is done, we may justly refuse our assent to this doctrine, for it is a sufficient ground for dissent to show the invalidity of the reasoning by which it is supported. Physical writers in their pretended proofs of infinite divisibility have advanced arguments which bear upon extension only, and not upon matter; I therefore beg the advocates of infinite divisibility to prove it by arguments in which the attraction of aggregation is considered, or else to discard it from their philosophical creed, and be in future guided more by the principles of common sense than the dicta of philosophers.

On the Co-existence of Cause and Effect.

"Now, to continue an effect, the producing cause must continue its energy. The stream from the fountain

will not continue to flow, unless the fountain itself supply the requisite quantum of water. All effects depend on their causes: so that when the cause ceases to act, the effect ceases to exist." Dr. A. Clarke.

The opinion that cause and effect are co-existent is so evidently opposed to fact, that I am surprised to find it advanced by so talented a writer as Dr. Clarke. I write: the letters and words I form will remain in existence after I have ceased to write. An injury done will excite anger: the anger continues after the commission of the injury. I throw a ball from my hand: the motion of the ball (the effect) continues after the motion of my hand (the cause) has ceased.

In short, this opinion is completely incompatible with succession of event, unless we suppose that events are independent of each other. But if we admit this, we deny causation, so that this opinion destroys its own foundation.

If the subject of causation is not too metaphysical for your readers, I may perhaps in some future communication show that every effect is the result of two causes.

On the absolute Zero.

(See page 173*)

I was wrong in charging MM. Dulong and Petit with placing the absolute zero at -448° Fahr.

I

Your printer omitted the minus sign before 448° F.

FLOORING-LEVER.

Sir,-In vol. x. p. 145, you have given a plan of a flooring-cramp; I now send you a plan of a lever for taking up flooring, and which will be found to answer well for many other purposes. A is the lever; B the bolt that rests on the joists, that give the power to the lever; C the lifter, which moves on a bolt at 2, by which means the lifter is always close to the board, and not pressing more at one part than another, but in all parts alike, so that it is not possible the board can be split or broken. The nails must either draw through the boards or out of the joists. There are three places for the bolt to pass through the lifter C, as 1, 2, 4; so as to make the lever end always be in the centre of the board, and F always to be fair with G. I have taken away part of the board, for the purpose of showing the apparatus more clearly. I remain yours, &c. M. SAUL.

Sulyard-street, Lancaster,
August 18, 1825.

VIBRATION OF PENDULUMS.

Mr. Editor,-On looking over the "Library of Useful Knowledge" under the head Mechanics, I do not find the subject of pendulums yet treated of; probably from a supposition that the exposition of the principles on

which their action is founded, would require the aid of a greater portion of mathematical knowledge than is supposed to be possessed by the generality of readers, for whom that work is intended.

As your excellent publication is destined for students of a higher class, permit me, through the medium of your columns, to ask a question on a subject which though treated of by many of the writers on fluxions, the solution given by them is in my opinion not quite so intelligible as could be wished.

This question-which forms the 106th Problem in Dealtry's Fluxions, and the 3354th Institute of Martinis this, What is the ratio between the time of vibration of a pendulum through an infinitely small arc of a circle, and through the entire semicircle?

In order to simplify the matter, let us take the case of a single pendulum, which is supposed to be an inflexible right line devoid of gravity, bearing at its lowest extremity a weight of no sensible magnitude, which, in order to vibrate seconds in the latitude of London, ought to be of the length 39-13929 inches.

If the time of its vibration through an infinitely small arc of a circle be denoted by unity, then, according to my solution, 1.16666, &c. ad infin. (er one second and a sixth), must be the time of vibration through the entire semicircle.

266

After devoting so much space to the merits of the New Almanacs, we should be guilty of a disrespect, which we are far from entertaining, for our older favorites in this department, were we to take our leave of the subject, without bestowing upon them a few words of remembrance.

WHITE'S is still the best ephemeris published: not even excepting that notable government job, "The Nautical Almanac." It contains several most desirable and essential things, which the government work (much to its disgrace, and not a little to the injury of our maritime interests,) does not contain. We allude particularly to White's tide tables of unrivalled accuracy, to its ephemerides of the new planets, Vesta, Juno, Pallas, and Ceres-the aspects of which are given for every sixth day in the year; and to a table of the eclipses of Jupiter's first satellite, by means of which, and the help of a telescope, navigators may ascertain the longitude with singular ease, at all times when Jupiter is 8° above the horizon. In order to enhance the value of this ephemeris, and make it more worth preserving in sets, the learned editor has recently adopted the judicious plan of giving every year some two or three pages of quite new tables and formulæ. One of the novelties for the next year, we consider to be particularly curious and valuable. It is a table under the head of " Degrees and Pendulums," showing the length of a degree of longitude and a degree of latitude at every five degrees of latitude, together with the lengths of a seconds' pendulum, at those latitudes respectively; and also the increase in the number of vibrations per diem of an invariable pendulum, that beats seconds at the equator on being carried towards either pole. The measures at the equator are here considered as unity; for example, the length of a degree of longitude is supposed to be 100,000 at the equator; at 5.99622; at 50°-64404; and so on; but we think the table would have been more readily comprehended, and of course more practically useful, if, instead

of showing the comparative increases and decreases in relation to an ideal standard, it had taken for its basis the actual numbers assignable to the equator. Thus supposing a degree of longitude at the equator to be 69 15 miles, and that' this had been adopted as the standard of comparison, it would have been at once seen by inspection of the table, what is the actual comparative length of a degree at 20o, 50°, 60°, or any other latitude. The computation to be sure is easy, but so also it would have been to make any computation unnecessary.

