falls to the ground. The very life and soul of that defence was, in almost his own words, that the disturbing forces produced the motion due to their action before friction had time to act; or, in other words, that the disturbing forces gave a pull so sharply and quickly that they did their work before friction, which the Archdeacon looks on as rather a sluggard, could rouse itself and counteract them, that they were, in short, able to steal a march on friction each time they gave a pull or a push.

Now it is clear that this explanation has no meaning in it, unless the action of the disturbances is intermittent. Archdeacon Pratt admits that he never supposed that this is the case, therefore he must find some new line of argument, if he wishes to continue his chivalrous defence of his old friend and, I believe, tutor, who can no longer speak for himself. I may add that all who knew Mr. Hopkins personally, and even those who, like myself, only knew of him through common friends, will appreciate and admire Archdeacon Pratt's championship, even if they are unable to agree with him.

In his last letter (NATURE, August 31) Archdeacon Pratt has given a new and independent method, which leads him to the conclusion that the earth is solid from surface to centre, or nearly so; so that if we accept his reasoning we must admit that, whatever may be said of Mr. Hopkins's method, his results at last are right. He mainly rests his argument on the consideration that such a limp thing as an earth with a crust not more than 100 miles thick could not stand the strains with which the disturbing actions of the sun and moon are for ever trying it.

How will it be, though, if we can show cause for believing that the crust of the earth is after all somewhat of a limp thing, and yet does stand these strains? All a priori reasoning must give way to fact, if that fact can be established; and though we may be surprised that so thin a crust is able to hold out against the violent treatment it has to undergo, yet, if we can show good reason for believing that the crust is, after all, thin, we must cease to wonder, and try to explain the seeming anomaly.

I shall content myself now with putting forward one of the several grounds on which the thinness of the earth's crust can be, I will not say established, but rendered highly probable; and if my arguments shall prove in the end to have any weight, I have no fear that the seeming contradiction between them and the reasoning of Archdeacon Pratt and Prof. Thomson in the other direction will sooner or later be explained away.

Everyone is familiar with what is known in Geology as Upheaval and Depression, that over and over again during the earth's lifetime portions of the solid crust have been raised, and others lowered relatively to a fixed datum, such as the sea level. Very naturally the idea springs up that the displacement is produced by a thrust acting vertically upwards, or by a removal of some vertical support below. Some cases of small local upheaval may have been brought about in this way, but this is not the machinery by which nature has acted on the large scale.

The fact of upheaval is brought home to us when we find strata originally formed beneath the sea now high and dry far above its level; how the upheaval was brought about we learn by recollecting that these strata were originally horizontal, noting whether they are displaced from that position, and, if so, after what fashion the displacement has taken place. Isolated observations show us strata in some places horizontal, in others inclined at different angles to the horizon; but when we combine into one view a large number of such observations, the result is that we see that the strata have been folded into troughs and arches, that when we find horizontal beds we are on the summit of an arch or the bottom of a trough, where inclined beds appear we are on the slopes. Further, we invariably find that the crumpling up of the strata has been most violent in those parts of the earth's surface which have been raised highest above their original position, that is, on mountain chains. We come, then, to the conclusion that the way in which upheaval has been produced has been by a folding of the strata into troughs and arches. That the crust of the earth, instead of being a rigid unyielding mass, has been from time to time bent into folds, and, so to speak, crumpled up and wrinkled; that it is not unlike, what it has often been compared to, the shrivelled skin of an old dried apple.

Again, the supposition of a thin crust and an internal molten nucleus, gives a very satisfactory explanation of the way in which the crumpling is produced. As the nucleus cools it contracts, and the crust has to accommodate itself to the diminished support within; it cannot shrink, and therefore it gets crumpled, just as in the case of the apple, the inside shrinks more than the skin, and the latter in consequence wrinkles up.

Here, then, is an argument in favour of no very great thickness

and a certain amount of limpness in the earth's crust, and it is not the only one of its kind; on the other side, are Archdeacon Pratt's and Sir W. Thomson's weighty reasons in favour of its rigidity. Far be it from me to attempt "tantas componere lite." I only wish to show that there are two sides, and two very good sides, to the question.

