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The Pamphlet Collection of Sir Robert Stout: Volume 20

Report of the Meeting of the Otago Institute

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Report of the Meeting of the Otago Institute,

An ordinary meeting of the Otago Institute was held in the University Building on Tuesday evening, November 14th, Robert Gillies, Esq., one of the Vice-Presidents of the Institute, in the chair.

After the usual preliminary business had been disposed of, it was announced that at this meeting the Institute had the right of nominating a gentleman to be an honorary member of the New Zealand Institute—the Governors of the Institute selecting three annually from amongst the nominees of the incorporated Societies.

Mr J. S. Webb moved that Dr Wm. Lauder Lindsay, of Perth, be nominated by this Institute. Last year Dr. Lindsay had been elected an honorary member of the Otago Institute, and it had been presumed that by this election he became a member of the New Zealand Institute also. The Governors had evidently been of a different opinion, and had subsequently passed rules for the election of Honorary Members. Under these rules this Society ought last year, in common with the other incorporated Societies, to have had the opportunity of nominating three gentlemen—the Governors electing nine out of the whole number nominated. He was informed that notice of the new rule had notbeen received here in time, and this privilege had been lost. In future one nomination annually would be allowed. Most of those who were present were aware of the grounds on which Dr. Lindsay had been elected an honorary member of their own body. He was one of the few well instructed naturalists who had personally examined the botany of Otago; he had always taken a great interest in the Province; had published an interesting book, "Contributions to the Botany of New Zealand," which was chiefly devoted to the plants of Otago, and had at the time of the Intercolonial Exhibition, held in Dunedin in 1865, made some valuable presents to the Province, which were now in the Museum. On these grounds, he now moved the nomination of Dr Lindsay for election as an honorary member of the New Zealand Institute.

Mr A. H. Ross seconded the motion.

The Chairman, on putting the motion to the meeting, remarked that Dr Lindsay was the first person to make the suggestion that a University should be established in Dunedin.

The motion was carried unanimously.

Mr D. Brent then read the following paper:—

On Proportion Applied to Geometry.

The last time I read a paper before this Institute I promised to make some remarks at a future meeting on the theory of Proportion in connection with Geometry. I propose now to give an outline of the treatment of proportion in the Fifth Book of Euclid, and to show how arithmetic should be applied to geometry, and to magnitude in general.

Geometry is the purest of all the sciences to which arithmetic or calculation is applied, for while all the other sciences involve ideas of space in connection with either time, matter, or force, geometry involves that of space only.

The fifth and sixth Books of Euclid, treating of the quantity of magnitudes, require a higher calculus than the first four Books, which treat only of the quotity of magnitudes; for a single number will always express quotity, but two numbers are in general necessary to express quantity. Now quantity involves the idea of ratio, which is a fundamental idea existing in the mind, and as such cannot be defined so that the idea it represents may be conveyed by words: we merely assert the existence of this idea in the following definitions which are those usually given both in arithmetic and geometry.

Ratio is the mutual relation which exists between two magnitudes of the same kind with respect to quantity.

Magnitudes which have the same ratio are called proportionals; so that if four magnitudes are proportionals, the ratio of the first to the second is the same as the ratio of the third to the fourth.

The ratio between two magnitudes is expressed arithmetically by the fraction which represents the multiple-part the one is of the other: in Euclid we find no reasoning about ratios considered by themselves, but only in connection with other ratios.

When two magnitudes are commensurable, that is to say, when they can be divided into equal parts of the same size, we can find an arithmetical expression for their ratio; but, when they are incommensurable, we cannot find a number which shall be identically equal to their ratio; and the fact of our being unable to do so depends upon the nature of number, and magnitude, for numbers are essentially discontinuous, whereas the latter are continuous.

