LIEUT. HOPKINS'S, R.N. NEW THEORY OF TIDES.

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CR. Hopkins has removed some of the difficulties under which philosophers have long laboured to account for anomalies which have baffled their ingenuity; and he has received the usual reward of the cold shoulder. His view is a simple and very ingenious one, viz-that the Tides are the result of two forces-the attraction of the sun and moon which draws the waters out of equilibrium, and the centrifugal force produced by the rotary motion of the earth which is constantly operating to counteract the disturbance and restore equilibrium.

Our philosophers, instead of attempting to prove his theory wrong, have simply picked at some of his details; and evidently misunderstanding some passages which, perhaps, might be rather obscure to them by being stated in popular, instead of technical, terms, have attempted to turn it into ridicule. But we will let the gallant gentleman speak for himself in an appendix which he has lately added to his work: strongly recommending his views to the serious attention of those who, dissatisfied with the obviously absurd mode of accounting for tides, which sufficed for less inquiring ages, are seeking for sounder reasons for this great fact of nature.

"Objections having (through an evident misunderstanding) been made to the assertion that the protuberance travels, or is thrown eastward by the earth's rotations, (p. 24,) and the question put, "How in the world is the rotary motion of the earth, which is uniform for every meridian alike, to cause a change of form to pass backward at the same rate?" [700 miles per hour,] I will endeavour to state my views more bricily and explicitly.

"1. Rotary motion is progressive motion. a It is matter advancing through space. The tire of a rotating wheel moves through space, and its effects are projectile (vide illustration, p. 23.)

"2. All projected or advancing masses necessarily move in direct lines, unless diverted into the curve by the presence of other matter, or some restraining or confining force.

"3. The equatorial circle of fluid, or homogeneous masses, in consequence of the above law, enlarges or contracts according to the velocity of rotation, making the body more or less spheroidal. These phenomena are owing to the drops, or particles, of which the mass is composed being either drawn or projected, from A. to a—

A

"The earth for the most part is surrounded by water, and having rotary motion, the equatorial circle would expand or contract, in a greater or less degree, (according to the above law,) in proportion to the velocity of rotation-flattening at the poles, but preserving a perfect equilibrium.

"Now apply this dogma. Truly the velocity of rotation is invariable, but the aqueous circle is subject to perpetual disturbance, since the necessary effect of the sun's or moon's gravity upon a body of water (fluid matter) is to raise a protuberance, and thus continually to disturbe the equilibrium of the aqueous circle, while orbital centrifugal force raises a similar protuberance on the opposite side.

"The effect of rotary motion upon fluid matter is, to restore equilibrium when disturbed, and so to counteract disturbance.

"The process of restoration, however, is not to throw the form of the protuberance castward, (or backward,') but to lengthen out the profile of its features, by an equatorial expansion of that portion of the ocean circle not already raised by gravity, and by a process similar to that already noticed, when there is an increase of rotary velocity: and so the wave advances in every respect according to the laws which govern other common waves. Hence the forces are antagonistic. Rotary force is the ruling force which determines the amount of expansion of the equatorial circle, and keeps it in perfect equilibrium, whilst the sun's and moon's gravity are perpetually disturbing its sphericity.

"If the aqueous circle were not broken by lands, it is possible that the two forces would so far counteract each other as to keep the surface near to equilibrium, the continual disturbances caused by the attracting bodies being counteracted by the constantly exerted rotatory force. In the present condition of the surface of the earth-the aqueous circle being broken by continents-the case is different. The attractive force is constantly acting, but has not, when the land surface is presented, any thing which it can affect. Therefore, the protuberance only reaches its maximum at or near the centres of the two oceans.

"Hence the rotatory motion of the earth can only partially restore the equilibrium of the aqueous circle, which is being continually disturbed, by acting in the direction of its own line of force, i. e. in the direction of its own rotations. And thus the form, or profile of the protuberance is thrown up, thrust, carried, or driven eastward ('backward,' if you please, from meridian to meridian,) by the earth's eastward motion, in the conservative effort (if I may use such a figure) to restore the equilibrium so disturbed.*

"Were it not for the intervention of the land, that protuberance, or the remains of it, would probably, but for fresh disturbances, be carried round the whole circle of the earth, until it reached equilibrium at or near the point of disturbance: That intervention forming an obstruction, it rolls upon the shores as a tidal wave, runs up coasts and rivers, fills the channels, and breaks into currents where fresh obstructions interfere; and only obtains an approximation to equilibrium as the form, or profile of the superabundant waters, or the remains thereof, roll back upon the eastern shores of the opposite continent forming the tide, or high water, there.