What Mr. Hopkins has done seems to me to amount to this! he has shown that with a solid earth the amount of precession would be almost exactly what it is; but he has not shown the this would not equally be the case with an earth having a thun and a viscous melted interior; that case he has not attempted to handle, the case he did examine being that of a thin crust and a perfectly fluid interior. If it can be conclusively proved thes the thin crust and viscous melted interior are incompatible with known astronomical and mechanical phenomena, we must give them up, but till that has been done we are bound to remembe that, whatever has been said against them, there is something n their favour also. A. H. GREEX Barnsley, Sept. 8

Temperature of the Sun

I HAVE just seen the interesting note of Mr. Ericsson in the number of NATURE for July 13 (p. 204), and I am very glad thit, this question should be thoroughly ventilated.

Mr. Ericsson and others have been startled at the high degree of temperature at which I have arrived, and the appellation of extravagant is not spared. I beg leave, however, to observe that this conclusion does not materially differ from that obtained by Mr. Waterston. I am surprised that my opponents, satisfied with rejecting the result as extravagant, do not examine if the method is correct or not. The only objection that could be made is, that, while from the experiments of Soret, the resultant figure is 5,334,840 C., I doubled it, on account of the absorption which the radiation suffers in the solar atmosphere, whose integral effect is a great deal larger than Mr. Ericsson supposes; and a would not be waste of time to discuss the experiments which prove that the absorptive power of the solar atmosphere is very considerable. Mr. Ericsson passes over this too slightly, saying that this absorption would be only oor of the whole, while I have found it considerably greater.

Mr. Ericsson refers to the explanation which I subjoined about this high temperature, that it is to be regarded as a virtual tem perature, as if these were words which I would not attempt to explain. The explanation was, however, given very clearly in my own book, perhaps too shortly, since it seems not to have been understood. The word virtual was also employed by Mr. Waterston to indicate the degree of temperature which would le produced in a thermometer by the accumulated radian of different transparent strata. And indeed this is not an absart statement and incapable of conveying information, as Mr. Ericsson seems to suppose.

First of all we must admit that a gas exposed to a radiating source does not always attain the same temperature as a solid body. It is obvious, for instance, that the temperature of the free air at the top of a mountain is a great deal lower than the temperature of the thermometer exposed to the sun. This # due to the small absorptive power of the gas. Therefore, at the boundary of the solar atmosphere the temperature of the transparent gas may be a good deal lower than that of a solid tha mometer (if by hypothesis it could preserve there its solidity! It is besides not incorrect to say that the different successive strata may add their own radiation, so that by two, three, of more radiating strata we could obtain a higher temperature than by a single one. At least this has been understood, even by M. Respighi, who, however, is of the same opinion as Mr. Ericsson about the exaggeration of my result. integral effect of all the strata that contribute to this eleva tion would be the indication of the thermometer, which may be higher than the temperature of a single outside stratum subjected

to external radiation.

Toe

Mr. Ericsson says that it is of no consequence whether the sun's photosphere belongs to the class of active or sluggish incandescent radiators. I think, however, this point to be very important. Since we cannot experimentally determine the temperature of the sun except by using its radiating power, it is very interesting to take into account this element as very substantial. Very few indeed, will allow that which Mr. Ericsson takes for granted, that

radiating power of the solar materials may be compared to it of pure lamp-black, as he assumes at the end of the note. Mr. Ericsson spends a great part of the note in proving that the v of the diminution of radiation according to the square of the stance is accurate, which certainly I have never questioned. le difference between his own result and mine may perhaps be e to a difference in the use or construction of the instrument; it as, unhappily, I have no information of this construction, I nnot attempt any discussion of his principles. I can only say at his table cannot be used in all seasons indifferently, since I ave proved that at the same zenith distance, the absorption of ›lar heat is very different in summer and in winter, on account f the different quantity of aqueous vapour which is found the atmosphere. And hence the deductions which he makes bout the difference of radiation in aphelion and perihelion may e merely accidentally accurate, and not very conclusive.