As an illustration, suppose there to be two lines, each of the same length, and suppose one of them to be produced to double of its former length, we cannot find a number which shall identically represent the ratio which the first line bears to the produced line at any stage of its lengthening. For, suppose the first line to be divided into a million equal parts, then the fractions 1.000,000/1,000,001, 1,000,000/1,000,002 and so on up to 1,000,000/2,000,000 represent identically the ratio which the first line bears to the produced line at each of a million times during the lengthening; but the intervals between these are unrepresented. By dividing the first lino into a greater number of parts, we may increase the number of these intervals, and diminish their size; we may, in fact, make them as small as we please, but they will never absolutely vanish: that is to say, we can at any point find a number which, if not identically equal to the required ratio, shall yet be the ratio which the first line bears to the produced line at a point distant from the required point by less than any assignable distance; and in this sense, and in this sense only, can it be said that numbers are capable of representing the ratio between two continuous magnitudes.

In arithmetic, the test of proportion is the equality of the ratios, this naturally follows from the definition; Euclid, however, gives a different test—the well-known fifth definition of the Fifth Book, "Four magnitudes are said to be in the same proportion when any equimultiples of the first and third are respectively either greater than, equal to, or less than any equimultiples whatever of the second and fourth, whatever be the two sets of equimultiples taken." This definition is objectionable, inasmuch as it is not elementary; it does not satisfy the notion of proportion already existing in the mind, namely, the sameness of relative magnitude. It is also not good in logic, for its converse contains superfluous conditions. Besides, adopting this, we should have two tests for proportion—one for arithmetic, and another for the purposes of geometry, or, more correctly speaking, for magnitude in general; for the Fifth Book of Euclid, although geometrical in form, is not geometry, hut arithmetic applied to magnitude, of whatever kind. For all magnitudes, whether of space, time, matter, or force, may be properly represented by straight lines, which are continuous magnitudes, and therefore capable of expressing all magnitudes.

Euclid has introduced no arithmetical expressions for quantity in his Fifth Book, and the want of this has made his treatment of proportion cumbrous and wearisome, although it is conducted with great ability and ingenuity, and characterised by rigid exactness of reasoning. It may be asked why Euclid did not introduce measures in his Fifth Book, which is really a chapter in general arithmetic. Probably because the Greeks, in consequence of their notation, were very bad arithmeticians (except in whole numbers, in which they made very great advances), whereas fractions are in general necessary for measuring quantity, and are capable of doing so to an ad libitum degree of accuracy. The first great advance was made by the introduction of our present system of notation, where the position of a figure indicates its value; the next is duo to the master-mind of Newton, who discovered fractional indices, and thus gave us another form for the representation of continuous magnitude, and it is worthy of note that no other simple forms capable of expressing continuity as nearly as we please have yet been discovered besides fractions, and fractional indices or logarithms. To Newton also we are indebted for the first Lemma of the first book of his Principia, the foundation of the application of arithmetic to the sciences.

I will now give a sketch of the application of arithmetic to the measurement of magnitude, and state the principles upon which it is founded.

The principles are these:—

1. Any magnitude may be conceived to be divided into as many equal parts as we please,

2. (Newton, Lemma I.) Finite magnitudes, and also their ratios, which in any finite time tend continually to equality, and which before the end of that time approach nearer to each other than by any assignable difference are ultimately equal to one another.

A perception of the fundamental ideas of ratio and proportion is also assumed, and they may be thus expressed.

Ratio is the mutual relation which exists between two magnitudes of the same kind with respect to quantity; this relation being estimated, not by the difference of the magnitudes, but by the multiple part the one is of the other.

Four magnitudes are proportional when the ratio of the first to the second is equal to the ratio of the third to the fourth.

As all our ideas of magnitude are merely relative, in measuring a magnitude we must necessarily fix upon some standard magnitude with which to compare it. This arbitrary standard is called the unit. Thus, in measuring a line, all we have to do is to express its magnitude relative to a line of arbitrary length, called the unit of length.

