been by express design that the period of the earth's rotation was made to bear this particular relation to the period of gyration in the mighty precessional movement; which is much as though one should say that by express design the height of Monte Rosa contains as many feet as there are miles in the 6,000th part of the sun's distance.* Then, they urge, the architects were not bound to have a square base for the pyramid; they might have had an oblong or a triangular base, and so forth-all which accords very ill with the enthusiastic language in which the selection of a square base had on other accounts been applauded.

Next let us consider the height of the pyramid. According to the best modern measurements, it would seem that the height when (if ever) the pyramid terminated above in a pointed apex, must have been about 486 feet. And from the comparison of the best estimates of the base side with the best estimates of the height, it seems very likely indeed that the intention of the builders was to make the height bear to the perimeter of the base the same ratio which the radius of a circle bears to the circumference. Remembering the range of difference in the base measures it might be supposed that the exactness of the approximation to this ratio could not be determined very satisfactorily. But as certain casing

* It is, however, almost impossible to mark any limits to what may be regarded as evidence of design by a coincidence-hunter. I quote the following from the late Professor De Morgan's Budget of Paradoxes. Having mentioned that 7 occurs less frequently than any other digit in the number expressing the ratio of circumference to diameter of a circle, he proceeds: A correspondent of my friend Piazzi Smyth notices that 3 is the number of most frequency, and that 34 is the nearest approximation to it in simple digits. Profes sor Smyth, whose work on Egypt is paradox of a very high order, backed by a great quantity of useful labor, the results of which will be made available by those who do not receive the paradoxes, is inclined to see confirmation for some of his theory in these phe nomena.' In passing, I may mention as the most singular of these accidental digit relations which I have yet noticed, that in the first.110 digits of the square root of 2, the number 7 occurs more than twice as often as either 5 or 9, which each occur eight times, I and 2 occurring each nine times, and 7 occurring no less than eighteen times.

stones have been discovered which indicate with considerable exactness the slope of the original plane-surfaces of the pyramid, the ratio of the height to the side of the base may be regarded as much more satisfactorily determined than the actual value of either dimension. Of course the pyramidalists claim a degree of precision indicating a most accurate knowledge of the ratio between the diameter and the circumference of a circle; and, the angle of the only casing stone measured being diversely estimated at 51° 50' and 51° 52', they consider 50° 51' 14'3" the true value, and infer that the builders regarded the ratio as 3'14159 to 1. The real fact is, that the modern estimates of the dimensions of the casing stones (which, by the way, ought to agree better if these stones are as well made as stated) indicate the values 3'1439228 and 3'1396740 for the ratio; and all we can say is, that the ratio really used lay probably between these limits, though it may have been outside either. Now the approximation of either is not remarkably close. It requires no mathematical knowledge at all to determine the circumference of a circle much more exactly. 'I thought it very strange,' wrote a circle-squarer once to De Morgan (Budget of Paradoxes, p. 389), that so many great scholars in all ages should have failed in finding the true ratio, and have been determined to try myself.' 'I have been informed,' proceeds De Morgan,' that this trial makes the diameter to the circumference as 64 to 201, giving the ratio equal to 3'1410625 exactly. The result was obtained by the discoverer in three weeks after he first heard of the existence of the difficulty. This quadrator has since published a little slip, and entered it at Stationers' Hall. He says he has done it by actual measurement; and I hear from a private source that he uses a disc of twelve inches diameter which he rolls upon a straight rail.' The 'rolling is a very creditable one; it is about as much below the mark as Archimedes

was above it. Its performer is a joiner who evidently knows well what he is about when he measures; he is not wrong by 1 in 3,000.' Such skilful mechanicians as the builders of the pyramid could have obtained a closer approximation still by mere measurement. Be

sides, as they were manifestly mathematicians, such an approximation as was obtained by Archimedes must have been well within their power; and that approximation lies well within the limits above indicated. Professor Smyth remarks that the ratio was 'a quantity which men in general, and all human science too, did not begin to trouble themselves about until long, long ages, languages, and nations had passed away after the building of the great pyramid; and after the sealing up, too, of that grand primeval and prehistoric monument of the patriarchal age of the earth according to Scripture.' I do not know where the Scripture records the sealing up of the great pyramid; but it is all but certain that during the very time when the pyramid was being built astronomical observations were in progress which, for their interpretation, involved of necessity a continual reference to the ratio in question. No one who considers the wonderful accuracy with which, nearly two thousand years before the Christian era, the Chaldæans had deter mined the famous cycle of the Saros, can doubt that they must have observed the heavenly bodies for several centuries before they could have achieved such a success; and the study of the motions of the celestial bodies compels 'men to trouble themselves' about the famous ratio of the circumference to the diame

ter.