REMOVAL OF DIFFICULTIES IN TEACHING.-A good teacher will constantly endeavour to lead his pupils on, and remove all unnecessary obstacles ;-he will not create difficulties for the mere sake of trying the strength of his pupils, nor task their endurance for the purpose of inculcating patience and humility. The little, pedantic mind, delights itself in making difficulties of trifles. The superior mind invests every subject with its own comprehensiveness and logical simplicity.-Miss Crampton's Practical Notes.

SELF-INSTRUCTION.-The grand principle of education is, making a child its own instructor. The most common mistake, I think, is, to suppose that it is an object to store the minds of children with a great number of facts, whereas it is far more important to inure them to application, which from the force of habit, will become easy and even agreeable, and which always brings with it its own reward. Writing, orthography, grammar, and composition may all be learned at the same time; and I believe that by such lessons the mind gains arrangement of ideas, as well as words.-Education for the People, by Mrs. Hippersley Tuckfield.

The protuberance has really a velocity even greater than 700 miles per hour, not in form or motion differing from other waves, but only in velocity. Since the phenomena now under review is sustained by a central-internal force, which affects simultaneously the whole equatorial circle, the disturbance being local, the undulating result must be progressive--unlike the dogma of wave-motion advanced by Dr. Whewell, (p. 19,) where the wave has not only to travel 700, but literally 5000 miles per hour, without any continuous force whatever.

TABLE OF QUARTER SQUARES.

USEFUL set of tables, containing quarter squares of integer numbers to 100,000, has been published by Messrs. Layton, 150, Fleet Street, compiled by Mr. S. L. Laundy. These tables, as is observed in the preface, will be extremely useful to the banker in computing interest, to the architect and civil engineer in estimating superficial and cubical quantities, to surveyors in the admeasurement of land, to the merchant and tradesman in carrying out quantities and prices in invoices, to the astronomer in his scientific researches, to the actuary in his investigations, and we may add, this being our special reason for commending the work to the schoolmaster in setting questions to his pupils. Every one engaged in any of the above occupations will be able to abridge materially the labour incident to his calculations, and to check computations made by the ordinary process. Indeed for most purposes we think it will be found far easier to work with than a table of logarithms.

The principle of these tables is contained in the following formula, which any one having the slightest knowledge of algebra will comprehend without difficulty:

(a x b) 2

(a-b) 2

In other words, if we want to multiply any two numbers together, subtract a quarter of the square of their difference from a quarter of the square of their sum, and you have the answer. These tables, by furnishing the quarter squares, enable us to perform the operation readily, and thus the labour of multiplying is reduced to a simple addition and subtraction sum. The work is very properly printed in the old form of numeral, at the price of £1. 18. This price is, we fear, too high for the pockets of most people, but the expense of the printing must have been enormous, and fully justifies the cost.

While on this subject, as cognate to it, we should like to ask what has become of Babbage's Calculating Machine? Here is a business for which it is exactly fitted, and in which its assistance would have been invaluable. The value of such tables of course depends upon their accuracy, and Babbage's machine would have made the requisite calculations with unerring truth, and also have stamped the plates for printing from. In fact the machine alone, far transcending all direct efforts of the human mind, would have produced such tables as Mr. Laundy's literally immaculate : and at a price too that would have removed the only impediment to their universal use. Surely the quarrel between Mr. Babbage and the Government, after a lapse of twenty years, might now be settled. Is there no peacemaking friend of science in this scientific age, who will step forward to rescue this magnificent invention from the dust and neglect of King's College, where in some dark vault we believe the half-finished machine lies unnoticed and almost forgotten? Let us hope that some man of science may be induced to devote himself to this good work, the neglect of which for so long a period is, in our opinion, a disgrace to the nation.

T

DECIMAL COINAGE.

HE question of a decimal coinage has not made the advance it deserves. The House of Commons has done its duty by completely beating the Government when the subject was last discussed, but the Commission that was appointed in consequence appears to have fallen asleep, and from inquiries we have made, we believe there is no chance of any report being made to Parliament at present. In spite of the vote of the House, the Ministry seem determined to shelve the subject, and they will succeed, unless the public keep up a succession of admonitory fillips. Besides the other numerous reasons in favour of the change, we consider it more especially an educational question. There is not a teacher who will not find his labour materially diminished by the introduction of the decimal system, nor a boy who will not throw up his cap for joy at getting rid of the mysteries of the pence and farthing tables and the compound rules. We can hardly think that any cause for delay can be found in the doubt as to what decimal system should be established. Nine-tenths of all who have given a thought to the subject concur in the opinion that the pound and mil system is the only one possible, and if the Government would only announce that they have decided on that system, though the immediate carrying it out be postponed, no small step in advance would be made.

