while the extremity of the axis
or point, K, describes on the
supporting surface and about
the projection G" of the cen-
tre of gravity, an undulating
curve a, b, a', b', a", &c., hav-
ing cusps a, a', &c., in the circle
described about G" with the
radius G"K" y sin a, and .
tangent, externally, to the
circle described with a radius
G" Ky sin,. But, as in
the case of the gyroscope, K
these little undulations speedi-
ly disappear through the re-
tarding influence of friction
and resistance of the air, and

the point of the top describes a circle, more or less perfect, about G".

The rationale of the self-sustaining power of the top is identical with that of the gyroscope; the deflecting force due to the angular motion of the axis plays the same part as the sustaining agent, and has the same analytical expression. Owing to friction, the top likewise rises, and soon attains a vertical position; but the agency by which this effect is produced is not exactly the same as for the gyroscope.

If the extremity of the top is rounded, or is not a perfect mathematical point, it will roll, by friction, on the supporting surface along the circular track just described. This rolling speedily imparts an angular motion to the axis greater than the horizontal gyration due to gravity, and the deflecting force becomes in excess, (as explained in the case of the gyroscope,) and the axis rises until the top assumes a vertical position. Even though the extremity of the top is a very perfect point, yet if it happens to be slightly out of the axis of figure (and rotation) the same result will, in a less degree, ensue: for the point, instead of resting permanently on the surface, will strike it, at each revolution, and in so doing, propel the extremity along. The conditions of a perfect point, perfectly centered in the axis of figure, are rarely combined, or rather are practically impossible; but it is easy to ascertain by experiment that the more nearly they are fulfilled, and the harder and more highly polished the supporting surface, the less tendency to rise is exhibited; while the great stiffness (or tendency to assume a vertical position) of tops with rounded points, is a fact well known and made use of in the construction of these toys.

The references throughout this paper are to my paper on the gyroscope in the June number of the Am. Journal of Education.

as a teacher, 165.

Association, Teachers, 252,

Astely, John, 165.

Astronomical observatory, 59.

Astronomy, on teaching, by Diesterweg, 243.
Attitude in reading, 227.

Asylum for Idiots in New York, 417.

Attendance, Luther on, 440.

Austin, Mrs., 14.

Bad language before children, 424, 426.
Baden, 257.

Backus, F. F., mover in behalf of idiots, 417.
Barbier, C., music printing for the blind, by. 137.
Barnard, Henry, articles by, 155, 183, 245, 359,
363, 417, 520.

Basedow, 125.

Belles-lettres, in University of Turin, 52.

Bowen, F., article by, 5.

Braille, L., music printing for the blind, 137.
Brockett, L. P., article by, 127.
Bridgman, Laura, training of, 383.

Burgdorf, Pestalozzi's school at, 71, 84, 91, 119
Burleigh, Lord, notice of, 161.

advice to his son, 161.
on school punishment, 155.

Caccia, his college, 485.
Cara, lectures by, 43.

Cecil, Sir W., see Burleigh.

Charitable endowments, 57, 127.

Charles Albert, 43, 58, 59.

Charles Emanuel, 43, 59.

Charles Felix, 61.

Cheke, Sir John, 165.

Chemnitz, industrial school at, 252.

Church authority in management of schools,

498.

Children, Lord Burleigh on management of, 162
Christopher and Alice, by Pestalozzi, 66.
Christianity, evidences of, study of, 336.
Cicero, Sturms' estimate of, 411.

Cincinnati, system of public schools, 520.
statistics of public schools, 520.
public high schools, 520.

Clindy, Pestalozzi's school at, 112.
Classes in reading, 227.

Cleomenes, remark by, 471.

Clergy and public schools in Sardinia, 500.
Colburn, W., arithmetical method, 293.
Colleges, public prayers in, 23.

educational office of, 268.

Commercial school, Dresden, 252.

Common schools in New England in 1824, 14.
Common schools in Germany before 1800, 343.

Benefactions, educational, by E. Dwight, 17, 22. Compulsory school attendance, 440.

J. Wadsworth, 14.

Caccia, 485

W. Woodward, 520.

J. Hughes, 520.

Amedeus VIII., 43.

Charles Albert, 43, 58, 59.

Charles Emanuel, 43, 59.
Charles Felix, 61.

Berti, D., 491.

Beuggen and Pestalozzi, 115.
Bible, Luther on study of, 443.

in high schools, 367.

Biography, in teaching history, 514.

Biography of Edmund Dwight, 5.

Lowell Mason, 140.

Compulsory teaching, 166.
Conception, mental, 204.
and perception, 323.

and memory, 324.
and imagination, 324.
Consciousness defined, 326.
cultivation of, 326.

Contents of Number 10, 3.

Contents of Number 11, 273.

Controversy, how to practice, 465.

Convent schools in Ireland, 375.

Conversation, Lord Burleigh on, 163.

Cooper Institute or Union, 526.

Cooper, Peter, 526.

Copying, in drawing, 194.

Coste, P. A., 490.

Course of study in Sardinia technical schools, 37.

Course of study in Sardinia University, 46.

Blind, institutions and instruction for, 127, 140. Course of study in Sardinia secondary schools, 42.

Cyrus Peirce, 275.

Henry Pestalozzi, 65.

John Sturm, 167.

number of, 128.

printing for, 134.

peculiarities of, 139.

statistics of, 127.

Blindness, causes of, 127.

Borrowing and lending, 163.

Books, educational effects of, 266.

Book notices, 272.

Botanic garden in Turin, 59.
Botta, V., articles by, 37, 479.
Boston Academy of Music, 144.

Blackstone's definition of an idiot, 386.

Course of study in Sardinia elementary, 490.
Paris institution for blind, 132.

Sturm's school, 169, 401.