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Suppose a line to contain the unit line a certain number of times exactly, say 3, then the number 3 is the measure of the length of the line. Every number, whether abstract or concrete, is in fact a ratio, the number itself denoting its relation to unity. Again, suppose the line not to contain the unit line a certain number of times exactly; then, if this line and the unit line are commensurable, we can measure the line. For suppose that when the unit line is divided into 10 equal parts, the line can be divided into 37 equal parts of the same size, then the line contains one-tenth of the unit line 37 times, and the measure of the line is properly expressed by the fraction 37/10

In the above, the line is supposed to be commensurable with the unit line. We will now suppose it to be incommensurable, as, for instance, the diagonal of a square described upon the unit of length. Suppose now the unit line be divided into 100 equal parts, the diagonal will contain one of these parts more than 141 and less than 142 times; that is to say, the measure of the diagonal lies between the two fractions 1.41 and 1.42. Again, if we were to divide the unit line into ten million equal parts, we should find that the diagonal would contain one of these parts more than 14,142,135 times, and less than 14,142,136 times; the measure of the diagonal lies therefore between the two fractions 1.4142135 and 1.4142136, that is to say, the fraction 1.414214 is the measure of the diagonal correct to six places of decimals, and it differs from the true measurement by less than half a millionth part of the unit line. By proceeding in the same way we may find theoretically the measure of a lino to any required degree of accuracy; I say theoretically, for practically we should soon be stopped by the imperfections of our instruments.

Again, since the unit may be conceived to be divided into as many equal parts as we please, we can approximate as nearly as we please to the measure of an incommensurable line, and we can find a fraction which shall differ from the true measurement by as small a quantity as we please; hence, by conceiving the number of parts into which the unit line is divided to be continually increased, we may obtain a fraction which will differ from the true value of the ratio by less than any assignable difference; it is therefore equal to that ratio, by Newton, Lemma I. Hence two numbers forming the numerator and denominator of a fraction are sufficient to represent quantity, for what has been said respecting a line is true for any magnitude whatever. It is also manifest that what is called in the above the measure of a line, is merely the arithmetical expression of its ratio to another line of arbitrary length, the unit line. Hence, in the same way, the ratio between any two magnitudes may be expressed arithmetically by a fraction.

Geometry being, as I have already pointed out, the first (in natural order) of the sciences to which arithmetic is applied, a chapter in general arithmetic applied to magnitude is not out of place therein, inserted, of course, distinct from the other chapters, and explicitly shewn to apply, not only to geometrical, but to all other continuous magnitudes. In the application of proportion to magnitude, the following theorem is the fundamental one, the proof of which is founded on the principles stated above.

If in any general theorem, four continuous magnitudes are shown to be proportional in all cases where they are commensurable, they will also be proportional in all those cases where they are incommensurable.

For let A, B, C, and D denote the four continuous magnitudes, and suppose that it can be proved that

A is to B as C to D

in all cases in which A, B, C, and D are commensurable, to show that they are also proportional, when the four magnitudes are incommensurable.

If A and B are incommensurable, we cannot find an aliquot part of B of which A is a multiple. Suppose, then, B to be divided into any number of equal parts, say n, and let A contain m but not m+1 of those parts, then by hypothesis if D is divided into n equal parts, C will also contain m but not m+1 of those parts.

Let P and Q denote magnitudes which contain exactly m of those aliquot parts of B and D respectively.

Then, since P contains the one-nth part of B m times exactly, and Q contains the one-nth part of D m times exactly, the mutual relations of P and B with respect to quantity are the same as those of Q and D; that is,

P is to B as Q toD.

Now P differs from A by less than the one-nth part of B, and as n is by hypothesis any number, we may take n to be as large as we please, that is, the aliquot part of B may be as small as we please. Suppose, now, we increase n continually, then the aliquot part of B diminishes continually, and by taking n sufficiently large we may make the aliquot part of B less than any assignable magnitude, and as P differs from A by less than this, P is ultimately equal to A.

Similarly, Q is ultimately equal to C, and since P is to B as Q to D., therefore A is to B as C to D.

The following well known theorems should also be inserted in this chapter of applied arithmetic, and are, I believe, all that are required for the purposes of geometry:—

1. Equal magnitudes have the same ratio to the same magnitude; and magnitudes which have the same ratio to the same magnitude are equal to one another.

2. Magnitudes have the same ratio that their equimultiples or submultiples have.

3. If of six magnitudes, the first is to the second as the third is to the fourth, and the third is to the fourth as the fifth is to the sixth, then is the first to the second as the fifth to the sixth.

4. If four magnitudes be proportional, and any equimultiples be taken of the first and third, and also any whatever of the second and fourth, then the multiple of the first is to that of the second as the multiple of the third is to that of the fourth.