On the whole, however, I see that the researches of M. Erics. on approach my results a great deal more nearly than those of M. Zollner, who fixes the temperature of the lower stratum of the olar atmosphere in contact with the photosphere at 68,400° C. only. And this is a number sixty times less than that of Mr. Ericsson, while mine is only thirty-seven times greater.

The conclusion which spontaneously flows from such extraordinary differences is, that we are yet far from having any exact information on the subject, and I hope that this question will now be better discussed, and that I may be able to find some improvement to be made in my book. Rome

Neologisms

A. SECCHI

I THINK the most suitable word to indicate plane-direction is "position," though the word "pose" would serve, and has, indeed, been used in that sense. The word "position" bears the I same relation to the word "direction" that " Stellung" bears to "Richtung," or "set" to "righting." "Position" is often (but incorrectly) used to indicate place, but we may reason with Colonel Mannering, Abusus non tollit usum-the abuse of any thing doth not abrogate the lawful use thereof. This recognised, the words "position of a plane " can bear no other meaning than that referred to by Mr. Wilson. For the purpose of indicating place, the word "location" would be convenient, but that it suggests to the Latinist a "setting to hire." Our American cousins (very wisely, I think) neglect such trifles.

By the way, is not the word "neologism" very ugly and unnecessary? We must have new words, but need we call them neologisms?

As to the invention of new words, I take it that every author who has anything new to say must sometimes want a new word, in which case he has as fair a right to invent and use such a word as to describe new ideas. If this is not the case, I must plead guilty to a grievous series of offences. In fact, I have received during the past year about a ream of letters rebuking a practice which I consider fully "in my right." You should not speak, writes one, of "a limitless expanse," but of an "unlimited expanse" you must not say "forceful analogy," urges another, but "forcible analogy; "not "star-cloudlet" says a third, but "nebula ;" not " square to" but either “perpendicular” or “at right angles to" says a fourth, and so on. So must you write if you wish to be understood, say these critics; or rather they say, It is indispensable for the adequate conveyance of your meaning that you should thus conform to established usage.'

I am not jesting; these words have not only been employed by one of my anonymous critics, but have been seriously suggested for my own use. In some cases modes of expression are vilified for instance, it seems you must not say of Venus that she is "nearer to the sun than the earth is," for this is inelegant; you must say that she is "nearer to the sun than the earth;" and, in like manner, for the sake of cuphony, one should say of Mercury that he is "nearer to the sun than the earth," rather than that he is "nearer to the sun than to the earth." My attention has been directed to each of the expressions here cor. rected as characterised by a vice of style. So that, since Venus in inferior conjunction is nearer to the earth than to the sun, but nearer to the sun than the earth is, she is (when so placed) at once nearer to the earth than the sun, and nearer to the sun than the earth, a statement which appears to me less instruct ve than might be desired. But possibly I am prejudiced.

It is well to keep (where one may) within dictionary precincts, nor need the writer neglect the rounding of his periods;

THERE remains but one point to notice in reference to the hybrid (or monster) prolificness. Dr. Latham pretty well ex. hausts its etymological bearings. There remains its phonological bearings to consider. No new word has a chance of being naturalised unless it can be pronounced as well as written; and the greater the difficulty of pronunciation the less is that chance. Now, in order to render Mr. Wallace's word acceptable, it must be pronounced as if it were written, prollyfickness, in which phonetic form we almost lose the parent adjective. The reason of this is, that the syllables ic and ness will not inosculate. To use Mr. Sylvester's phraseology, there is not a perfect anastomosis, and this imperfection is remediable only by change of accent, viz., passing on the accent from lif to ic; otherwise we must sacrifice anastomosis, and write the word as a compound, prolific-ness, ie., with a hyphen to indicate the necessity of a pause in that place. Surely on all accounts prolificence is by far the better word. C. M. INGLEBY

Yoxford, September 7

The Aurora

I HAVE just read Mr. Wilson's interesting paper entitled "Some Speculations on the Auroras," published in your periodical for September 7. In the Philosophical Magazine for July 1870 I made a suggestion as to the origin of auroras similar to that just published by Mr. Wilson.