In the meantime, the department of Government connected with education has done what it could to advance the question. In the two last examinations for certificates and registration, questions on decimal coinage have been introduced, and we warn all teachers who, either themselves or through their pupils are looking to pass any government examination that their chances of success will be much increased by an acquaintance with the subject of decimal coinage. In the examinations of Christmas, 1855, several failures occurred owing to ignorance on this point,-ignorance, which now we will venture to stigmatise as unpardonable.

Messrs. Longman have published a work by Mr. Tate at the price of 9d. which will enable any person to make himself thoroughly conversant with the subject. The Companion to the British Almanack for 1857 contains an article by Professor De Morgan well worth perusal. It is written in his usual clever, dogmatic, flippant, knockdown style, qualities which rather detract from its persuasiveness; but no writer better understands the question, and it, as well as articles on the same topic in former Companions, should be read by all who wish to comprehend the matter in all its bearings.

VALUE OF LABOUR.-We must beware of pouring in upon the young mind knowledge which has not been earned by labour. "In the sweat of thy face thou shalt eat bread." I am pretty sure that the mental bread should be earned in the same way. Experience almost daily convinces me of this truth, and leads me to suspect that we are on the brink of error when we use oral instruction without much judgment and caution. It ought to be the occasional reward of labour but it is no substitute for labour. -Education for the People, by Mrs. Hippersley Tuckfield.

SCHEME FOR A MODIFICATION IN WRITING LESSONS.

GOOD handwriting is a desirable acquirement, and we are quite justified, together with attention to the outward appearance of the daily compositions, to set apart particular hours for improving in that art. However a due proportion between time and trouble spent, and the object to be obtained, ought to be observed in all things, and so much the more if the neglect of this principle only tends to frustrate our exertions. There is no doubt that this remark fully applies to the manner in which caligraphy is taught in most schools, a great deal of time is spent for that purpose, masters and pupils often silently agree that the frequent and long copies are tedious work, but nevertheless the routine is upheld either by mere custom or for some specious reasons. It is therefore not to be wondered at, if copy books do not show any remarkable improvement from the first to the last page. We defy any body, especially young persons, to fix day after day, their whole attention for half an hour or longer, to the incessantly recurring few letters of the alphabet. The letters are too well known and too simple to admit of sufficient variation for attracting continued attention, and without this, no real advantage can be gained for our purpose. The following scheme for a modification of the prevalent system in writing lessons is based on these observations and has chiefly two objects in view: time to be gained, and a more suitable method for fixing the attention of our pupils to their work. If we succeed in the latter point the object of our lesson must be obtained, for it is impossible that a careful comparison of a copy with good models should not be attended with constant improvement in our own writing.

These modifications are the following:-Let the times appointed for caligraphy be short enough, say ten minutes or a quarter of an hour, to take away all tediousness; let them likewise not be too frequent; to have them on alternate days will perhaps be sufficient. Secondly, remember that attention is the chief requisite for success; make it therefore a rule to point out to the pupil, and have it found out by himself and distinctly expressed where there is a difference between the model and his copy; in classes it may even be arranged that from time to time all together take part in this kind of criticism. Thirdly, in accordance with the shortness of time, have the same copy repeated not more than three or four times in one lesson. Finally, induce the pupil to judge for himself as well as to enable others to judge of his progress, by writing the same copy on the same page at long intervals. For this purpose divide each page into three or four divisions, consisting of very few lines each. The top division of each page is filled up first, but the remainder left blank; then, that is to say in about two or three months, we return to the first page and fill another division, and so on. This arrangement has many advantages, particularly as has been said, that of being a stimulus to exertion, and where prizes are given, it offers the most unmistakeable test of respective merit. The whole plan may at the beginning of the half-year be laid before the pupils and often. referred to. It has, to a limited extent, been tried and found successful, and being calculated to avoid undeniable inconveniences, and grounded upon the nature of the object as well as on sound pedagogical principles, it may perhaps deserve the further attention of those who are concerned in school business or who are anxious for improvement.