5. If four magnitudes be proportional,

Then (i.) the second is to the first as the fourth is to the third—(incertendo.)

Also (ii.), the sum of the first and second is to the second as the sum of the third and fourth is to the fourth—(componendo).

Also (iii.), the difference of the first and second is to the second as the difference of the third and fourth is to the fourth—(dividendo).

Also (iv.), if the first be greater than the second, the third will be also greater than the fourth; if equal, equal; and if less, less.

6. If four magnitudes of the same kind be proportional, the first is to the third as the second is to the fourth—(alternamlo).

7. If any number of magnitudes of the same kind be proportionals, then the first is to the second as the sum of the antecedents is to the sum of the consequents. (addendo.)

8. If of six magnitudes, the first is to the second as the fourth is to the fifth, and the second is to the third as the fifth is to the sixth, then the first is to the third as the fourth is to the sixth. (ex equali.)

The adoption of Newton's Lemma is tantamount to a new definition of equality, and it may be urged as an objection against it that although two quantities may be equal according to the Lemma, yet if multiplied by very large numbers, it might be then possible for them to differ by an appreciable quantity. The answer to this is, that by hypothesis the two quantities continually approach to equality, and ultimately differ by less than any assignable difference, so that if they had any finite difference when subjected to any processes of arithmetic, we might invert those processes and name a quantity by which they originally differed, which is contrary to the hypothesis. Hence no error can arise in reducing theory to practice.

I will now point out the close connection existing between Euclid's definition and our common ideas of proportion; a proof of the former as following from the latter, and vice versâ, is given in most algebras. In the first place it is easily seen that the idea of the equality of submultiples connotes also the idea of the equality of equimultiples for if one-fortieth of a £ is one-half of a shilling, it follows that two £ are forty shillings. Now, if all magnitudes were commensurable, and therefore capable of being multiplied so as to become equal to one another, Euclid might have given as his test of proportion the equality of corresponding multiples, which would have been virtually the same as the equality of corresponding multiple parts; but this test would not apply rigorously to incommensurable magnitudes. In such cases, strictly speaking, the arithmetical test fails, but not so Euclid's, for he takes as his test not only the equality but also the like inequality of corresponding multiples for every possible set of multiples; and he says if it can be shewn from the nature of the four magnitudes that whatever be the equimultiples token of the first and third, and whatever those of the second and fourth, the multiples of the first and second will he always similar, in excess or defect, to those of the third and fourth, then the four magnitudes are proportional.

From the proof of the general theorem: given above it is seen without much difficulty that the adoption of Newton's Lemma virtually amounts to this alteration in the definition of proportion. Four magnitudes are proportional, when the first and third contain respectively the same aliquot part of the second and fourth the same number of times exactly, or the same number of times with remainders less than the parts respectively, whatever be the aliquot part taken.

The fundamental propositions of Euclid's sixth book, the first and thirty-third, admit of a simple proof based on the above principles. I may add that Professor Challis, in his recent work on the Principles of Mathematics and Physics, advocates the admission of those two theorems without formal proof. Firstly, two rectangles between the same I parallels are to each other as their bases; as will, he says, "be perceived immediately by conceiving them placed so that one extremity of the base of the one coincides with one extremity of the base of the other, and the; larger rectangle includes the less." Hence, Euclid VI., I. follows at once, it having been shewn in Book I. that parallelograms are: equal to rectangles of the tame base and altitude. Secondly, Two arcs of the same circle, or of equal circles, are proportional to the angles at the centre which they subtend; "for it is not possible to insert any argument between this statement and a rational perception of the truth of the statement. The proportionality is seen at once by an unaided exercise of the reason, and consequently there is no room for the application of reasoning such as that founded on Def. 5."

For my part, I must say that I do not agree with him here, for I think that no rem capable of proof should be assumed as an axiom, however simple it be, and it appears to me that there is an argument which must be inserted between the statement of the latter proposition and a rational perception of its truth, and that is one based on the theorem that in equal circles equal arcs equal angles at the centre, and on this theorem depends the truth of the second proposition; and on the fact that parallelograms, or triangles, on equal bases, and of equal altitudes are equal depends the truth of the first one. Moreover, the mental superposition is in itself an argument, unless I misapprehend the meaning he attaches to the word argument.