The periodicity in auroral displays noticed by Mr. Wilson had not attracted my attention. It would doubtless, if it were well established, be confirmatory of the views independently put forward by Mr. Wilson and myself. A. S. DAVIS

Meteor

ON Saturday, September 2, at 8. 14 or 8.15 P. M., I saw a fine meteor under very favourable circumstances. I was standing with several friends at the door of Mr. W. F. Moore's house at Croakbourne, in the Isle of Man, and we were looking up at the western sky at the moment when the meteor came. It started between, I think, and Herculis (it was too cloudy to see those stars), descended nearly vertically, passing through Corona Borealis, and vanished a little below & Bootis, at about 15° above the horizon. It moved slowly but continuously, taking from two to three seconds in travelling over 45°. It broke into three, which followed one another, connected and followed by a luminous train which was visible for about one second. The

first part of the three was brilliant white, and was estimated by Mr. A. W. Moore and myself independently as equal in size to 4th of the moon's surface. It was very brilliant, being mistaken by the Rev. John Howard, who was looking in another direction, for a flash of lightning. The two latter globes were blue. Rugby, September 6 J. M. WILSON

The Earthquake at Worthing

IN your issue of the 31st ult. is an extract from a letter which appeared in the Times a day or two before, giving a very circumstantial and a somewhat sensational account of an earthquake which took place at Worthing, at 3.45 on Monday morning, the 28th of August. Is it not possible that there may be some connection between the said earthquake and the circumstances narrated as under in the Brighton Gazette of the Thursday following? If so, might it not be on the whole more prudent of correspondents of the Times or other papers, before they rush frantically into print on such subjects, just to put a question or two to some imperturbable old fisherman (if they be shaken out of their wits again at a watering place) instead of appealing to hysterical ladies and excitable old gentlemen for their notes of an event of great scientific interest?

"What's that? An earthquake! There it is again! Now again! And now again!' These were the exclamations which paterfamilias and materfamilias and lots of juveniles, roused from their slumbers, uttered on Monday at 3.40 A. M., just before the break of day. It was a strange noise; lights flashed from win

dows, bells were rung violently, windows were thrown up, and cries of Thieves' and 'Police' were shouted. But there was no earthquake, there were no thieves, although there were the police, by whom the sounds were dis inctly heard. It was some time before all was again quiet, and not even then in many a household until proces-ions in curious urb, armed with sticks, pokers, shovels, and fire-irons, in place of fire-arms, had paraded from kitchen to garret in search of the supposed nocturnal marauders. And now the cause of all this has been discovered. It was the coastguard squadron, a few miles out at sea, having what is termed their night quarter exercise-a turn-out drill in the middle of the night, so as to fit the men for action in an emergency." E. A. PANKHURST

Church Hill, Brighton, September 11

A Fossiliferous Boulder

DURING a visit I made in July last to a respected friend at Dinnington, Northumberland, I observed a travelled bulder in the corner of his field, and, on closer inspection, found that it cont ined a number of ammonites, encrinites, and the detached portions of the stems of the stone lily, usually found in the Lias in the vicinity of Whitby. The compo-ition of the boulder, which was about two feet in length, and of proportionate breadth and depth, was basaltic or rap, and had vidently taken up the fossils when in a state of fusion; some of the ammonites being compressed or disturbed. Upon inquiry, it appeared that my frien had sunk for a well, and came at the depth of about twelve feet upon the native freestone rock, upon which this boul ier was found. Of course it must have been transported to its place of deposit by ice during the glacial period of our world's history, and then covered over by the subsequent boulder-clay; but from whence was it transported? From Yorkshire or the Hebrides? I also visited in the immediate vicinity what was formerly the site of an ancient lake of about 1,200 acres, Prestwick Car. This sheet of water was drained a few years ago into the Pont rivulet, and the bed of the old lake is now, through the enterprise and skilful industry of the farmer, covered by luxuriant crops of oa s with magnificent heads, approaching six feet in height, and immen-e thickne-s of s'em. The laud, as might be expected, is a deep bog earth; the surface, however, is remarkably light, ap parently a leaf soil, and easily disturbed, or blown away by the winds. The remarkable point here was, that after the drainage had been completed, the earth solidified and put under colture, the roos and a portion of the stems of trees broken off near the roots, appeared as if rising from the earth, the prior existence of which was unseen and unknown, indicating the remains of a primæval forest: no branches appeared. The wood is that of the alder. Was not the lake ori, inally formed by the destruction of this ancient forest by the agency of wind? Barbourne, Worcester, Sept. 9 J. BROUGH Pow