THELADY'S ANDGENTLEMAN'S DIARIES will be found, as usual, an odd compound of excellence and (must we say it?) frivolity. Dear they certainly are to philosophy, for the services they have rendered, "in creating and fostering a love of science in some of the highest mathematicians and astronomers of this country;" but dear also to riddle-me-ree-ism, for preserving, amid the devastations of modern intelligence, a sacred corner, where pedants in petticoats and wiseacres in wigs may puzzle each other to admiration, about the veriest nothings-where all sorts of silly

"Maggots, half-formed in rhyme exactly meet, And learn to crawl upon poetic feet.' The worthy Company of Stationers" have dropped a hint in reference to these almanacs about the propriety of "supplying innocent employment for the ingenious.' "Innocent employment!" and for "the ingenious" too!! We must be permitted to doubt, in the first place, whether any appropriation of time, to what is not useful, can be innocent; and, secondly, whether any truly "ingenious" person would think of resorting, in the way of useful (the only allowable sort of) recreation, to the solution of such problems as:

"My first is a B,

My second not I,
Third plain as B C,

My whole on the banks of-
The Wye."

We have not copied this rebus from either the Lady's Diary or the Gentleman's, but we give it at the request of a young lady at our elbow, as being quite as useful, if not as soul-inspired, as any thing of the kind to be found in either publication. Could not Messrs. the Company of Stationers venture to bring this reign of verbiage to an end? Are they aware that it rests with them entirely? One other publication there is, we believe, which delighteth in what is "enigmatical;" but let every thing of the sort be once excluded from the "Lady's and Gentleman's Diaries," and

it would henceforth cease to be respectable.

"FRANCIS MOORE, PHYSICIAN !" most popular and oldest of living authors!Whence thy unrivalled popularity ?Whence thy antediluvian length of years? There are those who say that "Francis Moore, physician," is and ever has been a great quack; that he has lived and flourished by cozening and cajoling the simple people of this country, generation after generation; that even bis living so long is all a trick; and that he should have been dead and buried years ago, under a mountain of his own lying prophecies. Nay, so bitter is their hate, that they have actually banded together and subscribed purses to compel the poor man, nolens volens, to give up the ghost. Yet, strange to say, in spite of all that has been said and done, to open the eyes of the people and stop the mouth of their "deluder," the redoubtable "Francis" still liveth, and still exhibits every symptom of a green old age. His patients (dupes they are called) are said to be as numerous a multitude as ever-not just a round million, but somewhere thereabouts. Can it be possible, our physician" is the vile quack he is called, and yet maintain so fast a hold on the affections of the people? We do not think it possible. It is not in the nature of things that sheer imposture should so triumph and endure. The quackery of Francis Moore must have long ere this succumbed to some other and newer quackery; for the love of folly ever hunteth after novelty. We are well satisfied it can only have been by the force of much rare and sterling worth, that his "Loyal Almanac has seen such a length of days. In what that worth consists, and by what demerits it is clouded, we took some pains to show last year; and succeeded, we trust, in demonstrating to the satisfaction of many, that to join in the outcry which has been lately raised against him, would be to lend our aid to make a few trivial faults, weigh heavier in the balance, than a world of useful service. His predictions, relating to the weather and other "mundane affairs," his annual "Hieroglyphics," and his " Astrological Judgments,' are all doubtless very foolish things, though perhaps more to be laughed at than cared for. Vain as all pretension to a foreknowledge of events is, there is a feature in the prophesyings of Francis Moore which we consider to be of very extenuating description. We allude to the ardent desire which they uniformly breathe for the spread of knowledge, liberty, and hap