Before concluding, I wish to state that although I am in favour of the substitution of a chapter of arithmetic applied to magnitude for the now nearly obsolete fifth book of Euclid, I do not therefore advocate the introduction of arithmetical or algebraical symbols of quantity into pure geometry; far from it, for in the very absence of these symbols consists its great value for mental training, inasmuch as at every step there is an appeal to the reason. The pure geometry also more clearly exhibits the processes of the demonstration, and the relations of the figure than does the younger and far more powerful sister-science analytical geometry, in which, by the use of symbols, the reasoning is carried on independent to a great extent of the ideas of the magnitudes themselves.

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Mr. J. S. Webb then read the following* "Notes upon the Experiments on the so-called Psychic Force recently made by Mr. Crookes."

I desire at the outset to state that I am not about to offer any argument for or against the theories of professed spiritualists. The subject is one of which, so far as regards its more recent manifestations, I know nothing. In common with many others I feel very much obliged to those scientific men who have taken in hand to examine the phenomena on which spiritualists base their theories, and offer the following criticism upon the most recently published statements of one of these gentlemen, simply because I think the position he holds in the scientific world is not unlikely to lead many persons to accept the results he may think he has arrived at as those of pure scientific research, without enquiring into the methods which he may have adopted. New results, when even of small importance, are not thus received by scientific men. The methods of experiment which have been employed, the precautious against error, and the strictness of the explanation offered for the result which is claimed as new, are all keenly scrutinized. Such is the case when a chemist announces a new organic compound, or an astronomer a new line in some stellar spectrum, a naturalist some new species of a well known genus, a metaphysician some new demonstration of the undemonstrable, a scholar some new reading of hieroglyphic or arrow-headed characters an Etruscan inscription or a corrupt passage. The scrutiny ought to be still more rigid, when anyone, however eminent he may be, asks us, on the faith of a short course of experiments made by himself, to believe in the existence of a force hitherto unheard of, and which, if it be what Mr Crookes supposes it to be, is so extraordinary in its habits and properties, that the true Spiritualist may well say to those who believe in it—"Our faith is more consistent with all the rest of human knowledge than yours."

The first point I have to note in regard to the experiments relied on by Mr Crookes, is the very small number of them. Those who were aware that he was investigating this subject expected that when he did speak he would present us with a long and carefully classified list of phenomena, and that before he ventured upon any important deductions he would prepare himself with a cumulated series of proofs, for any theory he might propound. Such expectations were natural, because this is the recognised method of scientific investigation in our day, and because we know Mr Crookes to be a person instructed in this method, and accustomed to use it. By far the most unsatisfactory feature of his paper, is the fact that it does not in the least fulfil these expectations. He does indeed speak of many experiments having been made, but he himself rejects as unreliable all but the two of which we have now the account. It is remarkable, too, that whilst one of the reasons which induced him thus to reject nearly the whole of the observations he had from time to time made as unworthy of the name of scientific experiments, viz.: that "it has but seldom happened that a result obtained on one occasion could be subsequently confirmed," has not been applied by him to those two experiments which he ventures to call "crucial.' Until they are repeated over and over again—until it is demonstrated that, given certain conditions this or that invariably happens, it is very hasty work to furnish us with a new theory, and to ask us to believe in a new law of nature, which, instead of harmonising with all other known laws, appears to interfere with and contradict them at every turn.

Verification is of the first necessity in physical investigations, and that not by repetition only, but by every other available device. All physicists know that in their work there is invariably a liability to error on their own part, over and above all the error which arises from slight imperfections of instruments, slight impurities of substances used, and so forth, This is known as "the personal error," and arises as often from mental as from physical characteristics in the operator. It ought, I think, to have suggested itself to Mr Crookes and his colleagues that their report of the peculiar investigation in which they were engaged would have been most securely verified by adding to it that of some competent person who should have played the part of an onlooker. Had some individual, trained in scientific observation, been a bystander, engaged in assuring himself that those who undertook these experiments omitted from their notice nothing that ought to have been taken into account, the report of such a person would probably have been written in a very different style from that which we now have, and would either have been much more convincing or much more hesitating.

