspects.

Pains should be taken to write a fair and open hand. This is attainable by writing large-hand copies for a sufficient period till the hand has obtained facility and the eye accuracy. One large-hand copy written well and carefully every day for some months, would go far to ensure a handwriting of character and firmness. Nothing, next to grammar and spelling, betrays caste and breeding so much as handwriting. This ought not to be; and with the present facilities for self-improvement which exist, and with the leisure left from their hours of labour, most young women of the industrial classes might learn to write a good hand and spell well. The acquirement of these advantages is so mere a fact of simple industry and attention, as to be scarcely excused when absent. When large hand is written well, and a smaller one undertaken, great advantage would be found in making short extracts in a copy-book from a book or newspaper: this would improve style and spelling, and lead to the habit of expressing ideas on paper, not only with facility, but without mannerism or vulgarity. Of all habits of self help, none exceeds this, especially when habit and facility are so far advanced as to enable the copyist to condense the material into a few lines and into her own language, so that it thus becomes what is called by lawyers and students "note taking.". In this way grammar and correct spelling are not only acquired, but a precision given to remembered facts and habits of thought

which become invaluable.

Lessons in Arithmetic are given in the POPULAR EDUCATOR, and my only duty here is to impress upon the minds of young women its two-fold value as an acquirement. It is obviously of much utility to those who have to make many small purchases, and to calculate matters connected with work or wages; but there is a higher point still, namely, that its acquirement and use have certain faculties in a woman's mind, which, by a curious physical law, are often reflected in the capacity of her children. And, as I shall presently show, no fact of this kind can be relevantly disregarded in woman's true culture of herself.

Of history a word must be said. Of that of her own country, every young woman of whatever rank should be ambitious to have some knowledge. The time will come, when she will prepare herself as though she were to je an open and wellwritten chronicle for her children to read, and think what homes will be, what domestic life-even where humble-when instead of scolding them, or telling idle tales, a mother can impart pretty facts and interesting points of history to her little listening children. There are hundreds of such alone in the history of our own country; and considering this history as a means, direct and indirect. of individual improvement, I know nothing better. The relation of the past to the present and the future can never, with advantage, be overlooked; and the knowledge of what noble men and women have done for the advance of civil and religious truth in this our country, should lead each individual to renewed efforts for self-improvement and culture. To such amount of historical knowledge there may be additions. The history of the Jews is a deeply interesting one: whilst some knowledge of both Greek and Roman history lays, as it were, the true foundation of much which is valuable and interesting in the history both civil and political of modern times-so much have the literature and fine arts of the Greeks, and the laws, the literature, and the conquests of the Romans, influenced all the circumstances of our modern civilisation and advance.

Passing from these matters connected with rudimentary learning and general self-culture, I have a still more important study to urge upon the attention of ALL sensible young women of the middle and operative classes. It is that of PHYSIOLOGY, or an acquaintance with the functions of the body, and how best disease is avoided and health ensured. It is a new study, at least as far as the general public are concerned; but it is not less a need or less true for all that-and it is especially a study befitting woman. On her depends so much the health of children and the health of homes, that were this admirable, this priceless knowledge spread, as I earnestly believe and trust it will be, two-thirds of the disease, the crime, the early deaths, would be prevented; whilst so far from there being anything indelicate or improper in a knowledge of the human body and its functions, that I think it is one which may be called emphatically, considering the office which is so especially hers-THE STUDY OF WOMAN! To meet this need of a general understanding of the laws of life and health, Lessons in Physiology have been given in the pages of the POPULAR EDUCATOR. An attentive perusal of these I would recommend, as well as that of two little books by the late Dr. Andrew Combe of Edinburgh. The first is entitled, "The Principles of Physiology applied to the Preservation of Health," and the second, "A Treatise on the Medical Management of Infancy." They are published at the price of half-a-crown each, by Simpkin and Marshall, London; and are thus placed within the reach of the provident and industrious, who, for the sake of a noble self-respect and self-improvement, will themselves, or joining with other young women, save an occasional sixpence from the week's wages.

But this is such an important subject, and so intimately connected with improved personal habits and domestic duties, that I must resume it in my next paper.

Les hommes sont tourmentés par l'opinion qu'ils ont des choses, non par les choses mêmes.-Epictèle.

L'homme n'a guère de maux que ceux qu'il s'est attirés luimême : c'est l'abus de ses facultés qui le rend malheureux. La nature lui fait payer cher le mépris qu'il fait de ses legons.-J. J. Rousseau.

Il n'est d'affreux que le commencement du malheur: au comble de l'adversité on trouve, en s'éloignant de la terre, des régions tranquilles et sereines.-Chateaubriand.

