fairly approximate to the 20,000,000th ruling the heavens for ages, and was repart of the earth's mean diameter; but corded in Jeezeh's ancient structure.' there seems no reason whatever for sup- To minds not moved to most energetic posing (even if the supposition were not forgetfulness by the spirit of faith, it antecedently of its very nature inadmis- would appear that when a square base sible) that they knew anything about the had been decided upon, and its dimencompression of the earth, or that they sions fixed, with reference to the earth's had measured a degree of latitude in diameter and the year, the diagonals of their own place with very wonderful ac- the square base were determined also; curacy. and, if it so chanced that they correBut here a very singular coincidence sponded with some other perfectly indemay be noticed, or, rather, is forced upon pendent relation, the fact was not to be our notice by the pyramidalists, who credited to the architects. Moreover, it strangely enough recognise in it fresh is manifest that the closeness of such a evidence of design, while the unbeliever coincidence suggests grave doubts how finds in it proof that coincidences are no far other coincidences can be relied upon sure evidence of design. The side of the as evidence of design. It seems, for inpyramid containing 365+ times the sacred stance, altogether likely that the archicubit of 25 pyramid inches, it follows tects of the pyramid took the sacred that the diagonal of the base contains cubit equal to one 20,000,000th part of 12,912 such inches, and the two diagonals the earth's diameter for their chief unit of together contain 25,824 pyramid inches, length, and intentionally assigned to the or almost exactly as many inches as there side of the pyramid's square base a length are years in the great precessional period. of just so many cubits as there are days No one whatever amongst men,' says in the year; and the closeness of the Professor Smyth, after recording various coincidence between the measured estimates of the precessional period, length and that indicated by this theory 'from his own or school knowledge, knew strengthens the idea that this was the anything about such a phenomenon, builders' purpose. But when we find until Hipparchus, some 1,900 years after that an even closer coincidence immedithe great pyramid's foundation, had a ately presents itself, which manifestly is glimpse of the fact; and yet it had been a coincidence only, the force of the evi dence before derived from mere coinci. * It may, perhaps, occur to the reader to dence is pro tanto shaken. For, consider enquire what diameter of the earth, supposed what this new coincidence really means. to be a perfect sphere, would be derived from Its nature may be thus indicated : Take a degree of latitude measured with absolute the number of days in the year, multiply accuracy near latitude 30o. A degree of lati. tude measured in polar regions would indi that number by 50, and increase the recate a diameter greater even than the equato sult in the same degree that the diagonal rial ; one measured in equatorial regions of a square exceeds the side—then the would indicate a diameter less even than the resulting number represents very approxa degree of latitude would indicate a diameter imately, the number of years in the great very nearly equal to the true polar diameter precessional period. The error, accordof the earth. In fact, if it could be proved ing to the best modern estimates, is about that the builders of the pyramid used for their one 575th part of the true period. This unit of length an exact subdivision of the is, of course, a merely accidental coincipolar diameter, the inference would be that, dence ; for there is no connection what. while the coincidence itself was merely acci. dental, their measurement of a degree of lati. ever in nature between the earth's period tude in their own country had been singularly of rotation, the shape of a square, and accurate. By an approximate calculation I the earth's period of gyration. Yet this find that, taking the earth's compression, at merely accidental coincidence is very from the accurate measurement of a degree of much closer than the other supposed to latitude in the neighborhood of the great be designed could be proved to be. It pyramid, would have made the sacred cubit, is clear, then, that mere coincidence is a taken at one 20,000,000th of the diameter very unsafe evidence of design. equal to 24.98 British inches; a closer approximation than Professor Smyth's to the Of course the pyramidalists find a estimated mean probable value of the sacred ready reply to such reasoning. cubit. argue that, in the first place, it may have They been by express design that the period stones have been discovered which indiof the earth's rotation was made to bear cate with considerable exactness the this particular relation to the period of slope of the original plane-surfaces of gyration in the mighty precessional the pyramid, the ratio of the height to movement; which is much as though the side of the base may be regarded as one should say that by express design much more satisfactorily determined the height of Monte Rosa contains as than the actual value of either dimenmany feet as there are miles in the sion. Of course the pyramidalists claim 6,000th part of the sun's distance.