267

piness; a desire which may have done good by helping to give a tone to public feeling, and cannot possibly have done harm. In one of the latest tirades which we have seen against this almanac, it is asked, "Would a copy of 'Moore' be bought if people did not yet believe in it?" We apprehend that if "Moore" was only to be bought by those who literally believe in him, there would be soon an end of "Moore," and all dispute about him; but, supposing he had as many implicit believers as his revilers pretend, it must surely be a source of great consolation to know that they are rarely, if ever, asked to believe (of political matters) what it would not be much to their benefit, and to the benefit of all mankind to see realized. Be the effect of "Moore's" prophecies, however, what it may-suppose there were not a word of prophecy in his book -we still maintain that there is merit enough in the other matters with which he annually supplies us-matter choice and useful beyond all dispute-to make him be universally sought after on account of that other matter alone. Had there been no "Moore" this year (which would have been according to the wishes of some people), we should like to know where we could have found such full, correct, and popular accounts, as are furnished by "Moore," of the various celestial phenomena for the year 1930 ? Not certainly in "The British," which was put forward as the grand substitute for "Moore," but is miserably deficient in astronomical information; nor even in the much superior "Englishman.""Moore" gives two articles this yearone under the head of "An Account of the Eclipses of the Sun and Moon," and the other entitled, " An Account of the most remarkable Lunar Occultations, Appulses, and other Celestial Configurations," which are alone worth the whole price of the Almanac; and leave at an immeasurable distance every thing of an astronomical description which the members of the Society for the Diffusion of Useful Knowledge have yes been able to supply.

In the first of the articles we have just alluded to, there is an interesting fact mentioned with respect to a total eclipse of the moon on the 2nd of September next, which we do not see noticed in any of the other almanacs; or, at least, only obscurely hinted at. It is said that, "at Greenwich, the moon will, from the effects of her parallax, appear a few minutes south of the fixed star A during the eclipse; and to lower latitudes. this conjunction will prove an occul

268

tation, at the time when the moon is immersed in the shadow of the earth. The nearest approach of the moon's northern limb to the star, as seen from the Royal Observatory, will be 9' 54"; this happens at 9h. 24. 24. or 23. 27. before she is totally obscured."

One thing there is in "Moore" which we are sincerely sorry to see still associated with so much excellence. We allude to the column appropriated to the "Dominion of the Moon in Man's body." It is not merely foolish-it is an utter abomination. The Stationers' Company say that the astrological predictions of "Moore" "deceive nobody," and serve only to amuse. can they say the same thing of his "Moon's Dominion?" If it is not intended that people should have faith in it, for what is it worth?

But

The observations which we have made with respect to Moore will apply, more or less, to his fellow-soothsayer, PARTRIDGE, in whom the same faults and the same compensating excellences are ob. servable.

MOORE'S IMPROVED, might, we think, be more improved; but, to all country persons, who have a horror of astrology, and no particular regard for astronomical matters-who seek only to know how they may raise the best crops, rear the fattest cattle, and find the likeliest markets-this almanac will prove a useful companion.

GOLDSMITH'S, though but a waistcoatpocket almanac, possesses merits which have been strangely (conveniently perhaps) overlooked in the denunciations of the Useful Knowledge Society. It has been published for about half a century, and contains a vast variety of matter of general interest, wholly free from any astrological intermixture whatever. It was almost as good an almanac as The British," long before "The British" appeared, and is now but little inferior to it in point of useful information.

The COUNTY SHEET ALMANACS, of which eight are published annually by the Stationers' Company, are deserving of favourable notice, for the great quantity of local information which they respectively embrace; but of notice also, of a different description, for exhibiting the same sort of abomination which we have just reprobated in "Moore." The "Dominion of the Moon" in "knees, arms, legs, ancles, feet, toes," &c.! What is it but an insult to the intelligence of the age to persist in such absurd conceits?

After all, we fear it must be confessed that, though there is undoubtedly

a marked spirit of improvement pervading all the Company's almanacs, it is a spirit of rather of a timorous cast; well-disposed towards such improvements as come in the shape of additions, (to giving, for example, a "Moore Improved," rather an "Improved Moore," but shrinking from every thing in the nature of absolute alteration or change. The Company seem to be too much under the influence of a notion that it is their duty to provide almanacs for all sorts of palates, and that there is nothing so weak or foolish which will not please some class or other. We do not dispute that

we

By some object every brain is stirred: The dull may waken to a humming-bird; The most recluse, discreetly opened, find Congenial matter in the cockle kind." But, if we recollect rightly, this was an observation addressed by the Goddess of Dulness to her children, among whom are far from ranking so active and intelligent a body as the members of "The Stationers' Company." If the Company would but authorise and direct the pruning-hook to be used a little more unsparingly, they might at once place their almanacs as much above competition as reproach. In every essential particular they are unrivalled; it is certain grotesque excrescences only which want to be lopped off. Nearly all that science can do for them has been already done; nor of all the faults which we have pointed out, is there more than one or two, which is not obviously to be referred to the operation of circumstances and usages, not subjected to the control of the highly-gifted and eminent individual, to whom their scientific superintendence has been intrusted.

NOTES OF DR. LARDNER'S LECTURES ON MECHANICS, AT THE LONDON

UNIVERSITY.

(Continued from p. 223.)

Attraction of gravitation is a particular instance of a general effect: the denomination "attraction" being the name for a class of effects, the leading feature of which is, that if two bodies are placed near each other, they will move towards each other and along a straight line supposed to join them. The strict and philosophical meaning of attraction is not required in mechanics: in this science the fact only is to be observed, viz. that the bodies approach each other. There is a cause which produces this effect,