I claim, then, that until the experiments related by Mr Crookes have been repeated over and over again, with change of operators, and until a very large number of others yielding similar results have been instituted, his deduction that a hitherto unknown natural force has been discovered has not the foundation which established physical theories possess, and has no claim to acceptance at all similar to that which has been made good for other natural laws.

The next point which attracts attention in these experiments is that annoying character which they possess in common with all true spiritualistic phenomena—viz., the fantastic circumstances under which they are made. The accordion operated upon in the first experiment was put into a cage, and the cage stowed away under a dining-room table. Thus situated, no very critical examination of its alleged performances appears to have been possible. Mr Huggins is obliged to confess that his "position at the table" did not permit him to be a witness of the withdrawal of Mr Home's hand from the accordion. This circumstance alone is sufficiemt to throw a suspicion over the whole investigation. Here are men of acknowledgeed scientific attainments undertaking an inveestigation, for no trivial ends, supposed to be earnestly in the pursuit of truth, who permit themselves to be placed during the experiment in such a position that they could not see distinctly what was going on. If they permitted Mr Home to suit himself with the surroundings he delights in—to seat a little company around a table in positions in which they must strain their necks in order to see what he was doing—to place the physical object he was about to operate on in a position, the peculiarities of which appear to be objectless unless intended to assist in a deception—if whilst themselves assenting to be placed in such positions as he might dictate, they appointed no assistant free from such improper trammels to check their enervations—they threw aside all that their training and personal experience had taught them of the conditions of accurate investigation. In connection with this part of the subject it is very striking that Mr Crookes gives us no preliminary account of the positions actually taken up by the observers. We only gather what we do know about this from chance expressions, a fact which is alone sufficient to stamp the narrative as wanting in scientific precision, and if the account of these experiments, written subsequently and at leisure, is thus wanting, it is a fair inference that during the experiments themselves the minds of the observers were not in a judicial frame.

Another point which struck me very forcibly when reading the account of the second experiment is very curious. The dimensions of the mahogany board used in this case are carefully given by Mr Crookes, and he informs us that when the apparatus was adjusted before the experiment began, that portion of its weight which affected the spring balance was 31bs. [Description quoted.] Now the specific gravity of mahogany, as ordinarily given in the tables, is 1060 (that of water being taken at 1000), and irrespective of that portion of the board which absolutely rested upon the table, we have in this case 342 cubic inches of mahogany suspended, one-half of the weight of which would, if the board were truly horizontal, have rested upon the balance. A cubic foot of water weighs rather more than 997oz avoirdupois, hence 342 cubic inches of mahogany at the specific gravity just stated, weigh rather more than 209oz, or 131bs 1oz. It is strange that a trained man of science should not have noticed this discrepancy. At the very least we might have expected that he would have assured himself of the absence of all suspicious circumstances by weighing the whole board before adjustment, since it was the effect of the so-called Psychic Force upon its apparent weight, which he had set himself to observe. It may be answered that mahoganies vary much in specific gravity, and that a light timber would naturally be chosen for the experiment. The discrepancy appears to me to be far too large to admit of such an explanation. Had the board been of ordinary Scotch pine, the indicator ought to have shown more than 31bs 4ozs pressure on the balance, and even had the common Canadian yellow pine been used, it could hardly have shown less than 31bs. Moreover, it is evident from the context that the weight of the cord or whatever else was used to suspend one end of the board from the balance is included in 31bs indicated, although with that want of precision on which I have already commented, Mr Crookes omits to tell us so. This makes the matter slightly worse, and I cannot avoid the conclusion that the circumstances under which this experiment was made are highly suspicious.