Chemnitz industrial school, 252.
Woodward High School, 521.

Cousin, V., report on Prussian schools, 14.
Cujacius, 44.

Deaf and dumb, institution at Turin for, 41.
Deschamp's proposed plan of blind instru'n, 130.
Development, human, Pestalozzi on, 66.
educational, Russell on, 329.

Examples of training idiots, by Dr. Wilbur, 419. Ireland, system of national education in, 363.

Lesson-bill, weekly, in Prussian gymnasia, 241.

of Rendsburg real school, 250.
Hanover girl's high school, 250.
Saxon real schools, 251.
Chemnitz, 252.

Lexington, normal school at, 289.

Liberty of instruction in Sardinia, 499.
Library of University of Turin, 58.

of King of Sardinia, 483.

of public schools of Cincinnati, 52.

Libraries, public, Luther on, 438.

physical exercise, 464.
punishment, 469.
excessive study, 468.

Moreau, Pierre, his letters for the blind, 130.
Mother tongue, study of, 473.
Munich, infant schools in, 257.

university, historical school in, 257.
Museums, at University of Turin, 61.
Music, as a pursuit for blind, 137.

Lowell Mason's career in teaching vocal,141.
Luther on, 448.

Lieber, F., vocal sounds of Laura Bridgman, 400. Musical works of Lowell Mason, 148.

Literature of education; extracts, 183.

Lloyd, poem on reading, 225.

Locality, educational influence of, 262,

Logic, right and wrong mode of teaching, 320.
Sturm's method in, 178.

Luther on studying, 447.

Louis of Savoy, benefaction of, 43.
Luther, educational views of, 421.

address to town councils of Germany, 429.

on dead languages, 432, 444.

public libraries, 438.

school organization, 442.
dignity of teaching, 441.

universities, 443.

compulsory attendance, 440.

seclusion of young, 426.
music, 448.

punishment, 425.

logic and rhetoric, 447.

physical exercise, 448.

duty of establishing public schools, 429.

parents' educational duty, 422.

studying the Bible, 443.

family education, 421, 424.

studying history, 445.

natural sciences, 445.

Lütken, Doris, infant school of, 257.

Macbeath and Milne, alphabet for blind, 136.
Mann, Horace, 16.

Manners, Lord Burleigh on, 163

Marriage, Lord Burleigh on, 162.

Mason, Lowell, memoir of, 141.

list of works of, 148.

Mason, Sir J., on punishment, 156.
notice of, 164.

Massachusetts, common school movement in,

1837, 14.

state reform school for girls, 359.

state industrial school for girls, 359.

family system in, 359.

visit to, 361.

Masson, D., lecture by, 262.

Musical institutions, Boston, 144.
Musical institutions, Turin, 485.

Nantucket, educational labors of Cyrus Peirce
at, 227, 285.

colored population of, 287.

Native language, Sturm's neglect of, 409.
when to learn, 473.

Natural bent of a child's mind, 461.

Natural history, Pestalozzi on teaching, 82.
Hintze on teaching, 240.

Natural philosophy, Diesterweg on teaching, 242.

Natural sciences, course of, University of

Turin, 54.

apparatus for, same place, 59.

Luther on studying, 445.

Natural theology, use of studying, 335.

Nature, how to use in educating, 264.

observation of, 330.

New England, common schools of, in 1800, 276.

state of schools in, in 1824, 14.

poem on district school in, 189.
Newspapers, Sardinian, 487.

New York State Idiot Asylum, 417.
building for, 417.

government of, 417.

success of, 418.

Nicasius, 165.

Niederer, appearance of, 88.

quarrel with Schmid and Pestalozzi, 103.
character of, 106.

Normal school at Lexington, Mass, 289.
Normal schools in Sardinia, 503.
Nuremburg, real schools in, 257.

Observation, Pestalozzi on, 75.

importance of student's own, 339.
Opinions, independent, 464.
Oral teaching, value of, 270.

Order, value of practicing, 338.

Orphan education; Pestalozzi at Stanz, 69.

Osgood, Rev. S., letter on Edmund Dwight, 22.

Mathematics, course of, University of Turin, 55. Paintings, sundry prices of, 197.

use of study of, 332.

May, Rev. S J., article by, 275.

Medical schools, Sardinia, 49, 55, 58, 483.

Medicine, course of, University of Turin,

55, 58.

Memory and conception, 324.

Memory, office of, 201.

right use of, 315.

training of, 323.

Men, knowledge of, 466.

Mental philosophy yet imperfect, 342.

Methods, catechisms on, 233, 505.

Mildmay, Walter, noticed, 164.

Military education, Sardinia, 480.

Model schools, Irish national, purpose of, 371.

Model School, Lexington, Mass., 294.

Modern languages, school of, 252.
Monitors, Irish national, salaries of, 379.

Montaigne, on education, 461.

his training in Latin, 473.

on moral culture, 477.

study of history, 465.
modes of instruction, 461.
study of Latin, 473.
knowledge of men, 466.
the mother tongue, 473.
pedantry, 475.

Parental authority, how to be yielded, 389.
Parental educational duties, Luther on, 442.
Paris, city schools in, 257.

49, Parsons, Hon. Theop'lus, letter on E. Dwight, 19.
Pedantry, Montaigne on, 475.
Peirce, Cyrus, memoir of, 275.

address by, extracts from, 285.
Perception and conception, 323.

Perkins' institution for the blind, 133.
Pestalozzi, portrait of, 65.

life and educational system of, 65.
writings of, sundry, 65, 72, 86, 115, 117.
on human development, 66.

at Stanz, 69, 350.

at Burgdorf, 71, 119.

and Fellenberg, 87

at Yverdun, 87.

chief followers of, 354.

Fichte on, 150.