We now come upon a new relation (contained in the dimensions of the pyramid as thus determined) which, by a strange coincidence, causes the height of the pyramid to appear to symbolise the distance of the sun. There were 5,813 pyramid inches, or 5,819 British inches, in the height of the pyramid according to the relations already indicated. Now, in the sun's distance, according to an estimate recently adopted and freely used, there are 91,400,000 miles or 5,791 thousand millions of inches -that is, there are approximately as many thousand millions of inches in the sun's distance as there are inches in the

* I have substituted this value in the article 'Astronomy,' of the British Encyclopædia, for the estimate formerly used, viz. 95,233,055 miles. But there is good reason for believing that the actual distance is nearly 92,000,000

miles.

height of the pyramid. If we take the relation as exact we should infer for the sun's distance 5,819 thousand millions of inches, or 91,840,000 miles-an immense improvement on the estimate which for so many years occupied a place of honor in our books of astronomy. Besides, there is strong reason for believing that, when the results of recent observations are worked out, the estimated sun distance will be much nearer this pyramid value than even to the value 91,400,coo recently adopted. This result, which one would have thought so damaging to faith in the evidence from coincidence - nay, quite fatal after the other case in which a close coincidence had appeared by merest accident-is regarded by the pyramidalists as a perfect triumph for their faith. They connect it with another coincidence, viz. that assuming the height determined in the way already indicated then it so happens that the height bears to half a diagonal of the base the ratio 9 to 10. Seeing that the perimeter of the base symbolises the annual motion of the earth round the sun, while the height represents the radius of a circle with that perimeter, it follows that the height should symbolise the sun's distance. That line, further,' says Professor Smyth (speaking on behalf of Mr. W. Petrie, the discoverer of this relation), 'must represent' this radius 'in the proportion of 1 to 1,000,000,000' (or ten raised to power nine), because amongst other reasons 10 to 9 is practically the shape of the great pyramid.' For this building has such an angle at the corners, that for every ten units its structure advances inwards on the diagonal of the base, it practically rises upwards, or points to sunshine' (sic) 'by nine. Nine, too, out of the ten characteristic parts (viz. five angles and five sides) being the number of those parts which the sun shines on in such a shaped pyramid, in such a latitude near the equator, out of a high sky, or, as the Peruvians say, when the sun sets on the pyramid with all his rays.' The coincidence itself on which this perverse reasoning rests is a singular one-singular, that is, as showing how close an accidental coincidence may run. It amounts to this, that if the number of days in the year be multiplied by 100, and a circle

be drawn with a circumference containing 100 times as many inches as there are days in the year, the radius of the circle will be very nearly one 1,000,000,oooth part of the sun's distance. Remembering that the pyramid inch is assumed to be one 500,000,000th part of the earth's diameter, we shall not be far from the truth in saying that, as a matter of fact, the earth by her orbital motion traverses each day a distance equal to two hundred times her own diameter. But, of course, this relation is altogether accidental. It has no real cause in nature.*

Such relations show that mere numerical coincidences, however close, have little weight as evidence, except where they occur in series. Even then they require to be very cautiously regarded, seeing that the history of science records many instances where the apparent law of a series has been found to be falsified when the theory has been extended. Of course this reason is not quoted in order to throw doubt on the supposition that the height of the pyramid was intended to symbolise the sun's distance. That supposition is simply inadmissible if the hypothesis, according to which the height was already independently determined in another way, is admitted. Either hypothesis might be admitted were we not certain that the sun's distance could not possibly have been known to the builders of the pyramid; or both hypotheses may be rejected: but to admit both is out of the question.

Considering the multitude of dimen

*It may be matched by other coincidences as remarkable and as little the result of the operation of any natural law. For instance, the following strange relation, which introduces the dimensions of the sun himself, nowhere, so far as I have yet seen, introduced among pyramid relations, even by pyramidalists: If the plane of the ecliptic were a true surface, and the sun were to commence rolling along that surface towards the part of the earth's orbit where she is at her mean dis

tance, while the earth commenced rolling upon the sun (round one of his great circles), each globe turning round in the same time, then, by the time the earth had rolled its way

once round the sun, the sun would have almost exactly reached the earth's orbit. This is only another way of saying that the sun's diameter exceeds the earth's, in almost exactly the same degree that the sun's distance exceeds the sun's diameter.'

sions of length, surface, capacity, and position, the great number of shapes, and the variety of material existing within the pyramid, and considering, further, the enormous number of relations (presented by modern science) from among which to choose, can it be wondered at if fresh coincidences are being continually recognised? If a dimension will not serve in one way, use can be found for it in another; for instance, if some measure of length does not correspond closely with any known dimension of the earth or of the solar system (an unlikely supposition), then it can be understood to typify an interval of time. If, even after trying all possible changes of that kind, no coincidence shows itself (which is all but impossible), then all that is needed to secure a coincidence is that the dimensions should be manipulated a little. Let a single instance suffice to show how the pyramidalists (with perfect honesty of purpose) hunt down a coincidence. The slant tunnel already described has a transverse height once no doubt uniform, now giving various measures from 47 14 pyramid inches to 47'32 inches, so that the vertical height from the known inclination of the tunnel would be estimated at somewhere between 52'64 inches and 52'85. Neither dimension corresponds very obviously with any measured distance in the earth or solar system. Nor when we try periods, areas, &c., does any very satisfactory coincidence present itself. But the difficulty is easily turned into a new proof of design.