* a degree of precision indicating a most Then, they urge, the architects were not accurate knowledge of the ratio between bound to have a square base for the pyra- the diameter and the circumference of mid; they might have had an oblong or a circle; and, the angle of the only casa triangular base, and so forth-alling stone measured being diversely estiwhich accords very ill with the enthusi. mated at 51° 50' and 51° 52}', they conastic language in which the selection of sider 50° 51' 14'3" the true value, and a square base had on other accounts infer that the builders regarded the ratio been applauded. as 3'14159 to 1. . The real fact is, that Next let us consider the height of the the modern estimates of the dimensions pyramid. According to the best modern of the casing stones (which, by the way, measurements, it would seem that the ought to agree better if these stones are height when (if ever) the pyramid termi- as well made as stated) indicate the nated above in a pointed apex, must have values 3'1439228 and 3'1396740 for the been about 486 feet. And from the com- ratio ; and all we can say is, that the parison of the best estimates of the base ratio really used lay probably between side with the best estimates of the height, these limits, though it may have been it seems very likely indeed that the inten- outside either. Now the approximation tion of the builders was to make the of either is not remarkably close. It height bear to the perimeter of the base requires no mathematical knowledge at the same ratio which the radius of a all to determine the circumference of a circle bears to the circumference. Re- circle much more exactly. 'I thought membering the range of difference in the it very strange,' wrote a circle-squarer base measures it might be supposed that once to De Morgan (Budget of Parathe exactness of the approximation to doxes, P: 389), that so many great this ratio could not be determined very scholars in all ages should have failed in satisfactorily. But as certain casing finding the true ratio, and have been determined to try myself.' 'I have been informed,'proceeds De Morgan,' that this * It is, however, almost impossible to mark trial makes the diameter to the circumany limits to what may be regarded as evi. dence of design by a coincidence-hunter. I ference as 64 to 201, giving the ratio quote the following from the late Professor equal to 3-1410625 exactly. The result De Morgan's Budget of Paradoxes. Having was obtained by the discoverer in three mentioned that 7 occurs less frequently than weeks after he first heard of the existence any other digit in the number expressing the ratio of circumference to diameter of a circle, of the difficulty. of the difficulty. This quadrator has he proceeds : 'A correspondent of my friend since published a little slip, and entered Piazzi Smyth notices that 3 is the number of it at Stationers' Hall. He says he has most frequency, and that 37 is the nearest ap- done it by actual measurement; and I proximation to it in simple digits. Profes: hear from a private source that he uses sor Smyth, whose work on Egypt is paradox of a very high order, backed by a great quan. a disc of twelve inches diameter which tity of useful labor, the results of which will he rolls upon a straight rail.' The 'rollbe made available by those who do not re. ing is a very creditable one; it is about ceive the paradoxes, is inclined to see con. firmation for some of his theory in these phe as much below the mark as Archimedes nomena.' In passing, I may mention as the was above it. Its performer is a joiner most singular of these accidental digit rela- who evidently knows well what he is tions which I have yet noticed, that in the about when he measures; he is not first .110 digits of the square root of 2, the wrong by 1 in 3,000.', Such skilful number 7 occurs more than twice as often as either 5 or 9, which each occur eight times, I mechanicians as the builders of the pyraand 2 occurring each nine times, and 7 occur mid could have obtained a closer approx. ring no less than eighteen times. imation still by mere measurement.. Be sides, as they were manifestly mathema- height of the pyramid. If we take the ticians, such an approximation as was relation as exact we should infer for the obtained by Archimedes must have been sun's distance 5,819 thousand millions well within their power; and that ap- of inches, or 91,840,000 miles-an improximation lies well within the limits mense improvement on the estimate above indicated. Professor Smyth re- which for so many years occupied a marks that the ratio was 'a quantity place of honor in our books of astronwhich men in general, and all human omy. Besides, there is strong reason science too, did not begin to trouble for believing that, when the results of themselves about until long, long ages, recent observations are worked out, the languages, and nations had passed away estimated sun distance will be much after the building of the great pyramid; nearer this pyramid value than even to and after the sealing up, too, of that the value 91,400,coo recently adopted. grand primeval and prehistoric monu- This result , which one would have ment of the patriarchal age of the earth thought so damaging to faith in the eviaccording to Scripture. I do not know dence from coincidence nay, quite where the Scripture records the sealing up fatal after the other case in which a of the great pyramid ; but it is all but close coincidence had appeared by certain that during the very time when merest accident—is regarded by the pyrathe pyramid was being built astronomi- midalists as a perfect triumph for their cal observations were in progress which, faith. They connect it with another for their interpretation, involved of coincidence, viz. that assuming the height necessity a continual reference to the determined in the way already indicated ratio in question. No one who considers then it so happens that the height bears the wonderful accuracy with which, to half a diagonal of the base the ratio nearly two thousand years before the 9 to 10. Seeing that the perimeter of Christian era, the Chaldæans had deter: the base symbolises the