A Vital Question

PRAY do not mind if I am alone in my venturesomeness, but in the name of Science, not that which is falsely so called, but that which depends upon evidence, let me protest against the doctrine contained in the concluding portion of Sir W. Thomson's address. Scholastic theology has for me nothing worse than the declaration, made on the strength of a mere dogma, that our dear mother earth is no mother at all, bu absolu ely in apable of filling any function in the production of her own children. The dogma that life can only proceed from life, a, pears, when analys d, like too many another dogma, but a meaningless jingle of words.

Here are thre counter propositions, which I advance in all confidence of their soundness:

1. We know nothing whatever of the nature of life to justify us in asserting its absolute difference in kind from many other phenomena, as of magnetism, chemistry, or Nature in general.

2 If, as astronomers hold, all the bodies compo ing the olar system are derived from the sun, they must contain identical el ments. That their element, are actually identical is, more over, indicated by the spec roscope. So that if those elements be incapable of producing lite on this planet, they must be incapable of producing it elsewhere. However much reason there may be to suppose they ha e not provine de n any particular instance as yet, as, e.g., in our satellite, that is no reason against

their doing so in the future. If Sir William's object had been & gain time for existing evolutions, I could have forgiven him, bat there was no hint of this.

3. To speak of life as necessary to the production of life, is to ignore all that Science has ascertained respecting the trans ference and convertibility of force, and to fill back upon the anthro pomorphism of the theologians, only with the difference, in th case, that it is not Jupiter, but "the s one that fell down from Jupiter," whom we are to hail as our father and mother. Moreover, to speak of life as necessary to the production of life, is to assume that we already know the limits of Nature's productive power; and to assert that life is not a natural product at a 1, is to restrict our definition of Nature by some arbitrary limit which exc udes the most important functions of Nature.

Doubtless it would be a very pretty idea to regard the planets as so many orchids in the flower-garden of the Universe, and the meteorites as their fertilising bees; but Sir W. Thomson entertains no such plea-ing sentiment respecting the earth He d grades this unhappy panet far below the meteorne.

Once upon a time when astray with a companion in a far Western wilderness, we were reduced to eating anything that we cou d find. On the question arising whether rattlesnakes were fit to eat, I propounded the dictum that whatever could itself live ought to be able to support lie in another, and our expe rience, so far as it went, confirmed the saying. I venture to vary it for Sir W. Thomson's benefi, and to suggest that whate ver can support life, as this earth does, can in alt probability produce it. Loving, as I do, bo h the world and the things which are in the world, I ho, e you will not refuse me a corner for this sorrow. ing dissent from a doctrine so depre iatory of the world, and whose enunciation cannot fail to give occasion to the many enemies of Science to bla pheme is sacred name on account of the eccentricities of its professors. EDWARD MAITLAND Oxford and Cambridge Club

Draining a Cause of Excessive Droughts

WILL you kindly allow me through the medium of NATURE to ask whether any of my feilow readers can give me any actually observed facts, to show that draining is justly considered an em in the sum of causes which have given rise to the lengthened periods of drought that we have experienced in these islands for the last few years. As a matter o reasoning I believe it is generally admitted that such is the case, for ample evidence ha been produced by actual experiment to show that draining raises the temperature of the land and the air above i.; and 11 10, 11 would le sen the chance of the vapour suspended in the amo sphere being condensed. Such observed facts are on record as regards the cutting of forests, eg, NATURE, vol. iv. p 3, Buchan's Meteorology," p. 88, and if my memory does t fa me, some information was given on both these points ma previous volume of NATURE, but I am at present unable to lay my hands upon it, though I have glanced over the pages as well as the index.