In relation to Geography, much that is valuable relating thereto may be acquired by the study of maps. There are excellent ones to be found in the POPULAR EDUCATOR, and in these pages, which will serve every purpose of study and reference. Points in history have an added interest, when Le malheur, loin de dégrader l'homme, l'élève, s'il n'est pas un their localities are thus prefigured to the mind, and in connec-lâche.-Silvio Pellico,

2. Those to whose stem the syllable vvu or vi is appended, The termination of the third person plural, vot, was changed and which receive the person-endings at the end of this sylla-into art, and then contracted with the foregoing stem-vowel of ble. The stem of the verbs of this class ends : the verb. The Attic dialect, however, admits the contraction only in the stems which end in a; thus:

LESSONS IN GREEK.

The same obtains in the optative of the passive aorists of all verbs, as τυφθείημεν = τυφθεῖμεν, τυπείημεν, τυπείεν (quite like τιθείην).

In the optative second aorist of the verbs ίστημι, τιθημι, διδωμι, on the contrary the shortened forms are very rare, except the third person plural.

Person-Endings of the Imperative Present and Second Aorist. ·

(δι-δο-θε)
δι-δο-τω

δι-δο-τον
δι-δο-των
δι-δο-τε
δι-δο-τωσαν
δι-δο-ντων.

The second person singular imperative present throws away the ending et, and in compensation the short characteristic vowel is lengthened, that is, a is changed into n, e into ει, ο into ου, and v into ῦ; thus:

ἱ-στα-θι becomes -στη

δι-δου

τι-θε-θι becomes τι-θει δεικ-νῦ. δεικνύ-θι "9 δι-δο-θι The ending in the present is preserved in only very few verbs. In the second aorist of τιθημι, ίημι, and διδωμι, the ending θι has been softened into σ, thus θε-θι becomes θες; εθιπές, δοθιπδος ; in the second aorist of ἱστημι, however, the termination θι remains, thus στῆθι ; also in the two aorists passive of all verbs, as τυ-πη-θι, παιδευθη-τι, instead of παιδευθη-θι.

aorist is ναι.

The termination of the infinitive in the present and second This syllable is in the present added to the short characteristic vowel, but in the second aorist is lengthened, as a into n, e into et, and o into ου.

Present

ἱ-στα-ναι

τι-θε-ναι
θεῖναι

δι-δο-ναι δεικνυ·ναι
δοῦναι

Second Aor. στῆναι The infnitive of all passive aorists follows στῆναι, as τυπῆναι, βουλευθῆναι.

The terminations of the participle in the present and second aorists are ντς, ντσα, and vr, which unite with the characteristic vowel according to the ordinary rules:

ἱ-στα-ντς=ἱστᾶς, ἱ-στᾶσα, ἱ-σταν
τι-θε-ντς = τι-θεις, τι-θεῖσα, τι-θεν
δι-δο-ντς = δι-δους, οὖσα, ον
δεικ-νυ-ντς = δεικνυς, ὖσα, ν.

στας, στᾶσα, στην
θεις, θεῖσα, θεν
δους, δοῦσα, δον

The participles of the two passive aorists of all verbs follow the participle τιθεις οι θεις, as τυπ-εις, τυπ-εῖσα, τυπ-εν; βουλευθ-εις, εῖσα, εν.

The person-endings of the middle voice coincide with those of the verbs in w, only that in the second person singular indicative and imperative of the present and imperfect they retain σαι and σo in their full forms ; yet επιστω, ηπίστω, δύνω, ηδύνω, πριω, επριω, are the regular forms of good prose.

The singular imperfect active of Tonμ, with the exception of the first person, is commonly formed from ΤΙΘΕΩ, and that of διδωμι generally from ΔΙΔΟΩ with the usual contractions. For the verbs in uμ you may employ the forms in vw in the whole present indicative, and generally in the imperfect, especially in the third person plural indicative and the participle; the forms in vw are to be exclusively used in the subjunctive of the present and the optative of the imperfect, as ενδεικνυω,. ομνύω, συμμιγνύω, together with ενδεικνυμι, ομνυμι, συμμιγνυμι. The middle, however, admits these forms only in the subjunctive and optative.

is lengthened, a into ne into, and into (in the perfect other tenses of the middle and in all the tenses of the passive active of τιθημι and iημι), also o into ω; but is retained in the ω, excepting the perfect and pluperfeet of τιθημι and ίημι, which receive the εt of the perfect active (τεθεικα, τεθειμαι, είκα, είμαι).