annual motion mined the famous cycle of the Saros, of the earth round the sun, while the can doubt that they must have observed height represents the radius of a circle the heavenly bodies for several centuries with that perimeter, it follows that the before they could have achieved such a height should symbolise the sun's dissuccess; and the study of the motions of tance. That line, further,' says Profesthe celestial bodies compels men to sor Smyth (speaking on behalf of Mr. trouble themselves' about the famous W. Petrie, the discoverer of this relaratio of the circumference to the diame- tion), ‘must represent' this radius 'in ter. the proportion of 1 to 1,000,000,000.' (or We now come upon a new relation ten raised to power nine), 'because (contained in the dimensions of the pyr- amongst other reasons 10 to 9 is practiamid as thus determined) which, by a cally the shape of the great pyramid.' strange coincidence, causes the height For this building ' has such an angle at of the pyramid to appear to symbolise the corners, that for every ten units its the distance of the sun. There were structure advances inwards on the diag5,813 pyramid inches, or 5,819 British vnal of the base, it practically rises upinches, in the height of the pyramid ac- wards, or points to sunshine' (sic) 'by cording to the relations already indi- nine. Nine, too, out of the ten characcated. Now, in the sun's distance, ac- teristic parts (viz. five angles and five cording to an estimate recently adopted sides) being the number of those parts and freely used, * there are 91,400,000 which the sun shines on in such a miles or 5,791 thousand millions of inches shaped pyramid, in such a latitude near --that is, there are approximately as the equator, out of a high sky, or, as the many thousand millions of inches in the Peruvians say, when the sun sets on the sun's distance as there are inches in the pyramid with all his rays. The coinci dence itself on which this perverse rea* I have substituted this value in the article soning rests is a singular one-singular, Astronomy,' of the British Encyclopædia, for that is, as showing how close an accithe estimate formerly used, viz. 95,233,055 dental coincidence may run. It amounts miles. But there is good reason for believing to this, that if the number of days in the that the actual distance is nearly 92,000,000 miles. year be multiplied by 100, and a circle ture. * once be drawn with a circumference contain- sions of length, surface, capacity, and ing 100 times as many inches as there position, the great number of shapes, and are days in the year, the radius of the the variety of material existing withcircle will be very nearly.one 1,000,000,- in the pyramid, and considering, furoooth part of the sun's distance. Re- ther, the enormous (number of relations membering that the pyramid inch is (presented by modern science) from assumed to be one 500,000,oooth part of among which to choose, can it be wonthe earth's diameter, we shall not be far dered at if fresh coincidences are being from the truth in saying that, as a matter continually recognised? If a dimension of fact, the earth by her orbital motion will not serve in one way, use can be traverses each day a distance equal to found for it in another; for instance, if two hundred times her own diameter. some measure of length does not correBut, of course, this relation is altogether spond closely with any known dimension accidental. It has no real cause in na- of the earth or of the solar system (an unlikely supposition), then it can be unSuch relations show that mere numer- derstood to typify an interval of time. ical coincidences, however close, have If, even after trying all possible changes little weight as evidence, except where of that kind, no coincidence shows itself they occur in series. Even then they (which is all but impossible), then all that require to be very cautiously regarded, is needed to secure a coincidence is seeing that the history of science records that the dimensions should be manipumany instances where the apparent law lated a little. Let a single instance of a series has been found to be falsified suffice to show how the pyramidalists when the theory has been extended. Of (with perfect honesty of purpose) hunt course this reason is not quoted in order down a coincidence. The slant tunnel to throw doubt on the supposition that already described has a transverse height the height of the pyramid was intended no doubt uniform, now giving to symbolise the sun's distance. That various measures from 47'14 pyramid supposition is simply inadmissible if the inches to 47*32 inches, so that the vertihypothesis, according to which the height cal height from the known inclination was already independently determined in of the tunnel would be estimated at someanother way, is admitted. Either hy where between 5264 inches and 5285. pothesis might be admitted were we not Neither dimension corresponds very obcertain that the sun's distance could not viously with any measured distance in possibly have been known to the builders the earth or solar system. Nor when we of the pyramid ; or both hypotheses may try periods, areas, &c., does any very be rejected: but to admit both is out of satisfactory coincidence present itself. the question. But the difficulty is easily turned into Considering the multitude of dimen- a new proof of design. Putting all the observations together (says * It may be matched by other coincidences Professor Smyth), I deduced 47*24 pyra. as remarkable and as little the result of the mid inches to be the transverse height of the operation of any natural law. For instance, entrance passage; and computing from thence the following strange relation, which intro. with the observed angle of inclination