If any one will kindly furnish me with the information, which may also be of interest to others, or refer me to a work nut difficult of access, I shall be extremely obliged.

Rainbow

THOMAS FAWCETT

ON Friday, the 8th July, about four P. M., as I was driving acro-s the Bog of Allen, about eight miles from Edenderry, observed the most brilhant rainbow I have ever beheld ener

Europe or Ina. It appeared in the North, and was low dond on the flat horizon, being an arc of 60° with the horizon as i chord. The ends of the tow were nearly due E. and W. The pe trum was intensely vivid. A second bow, imperfect towards the centre, shortly afterwards appeared above is; in perhaps five minutes, the E. end of this upper bow faded, and immediately I perceived for a corresponding length of the true rainbow, br dering the violet, a well defined rim of sea green, this bounded by a band of almost mauve-coloured violet, which shaded ul into the indigo sky.

The underside of the opposite end of the bow (above which the portion of the upper bow was still visible, presen ed no su h

diately around the lake; but at a short distance it was said to be very abundant. In addition to the topographical and geological collections, others were being made in all branches of natural history, for a full account of which, as well as a description of the phenomena in general, we shall look with interest to the forthcoming report of the expedition.

MR. GEORGE HODGE

WE greatly regret to record the death, at Seaham Har

bour, on the 7th of September, after a short illness, at the age of thirty-eight, of this accomplished naturalist. Although from his retiring and unassuming disposition, little known beyond the naturalist circles of the north, George Hodge realised, as few do realise, the objects of a local naturalist. Living on a portion of the north-east coast, the marine fauna of which was practically uninvestigated when he first settled there, he made its patient and honest study the business of the scanty leisure left him by is best evidenced by the Natural History Transactions of Northumberland and Durham, his favourite medium of publication for his careful observations and exquisite drawings of the lower animal forms. During a temporary residence in Newcastle, he was honorary secretary to the Natural History Society, and was to the last a valued member of its committee.

the election.

WE

F. R S.

PROF. HAYDEN'S EXPEDITION E learn from Harper's Weekly that advices from Prof. Hayden's exploring expedition in the Yellow Stone Lake region have been received up to the 8th of August last, and contain a satisfactory exhibit of progress. After establishing the depôt of supplies already referred to on the Yellow Stone River, about one hundred and forty miles below the lake, the party ascended the river, and reached the lake on the 26th of July, where they made a new camp. They then began at once to survey the lake with the most approved apparatus, by the aid of a boat taken along for the purpose, and expected to be able to ascertain the exact contour, as well as the principal depths. They had already found several places in the lake where the depth reached three hundred feet, especially along the line of a certain channel way, and they confidently expected to find soundings of at least five hundred feet.

They explored one of the islands in the lake, which they called Stevenson's Island, and found it to contain about fifteen hundred acres, densely wooded, and with thick and almost impenetrable underbrush, consisting largely of gooseberry and currant bushes, loaded down with ripe fruit. On the threshold only of the wonderful natural phenomena in the way of geysers, boiling springs, &c., described by Lieut. Doane and Governor Langford, they were satisfied that the description fell far short of the reality, which they, indeed, despaired of being able to pourtray, even with the aid of photographic views and sketches.

One of these geysers once in thirty-two hours threw up a column of water about eight feet in diameter to a height of over 200 feet. Hundreds were met with having columns of from ten to fifty feet high, some playing all the time, and others only at intervals The hottest springs were found to vary in temperature from 188° to 198, the boiling point at that altitude amounting to about 195°. Most of the springs were ascertained to be divisible into two principal classes, one class containing silica, sulphur, and iron, and the other silica and iron only.