The first aorist active and middle of τιθημι, ἵημι and διδωμι have for their tense characteristic not but :

The forms of the first aorist active, έθηκα, ήκα, and εδωκα, however, are used only in the indicative and especially in the singular; in the other persons commonly, and always in the other moods and the participle, the forms of the second aorist are employed. So instead of the forms of the first aorist middle of τιθημι, ίημι, and διδωμι, those of the second aorist middle are used. On the contrary the indicative forms of the singular second aorist of τιθημι, ίημι, and διδωμι (εθ-ην, ήν, and dw) are not to be employed.

The verb iornu forms the first aorist active and middle, like the verbs in w, with the tense characteristic σ, as e-στη-σ-α, The second aorist middle εoraμηy is never ε-στη-σ-αμην. used. Some other verbs, however, have the form, as επτάμην, επριάμην.

The second aorist passive and the second future passive are wanting in these verbs, also the third future, except in ίστημι —έστηξω, οι έστήξομαι.

In regard to the signification of ίστημι, observe that the present, imperfect, future, and first aorist active, have the transitive import of to place, the second aorist, the perfect, and the pluperfect active, and the third future, on the contrary, have a reflex or intransitive meaning, to place oneself, or to stand, thus εστην, I placed myself, I stood, έστηκα, I stand (in Latin sto), ἑστήκειν, I stood (stabam) έστηξω, I shall stand (stabo), αφεστηξω, I shall stand away, that is, I shall leave or abandon, desert. The middle signifies either to place for yourself, or to cause to be done, or to stand in or consist of (Lat. consistere). The passive means to be placed.

2. The Second Class of the Verbs in μι.

με

The tense formation of the second class of the verbs in has no difficulty. After cutting off the termination vvuμe and νύμι you add the tense-forms to the stem. The verbs in o which lengthen this o into w in the present, retain the w in all the tenses, as στρωννύμι, ῥω-ννῦ-μι, ἑω-ννῦ-μι, χω-ννῦ-μι; future στρω-σω, ῥω-σω, έω-σω, χω-σω, and so on.

But the verbs whose stem ends in a liquid take for the formation of some tenses a theme ending in a vowel, as ομ-νύμι, aorist ωμ-ο-σα, from the theme OMO. The second aorist and νυ-μι, aor. 2. pass. εζύγην, fut. 2. pass. ζυγησομαι. second future passive are found in only a few verbs, as ζευγ

Remarks on the Models.

In the dual and plural of the indicative, and in the other moods and the participle, for the first aorist active, the second aorist active is used.

Instead of the forms ε-θη-κα-μην, ε-δω κα-μην, first aorist indicative middle, the Attic forms are used.

The middle optative forms of the imperfect and second aorist of the verbs in e, namely, οι, as τιθοιμήν, θοιμην, are preferred to those in et, us τιθείμην, θείμην.

The perfect and pluperfect, έστηκα, έστηκειν (but not είστηκειν), form the dual and the plural immediately from the stem, as perfect, έ-στα-τον, ἑ-στά μεν, ἑ-στα-τε, ἑστᾶσι(ν) ; pluperfect -στα-τον, ἑ-στα-την, ἑ-στά-μεν, ἑ-στα-τε, ἑστᾶσαν; instead οἱ ἑστηκεναι, ἑστᾶναι is usually employed. The participle runs έστως, ώσα, ως, g, ὦτος, ωσης, as well as έστηκως, υία, ος, 8. With έστατον compare τετλαμεν (ΤΛΑ), and In the tense-formation of the entire active, as well as of the | τεθναμεν, τεθνατε, τεθνάσι(ν), inf. τεθνάναι from τέθνηκα, middle future and first aorist, the short characteristic vowel | θνησκω (ΕΝΑ).

Imperfect.

Indicative.

Par. Inf.

ACTIVE.

PARADIGMS OF VERBS IN μι.

MIDDLE,

Imperative.

διδῶνται

τι θει

δεικνύ

διαδρασο, οι

δεικνύσο

ί-στω

τι-θου

δι-δου

P. 2

32323

τι θες τω

δι-δο τω

D. 2 . ἱ-στά του

δεικνύτω
δεικνύ τον

ἱ-στα-σθω

τι-θε-σθω

διδο-σθω

δεικνυσθω

δι-δο-τε

δεικ-νύ-τε

δι-δο-τωσαν δεικ-νύ-τωσαν ἱ-στα-σθωσαν τι-θε-σθωσαν δι-δο-σθώσαν δεικ-νυ-σθωσαν

I and δεικνύω, εις, and so on. especially δεικνύουσι (ν). So in the impl. ; εδεικνύον, ύες, νε(ν), and in the partic, commonly δεικνύων, ουσα, ον.

1