the duces the dimensions of the sun himself, no. vertical height, that came out 52976 of the where, so far as I have yet seen, introduced same inches. But the sum of those two among pyramid relations, even by pyramidal. heights, or the height taken up and down, ists : *If the plane of the ecliptic were a true equals 100 inches; which length, as elsesurface, and the sun were to commence roll. where shown, is the general pyramid linear ing along that surface towards the part of the representation of a day of twenty-four hours. earth's orbit where she is at her mean dis. And the mean of the two heights, or the tance, while the earth commenced rolling height taken one way only, and impartially upon the sun (round one of his great circles), to the middle point between them, equals each globe turning round in the same time, fifty inches; which quantity is, therefore, the then, by the time the earth had rolled its way general pyramid linear representation of only once round the sun, the sun would have half a day. In which case, let us ask what almost exactly reached the earth's orbit. This the entrance passage has to do with half is only another way of saying that the sun's rather than a whole day? diameter exceeds the earth's, in almost exactly the same degree that the sun's distance On relations such as these, which, if exceeds the sun's diameter.' really intended by the architect, would imply an utterly fatuous habit of con- ant idolaters, in a primal age of the world, to cealing, elaborately what he desired to work mightily both for the future glory of the one true God of Revelation, and to establish symbolise, the pyramidalists base their lasting prophetic testimony touching a further belief that development, still to take place, of the abso. lutely Divine Christian dispensation. a Mighty Intelligence did both think out the plans for it, and compel unwilling and ignor Fraser's Magazine. THE KITCHEN AND THE CELLAR.* It is now more than forty years ago in England! It would be unreasonable since a writer in this Review discoursed, to expect that material prosperity should with a perfect knowledge of the subject, bring in its train the plain and simple on the Science with which a dinner should refinement of taste due to other condibe served and the art with which it tions than those of mere wealth. should be eaten. The popularity which Our present object being entirely prachis remarks obtained, when separatelytical, we do not propose to go into the published under the title of 'The Art of history of cookery. Nor, indeed, is it Dining,' proved that that generation ap- necessary to do so; for it would be diffipreciated his summary of the laws of cult, if not impossible, to improve on the gastronomical observation in relation to general sketch, given by the author of the their food and wines. Would that it "Art of Dining,' of the history of cookery were in our power to say that there has from the earliest period up to 1789; and been since that day real progress as well his account of the celebrated cooks of in that Art as in the Science of Cookery the Empire and the Restoration is one of the most interesting contributions to * 1. Le Livre de Cuisine. Par Jules Gouffé, the literature of the subject. comprenant la 'Cuisine de Ménage et la Grande Cuisine,' avec 25 planches imprimés en chromo- nomical science will show us that the A glance at the present state of gastroäthographie, et 161 vignettes sur bois. Paris, 1867. French, while still very perfect in it, are 2. l’Art de la Cuisine Française au Dix-neu- scarcely on a par with their forefathers vième Siècle. Traité élémentaire et pratique, of the period of the Restoration; nor suivi de Dissertations Culinaires et Gastronomi- shall we accept the Café Anglais, the ques, utiles aux progrès de cet Art. Par M. An. ionin Carême. Paris, 1833. Café Voisin, good as its cellar is, still 3. Modern Domestic Cookery. By a Lady. A less the Maison Dorée of the present day, new edition, based on the Work of Mrs. Run- in place of the Frères Provençaux, If 4. Cuisine de Tous les Pays : Etudes Cosmo- Philippe's, and Véfour's of the past. polites, avec 220 dessins composés pour la démon. we turn northward to Belgium we shall stration. Par Urbain Dubois, chef de cuisine find much that is good in cooking and de leurs Majestés Royales de Prusse. Paris, eating known, if not universally practised, 1863. whilst in reference to wine the Belgians 5. Cosmopolitan Cookery. Popular Studies, with 310 Drawings. By Urbain Dubois. Lon: surpass all other countries in their intidon, 1870. mate acquaintance with, and accurate 6. Gastronomy as a Fine Art, or the Science of knowledge of, the best vintages of BurGood Living A Translation of the Physio- gundy. In Great Britain we may hope logie du Godt' of Brillat-Savarin. By R. E. Anderson, M.A. London, 1877. that we are on the path of progress, some 7. uckmaster's Cookery : being an abridgment elements of race not unfavorable to gasof some of the Lectures delivered in the Cookery tronomical observation at times appearSchool at the International Exhibition for 1873. ing in our strange mixture of Teutonic and 1874; together with a collection of approved with other blood. Recipes and Menus. London. The wealth of America brings in its 8. The Art of Dining ; or Gastronomy and Gastronomers. New Edition. London, 1853. train some new recipes in the prepara9. Report on Cheap Wines. By Dr. Druitt. tion of oysters and lobsters, and its inLondon, 1873. digenous birds offer to the 'gourmet 'a + See Quarterly Review 'Article on 'Gas new subject for discourse, and fresh test tronomy and Gastronomers,' in July 1835, and Article on Mr. Walker's Original' in Febru. for the faculties he possesses. ary, 1836. Passing again northward, we find the |