Other reasons might be adduced why these experiments cannot be accepted as having been made in a really scientific spirit. Some of these have been concisely stated by a writer in "Nature" (No. 92, August 3rd, 1871, p. 279) from whom, with the permission of the meeting, I prefer to quote them:—

"Let us now examine the experiments in detail. Firstly, with regard to the accordion, we are not told why the cage was constructed at all, and why, moreover, when constructed, it was placed under a dining-room table of all places in the world. Does Mr Crookes wish us to believe that it is only inside such wooden cages, and in such peeuliar positions, that this 'psychic force' manifests itself If that is not the ease, why: was not the cage placed openly in the room, so that Dr Huggins might not have had to confess that he did not see the accordion freely suspended in air, which Mr Crookes and others, by dint of straining under the table, did sec? Then, again, the accordion was confessedly placed in Mr Home's hands before it was placed in the cage under the table—this was certainly unnecessary, and is very unsatisfactory. Then, it is obvious that to play the accordion the keys must in turn have been depressed. Yet Mr Crookes does not volunteer a single word to show that he noticed whether the keys were successively pressed down or not; in fact, he rather leads us to infer that they were not. Again, it is clearly a physical impossibility for the accordion to have go no round and round the cage if Mr Home's hand was quite still; for, if he held the accordion at all, his hand must have followed its movements, and what is there to show that the accordion moved his baud or his hand the accordion? Then, again, as to the instrument chosen: would a concertina act in the same manner or not? for, from the frequency with which an accordion has been appealed to by 'spiritual mediums,' it has acquired anything but a good reputation. It is a pity we are not informed whether Mr Home could in the moments when he is free from 'psychic influence' play on the accordion or not, and also, as to what were the names of the 'simple air' and the 'sweet and plaintive melody' which it so obligingly played. We are also not told either how long the experiment lasted, or how long the accordion was playing, or, what is much more to the point, how long it contravened all the laws of gravity and of the acoustics of wind instruments. Surely this is an important question—quite as important as that the temperature varied from 68° to 70° Fahr.

"Such are some of the questions which page 4 arise with respect to the first experiment, and which must he answered before any reliance can be placed on the results attained.

"There still remains the second experiment, which was of an entirely different kind: the one with the spring-balance. Mr Crookes here says—'Mr Home's lingers were never more than one and a-half inch from the extreme end, and the wooden foot being only one and a-half inch wide, and resting flat on the table, it is evident that no amount of pressure exerted in that space could produce any action on the balance,' and in this I quite agree; but did Mr Crookes notice if the table itself was moved at all? From a very slight consideration of the peculiar apparatus employed, it is obvious that were the table to tip up in any so small a manner, the index of the balance must descend; and if the table was to tip up and down successively, the very same effect would be produced on the index of the balance as that which Mr Crookes ascribes to 'successive waves of psychic force.' I do not say that the table was tipped up—that would have been trickery—but we have to account for certain results, and I do say that the tipping of the table would produce those very results, and that, moreover, there is nothing said about the table being immovable, or even heavy, or in any way fastened to the ground, as it most assuredly ought to have been. It does not appear so difficult to imagine that the Psychic Force' which could produce such a strange effect upon an accordion could also so agitate the table that it also should show tendency to move; and, if this were the case, the whole apparatus was so placed that the very slightest movements of the table would be magnified by the index of the balance."

In conclusion, I may remark that, had we as accurate a measure of the meental temperament of the observers as Mr Crookes has taken the pains to giveve us of the temperature of the apartment in which his experiments were conducted, we should know better what to think about the whole of this curious affair.

At the request of the M Meeting Mr. Webb then road so much of M Mr. Crooke's article as contains the descripription of his experiments.

Mr Brent, referring to the he balance apparatus, said that Mr Crookookes had de-scribed the board as beinging arranged perfectly horizontally, but had not said what means he had taken fo for proving it to be so. A scientific man ought to have registered the upward oscillations as well as the downward ones. If the he board had been moved by pushing it wirith the hand (which he did not say had been the case), then, if the oscillations each way had been registered, it would have been seen that the upward and downward oscillations were about the same in quantity. Again, assuming the apparatus to have been perfectly accurate when Mr Crookes put his foot upon the end of the board, there would have been no difference in the register. Now, Mr Crookes accounted for the downward pressure merely by saying that he might have put his foot beyond the fulcrum, a point he might easily have made himself sure upon.