The elevation of the lake was determined to be about 8,500 feet; the altitude of the surrounding peaks being, of course, very much greater. An abundance of trout was found in the waters, of excellent flavour, although much infected with intestinal worms. Game was scarce imme

Mr. Hodge was a most enthusiastic dredger; if he could get a boat to sea on a fine day (this being even more of a desideratum with him than with most men, as he was rather easily upset), he was perfectly happy. The last two dredging expeditions conducted by the Tyneside Naturalists' Field Club, with grants from the British Association. were undertaken chiefly by him in conjunction with Mr. G. S. Brady. The Echinodermata were his favourite subjects of study, but he was also specially interested in the Zoophytes, Pycnogons, Crustacea, and marine Acari, among all of which he had done good work. To his influence chiefly may be ascribed the establishment of the very useful and flourishing Natural History Club of Seaham Harbour, in whose proceedings he always took great interest.

ELEMENTARY PRACTICAL GEOMETRY

AS S "A Father" has asked me by name in your columns what book I can recommend as laying a foundation for the geometry of the future, I suppose I ought to answer him, though I cannot do so by a simple reference to a book. I think the main object of early geometrical teaching should be to lay a foundation of familiar facts on which the science will afterwards be built up. This is unquestionably the true scientific method in teaching all subjects; and as yet it has never, or very rarely, been applied in Geometry. For example, no intelligent teacher of botany will begin by classifying flowers, or teaching theories about their structure; he begins by giving his class flowers to dissect, and then they will know what he is talking about; and teachers of chemistry who follow any other plan find themselves inevitably compelled to cram their pupils. The question is, how is this method to be applied in Geometry? I know from various sources that there is a pretty wide-spread conviction that it ought to be so applied, but there is a difficulty that meets teachers at once: there does not seem to be enough of practical geometry that is sufficiently easy for children; and practical geometry, as presented in text books, is dull and uninteresting, as well as rather hard. Still my conviction remains that to lay a foundation of knowledge of facts is as necessary in Geometry as in other sciences, though the range of facts easily observed is somewhat less, and the science becomes much sooner a deductive

one.

And I think it is admitted that because this observational or practical geometry is wanting in our elementary mathematical teaching, geometry is generally found so difficult, so inexplicably difficult, by boys.

It does not suffice to give a child a box of geometrical solids, and let him handle them and learn their names, though this is not useless. Nor does it suffice to give him a ruler and a pair of compasses to play with; and, in fact, the more we reflect on what is required to give an interest to the observations out of which familiarity with geometrical facts is to spring, the more inevitably, it seems to me, are we led to the conclusion that practical geometry is to be taught not per se, but by practical work, by interesting and varied applications of geometrical methods to measure and copy actually existing things.

And this at once suggests that the elementary teaching of practical geometry should consist in the manipulation of measuring instruments, and the calculations based on these measurements, which lie at the foundation of sound scientific work. I believe that all such measurements and calculations and practical constructions as are within the range of a boy, might be profitably laid before him as his work in elementary geometry: and I believe that this kind of training would moreover be of the very highest value in preparing him for good experimental work, and for a sound appreciation of scientific methods and results.

It will be advisable, however, to go into some degree of detail in order to explain my meaning to such as are not familiar with these parts of education; and in doing so, I must confess that I have not tested these details throughout by actual experience. For we have at Rugby to deal with older boys than those whom I am now contemplating, and though we do something of the kind with our younger boys, yet it is not what I should choose if I had the control of boys' education from an earlier age. Any one who wishes to see our actual course of practical geometry can do so by ordering Kitchener's "Geometrical Note-book" from the publisher of NATURE. But it must be understood to be a stopgap, and not a complete work. (I trust the author will forgive me for saying so.)

Let a boy be furnished with a ruler, a triangle (in plain wood), a pair of compasses, and a protractor. Let him have a hard pencil, and be taught how to sharpen it. First let him draw on card a decimetre scale, divided into centimetres, and in part into millimetres. This, of course, he must copy from some trustworthy scale. Insist on this, and on every part of his work being done with great care and perfect neatness, and therefore not in ink.