Putting all the observations together (says Professor Smyth), I deduced 47 24 pyramid inches to be the transverse height of the entrance passage; and computing from thence with the observed angle of inclination the vertical height, that came out 5276 of the same inches. But the sum of those two heights, or the height taken up and down, equals 100 inches; which length, as elsewhere shown, is the general pyramid linear representation of a day of twenty-four hours. And the mean of the two heights, or the height taken one way only, and impartially to the middle point between them, equals fifty inches; which quantity is, therefore, the half a day. In which case, let us ask what general pyramid linear representation of only the entrance passage has to do with half rather than a whole day?

On relations such as these, which, if really intended by the architect, would

imply an utterly fatuous habit of concealing elaborately what he desired to symbolise, the pyramidalists base their

belief that

a Mighty Intelligence did both think out the plans for it, and compel unwilling and ignor

ant idolaters, in a primal age of the world, to work mightily both for the future glory of the lasting prophetic testimony touching a further. one true God of Revelation, and to establish development, still to take place, of the absolutely Divine Christian dispensation. Fraser's Magazine.

It is now more than forty years ago since a writer in this Review discoursed, with a perfect knowledge of the subject, on the Science with which a dinner should be served and the art with which it should be eaten. The popularity which his remarks obtained, when separately published under the title of 'The Art of Dining,' proved that that generation appreciated his summary of the laws of gastronomical observation in relation to their food and wines. Would that it were in our power to say that there has been since that day real progress as well in that Art as in the Science of Cookery

*1. Le Livre de Cuisine. Par Jules Gouffé, comprenant la 'Cuisine de Ménage et la Grande Cuisine, avec 25 planches imprimés en chromolithographie, et 161 vignettes sur bois. Paris, 1867.

2. L'Art de la Cuisine Française au Dix-neuvième Siècle. Traité élémentaire et pratique,

suivi de Dissertations Culinaires et Gastronomiques, utiles aux progrès de cet Art. Par M. Antonin Carême. Paris, 1833.

3. Modern Domestic Cookery. By a Lady. A new edition, based on the Work of Mrs. Rundell. 245th Thousand. London, 1865.

4. Cuisine de Tous les Pays: Etudes Cosmopolites, avec 220 dessins composés pour la démonstration. Par Urbain Dubois, chef de cuisine de leurs Majestés Royales de Prusse. Paris,

1868.

5. Cosmopolitan Cookery. Popular Studies, with 310 Drawings. By Urbain Dubois. London, 1870.

6. Gastronomy as a Fine Art, or the Science of Good Living. A Translation of the Physiologie du Gout' of Brillat-Savarin. By R. E. Anderson, M.A. London, 1877.

7. Buckmaster's Cookery: being an abridgment of some of the Lectures delivered in the Cookery School at the International Exhibition for 1873, and 1874; together with a collection of approved Recipes and Menus. London.

8. The Art of Dining; or Gastronomy and Gastronomers. New Edition. London, 1853. 9. Report on Cheap Wines. By Dr. Druitt. London, 1873.

See Quarterly Review' Article on 'Gastronomy and Gastronomers,' in July 1835, and Article on Mr. Walker's 'Original' in February, 1836.

in England! It would be unreasonable to expect that material prosperity should bring in its train the plain and simple refinement of taste due to other conditions than those of mere wealth.

Our present object being entirely practical, we do not propose to go into the history of cookery. Nor, indeed, is it necessary to do so; for it would be difficult, if not impossible, to improve on the general sketch, given by the author of the Art of Dining,' of the history of cookery from the earliest period up to 1789; and his account of the celebrated cooks of the Empire and the Restoration is one of the most interesting contributions to the literature of the subject.

A glance at the present state of gastronomical science will show us that the French, while still very perfect in it, are scarcely on a par with their forefathers of the period of the Restoration; nor shall we accept the Café Anglais, the Café Voisin, good as its cellar is, still less the Maison Dorée of the present day, in place of the Frères Provençaux, Philippe's, and Véfour's of the past. If we turn northward to Belgium we shall find much that is good in cooking and eating known, if not universally practised, whilst in reference to wine the Belgians surpass all other countries in their intimate acquaintance with, and accurate knowledge of, the best vintages of Burgundy. In Great Britain we may hope that we are on the path of progress, some elements of race not unfavorable to gastronomical observation at times appearing in our strange mixture of Teutonic with other blood.

The wealth of America brings in its train some new recipes in the preparation of oysters and lobsters, and its indigenous birds offer to the 'gourmet' a new subject for discourse, and fresh test for the faculties he possesses.

Passing again northward, we find the