Mr Stout said that Mr Webb's first objection was that the experiments had not been numerous enough. Mr Crookes had stated in his article that although space would only allow the publication of the details of one trial, that it must be clearly understood that he had for some time past been making similar experiments with like results, and that his conclusions had not been arrived at hastily or on insufficient evidence. Another objection was, that Mr Crookes, though a scientific man, had not paid sufficient attention to the experiments he made. No scientific man would detail in a report every circumstance that occurred in experimenting on anything, except he conceived it had some especial bearing on the subject in hand. Besides, they must assume that Mr Crookes, as a scientific man, had skill which those who were not scientific men did not possess. They must rely on his reputation in the scientific world, and, in fact, it was his reputation in the scientific world that had caused so much attention to be drawn to this psychic force, for Mr Crookes was not the first person who had discovered the existence of some such force. They had not only the scientific reputation of Mr Crookes, but also that of Dr Huggins, in support of the statement that no fraud had been practised upon them. Even granting that they were not scientific men, the meeting must surely credit them with possessing common sense, and sufficient ability to detect any fraud on Mr Homo's part, or any attempts to dupe them. Another objection urged was that Dr Huggins did not see all that was taking place under the table, but Mr Webb must have overlooked the fact that it was stated in Mr Crookes' paper that while the accordion was waving about and playing, Mr Crookes' assistant got under the table, and reported that the accordion was expanding and contracting; and that at the same time it was seen that the hand of Mr Homo which held it was quite still, and his other hand was resting on the table. That, surely, was a sufficient reply to any charge of fraud that might be urged against Mr Home. Even taking the experiments as a whole, they must admit that, call it what they may, something had been discovered that had been as yet unknown to the scientific world, though it should be kept in mind that Mr Crookes was not the first scientific man to investigate the subject, that there were men well known in the scientific world, Fellows of the Roya! Society, who had gone far further than Mr Crookes in their investigations of the new force. Professor Varley, for example, a Fellow of the Royal Society, and one who had made assertions regarding this new force far more decided than Mr Crookes had ventured to express, says that he had in broad daylight seen a small table raised off the floor and carried horizontally through the air for a distance of ten feet. Mr Webb in his paper had dealt with petty and trivial details, overlooking the main fact acknowledged by Crookes, Huggins, and Sergeant Cox, and which was the exist ence of some force. Some of the details to which he alluded were perfectly valueless; for example, that of the weight of the mahogany board. Granted, that the weight was inaccurately stated, still there was this fact not explained by Mr Webb, that Mr Crookes could not show on the index of the spring balance with his full weight resting on the mahogany board, as great a pressure as Mr Home could by merely putting his finger on the board. There was also the fact, which Mr Webb and those who found fault with every petty detail that might have been over-looked by Mr Crookes had yet to explain, and it was this: How was it that, no matter what the scientific training, or the reputation, or the intellectual ability of any person might be, no sooner did he come into the presence of Mr Home than he seemed to lose his senses I What sort of force was it that Mr Home had mastery of that enabled him to dupe, as it is said, his observers? Would not the fact of Mr Crookes being duped, of Dr Huggins being duped, of Sergt. Cox, notwith-standing his legal training, being duped, and of all those scientific men who had given in their adhesion to what is termed speculation, being duped, be far more wonderful than even the existence of a Psychic force? Until Mr Webb, or some of those who objected to Mr Crookes' conclusions, could explain this strange anomaly, it must be accepted, as being more probable, that Mr Crookes and other observers had observed the manifestation of some force not previously known to them, than that they, notwithstanding all their scientific training and intellectual ability, had been duped. Mr Crookes' reputation was well known, he being a Fellow of the Royal Society, editor of the Quarterly Journal of Science, and also of the Chemical News. Dr Huggins had also a scientific reputation to lose, and Sergt. Cox was a well trained lawyer. Could it be said that these men were all, on the occasion alluded to by Mr Crookes, duped by Mr Home, and that their "mental temperature" was suddenly increased.

A short conversation ensued, and Mr Webb briefly replied to some of the remarks made by Mr Stout.

Some fossils from the Caversham Tunnel were exhibited by Mr. Blair, and the meeting then adjourned.

* The article referred to In tills Paper appeared in the Quarterly Journal of Science for July, 1871, and was reprinted in the Otaqo daily Times of Tuesday, December 5, 1871.