These are his tools. He must proceed to measure some figures provided him for this purpose; a few triangles, quadrilaterals, &c, in wood, or figures drawn on paper, are sufficient for this purpose. Every one of his measurements is neatly written in a suitable note-book, and the figure to which they apply is drawn (freehand) therein.

The next thing to proceed to is the measurement of angles, and the expression of the result in degrees and minutes, with exercises suggested by Euclid, i. 32, and its corollaries, properties of the circle, &c., which are to be practically verified, the observed results being written down, and compared with the theoretical results.

Then the lad may go on to the practical measurement of areas, beginning of course with a rectangle, which he divides into square centimetres and millimetres; he goes through the practical proof that the area of the triangle is half that of the rectangle of equal altitude on the same base; he proves Euclid, i. 47, and iii. 35; he finds the areas of various polygons of which drawings or models are given him.

Mensuration of solids is next approached, and here probably a few rules will have to be given, by which volumes are calculated from linear measurements. But in all cases the measurements must be made by the boy himself with his compasses and scale. Any one who

pleases can show his pupils how to prove the relation between the volumes of pyramids and prisms by weighing models of suitable dimensions. The same method may easily be applied to determine approximately the area of a circle; and in this, as in some other measurements, it will be well to require an estimate of the degree of approximation attained, and a mean to be taken of several measurements.

If more applications are wanting, the use of co-ordi. nates to express position may be explained, and some examples may be given of their application in simple problems, such as to make a plan of a room or of a garden, the scale being specified; and to copy a drawing, such as the sun with a group of spots. More advanced work to any amount will be offered by projections. The boy would be required to draw the projections of the various regular solids given to him, and perform the usual exercises of geometrical drawing. The construction by ruler and compasses of exact copies of triangles and other figures may be introduced almost anywhere, and a clear statement given of the different data from which a triangle can be constructed.

I wonder what "A Father" and mathematical teachers say to these suggestions. It will be obvious that they do not aim at making a boy a rapid analyst, or an expert problem solver; but I hope it is equally obvious that they are really calculated to make a careful and exact worker, one who shall attach precise meaning to his words, and shall be capable of using his head and hands in combi nation with one another in practical problems. The method is, moreover, applicable to a class, as well as to an individual pupil, and involves a very trifling expendi ture on materials.

When some such course of practical geometry has been gone through, a boy may begin any scientific or deductive geometry; he had better read whatever book is read in the school to which he is going. A boy so prepared will find Euclid easy enough, but rather unaccountably indirect and clumsy; but he may be fortunate enough to be going to a school which has adopted some better arranged text book. In a year or two there will be better modern text books than now exist. Whatever book he reads, he ought to work many examples, and do original work. It is not a bad plan to give him the enunciations alone, and let him discover the proofs as far as he can. Perhaps the best text book now existing is the "Eléments de Géometrie," par Ch. Briot.

My remarks have run to considerable length, much greater than I intended, and I can apologise for it only on the ground that many teachers are thinking of the question handled in it, and that it is only by imparting our notions and our experience to one another that we shall improve our methods. I sincerely hope that "A Father's" letter to you may elicit answers from teachers more experienced and successful than I am.

J. M. WILSON

on fresh discoveries OF PLATYCNEMIC MEN IN DENBIGHSHIRE

IN the course of 1869 I had the good fortune to discover and explore a sepulchral cave at Perthi Chware, a farm about fourteen miles north of Corwen, and high up in the region of hills. It contained fifteen or sixteen skeletons, some of which were buried in a sitting pos ture, of ages varying from infancy upwards, and associated with the broken bones of animals that had been eaten, which belonged to the dog, fox, badger, horned sheep, Celtic shorthorn (Bos longifrons), roe, stag, horse, wild boar, and domestic hog. The solitary work of art left behind by man consisted of a flint flake, but there were also frag ments of Mya truncata, and of mussel and cockle-shells. The cave had been evidently used as a place of habitation