What degree of error, then, shall we attribute to each of these items? A precise determination of this coLet us put our quæsitum in the form of a fraction, efficient is, as we have already observed, impossible it thus:

may just possibly be 20 per cent. Then we should ascribe half this degree of inaccuracy to the figure 1'175, which, according to Mr. Giffen's computation, is the ratio of the total capital in 1885 to the total capital in 1875. It would be conceivable that the real increase, as measured by some superior being, is not 17 per cent., but as little as 7, or as much as 27, per cent. Perhaps the defect is a little more likely than the excess, if there exist any constant cause making for depression such as the increased stringency of the tax-collectors in later years.

The growth of 17 per cent. in the decade under consideration may appear surprisingly small compared with the 40 per cent. recorded for the preceding decade. The general accuracy of the contrast is, however, confirmed by a comparison of the growths in each item for the two decades. Mr. Giffen points out that in the former decade, unlike the latter, there are no growths downwards. Also the percentages which measure increase run mostly at a higher level for the earlier period. His detailed examination of the figures leaves nothing to desire. For a summary contrast between the two sets of percentages we might submit that a proper course would be to compare the medians of the respective sets of figures (the arith. metic means would not be suitable owing to the very unequal importance of the figures relating to such miscellaneous items). Operating in the manner suggested, we find as the median of the first set of percentage growths 50, and of the second 25, thus confirming Mr. Giffen's conclusion that the former movement is about double the latter.

The conclusion that in the last decade our progress has been only half what it was in the preceding decade is at first sight disappointing. But we must remember that as yet we have accomplished only part of our calculation. We have still to make a correction for the change in the value of money which may have occurred between the two periods. This is a problem familiar to Mr. Giffen. In his classical computations of the changes in the volume of our foreign trade he encountered and surmounted a similar difficulty. In that case he ascertained the change in the level of prices at which exports and imports ranged in different years without going beyond the statistics of foreign trade, and by operating solely on the prices and quantities of exports and imports. It might be expected, perhaps, that he would pursue an analogous course in constructing a measure for the change of prices affecting the volume of capital. He would thus have been led to adopt the very ingenious method of measuring changes in the value of money which has been proposed by Prof. J. S. Nicholson. But, however cognate that original idea may be to the theory of the subject, it will be found in practice not easy to apply to the present computation. At any rate, Mr. Giffen has taken his coefficients for the correction in question, not, as before, from the subject itself, but ab extra, from Mr. Sauerbeck, Mr. Soetbeer, and the Economist. Averaging their results, he finds that money has appreciated to the extent of 17 per cent. during the interval under consideration. This correction being made, the growth of capital in the period 1875-85 proves to be about the same as the growth in 1865-75.

The soundness of this conclusion is confirmed by some reflections which at first sight might appear open to criticism. After using the fall of prices to prove the

increase of capital, Mr. Giffen turns round and scems to reason from the increase of capital to the fall of prices.

"If two periods are compared in which the increase of population is known to be at much the same rate throughout, and the increase of productive capacity may be assumed to be at the same rate, or not less, in one of the periods than in the other, then, if the apparent accumulation of capital in the one period proved to be less than in the other, it must be ascribed to some change in the money values."

This reasoning may appear circular to the formal logician. But, in the logic of induction, we submit that it is very proper for two arguments archwise to support each other. The consilience of different lines of proof is indeed an essential feature of the logic of fact, as formulated by J. S. Mill. We venture to interpret Mr. Giffen's double line of proof by the following parable. Has it never occurred to you, reader, on looking at your watch, and finding the hour earlier than you expected, to suspect that the instrument has played you false? You review what you have been doing; recollect, perhaps, that you began work or got up earlier than usual; and, on reflection, see no reason to distrust your watch. You test the watch by the time, and you measure the time by the watch. Similarly, Mr. Giffen is quite consistent when he measures the extent of the growth of capital by the extent of the fall in prices and confirms the fact of a fall in prices by the independently inferred fact of a considerable growth of capital.

In connection with the fall of prices we should notice an important contribution which Mr. Giffen makes to monetary science by defining the ambiguous term "appreciation." The readers of NATURE who may be more familiar with physical than social science will smile when they understand that there has been in economical circles a stiff controversy on the following question: Whether, if there is not now in circulation a sufficient amount of money-in proportion to the quantity of commodities circulated-to keep up prices to a former level, the cause of the fall is the scarcity of gold or the abundance of goods. It is as if, when the shoe pinched, people should dispute whether the shoe is too small, or the boot too large. The mirth of the physicist seems for the most part justified. However, as Coleridge or somebody said, before we can be certain that a controversy is altogether about words, there is needed a considerable knowledge of things. The better class of controversialists in the matter before us have doubtless had a meaning, but a latent and undeveloped one, which it required our author, like another Socrates, to bring to birth. The issue appears unmeaning, as long as you consider the question in Mr. Giffen's phrase "statically," without reference to the rate at which the quantity of goods and gold are growing. But “dynamically,” if goods and gold cease to move abreast, it is intelligible to attribute the separation between the two to the operation of one rather than the other. As we understand the matter, using our own illustration, let us liken the constant growth of goods to the uniform velocity of a boat carried onward by a steady stream; and the parallel increase of money to the movement of a pedestrian on the bank. If the pedestrian, after keeping abreast with the boat for some time, is at

66

length found to be behind it, it is reasonable to attribute the
change to the man, and not the stream. But all turns upon
the assumed steadiness of the stream's onward move-
ment. Looking back on past experience, Mr. Giffen
entertains the hypothesis of a constant or cent rear",
growth of property. But with respect to recent years,
it would be possible to cite, from other high authorities,
expressions of a contrary opinion. But, if the steady
motion of goods is not accepted, presumably the issue
between "scarcity of gold" and the opposed theory of
appreciation will turn upon a comparison of the rates at
which the rate of increase varies for money and com-
modies respectively-an investigation of second
entials which we could not regard as serious.

MERGUI.

Contributions to the Fauna of Mergui and its Archipelago 2 Vols. (London: Taylor and Francis, 1889.

THE materials which have been brought together in these volumes are now made accessible to those specially interested in the fauna of this group of islands in a connected form. The collections were made in 188182 by Dr. John Anderson, F.R.S., till recently Director of the Indian Museum at Calcutta, who brought the specimens to England with him, and placed the different groups in the hands of specialists for their proper identidiffer-fication and description. The result has been the publication of a number of faunistic papers in the Journal of the Linnean Society and elsewhere, and these papers are now published in the form of two volumes, well illustrated with plates, and containing altogether nearly two dozen distinct memoirs by recognized authorities in the different departments.

The difficulties of monetary theory do not attend some of the uses to which the estimate of national capital may be applied. It is not necessary to make a correction for the variation of money when we compare our own with a foreign country in respect of absolute quantity, and even growth, of accumulation. Our colossal capital compares not unfavourably with the capital of the United States, perhaps equal in amount, but much less per head. The £10,000,000,000 of the United Kingdom compares favourably with the £7,200,000,000 of France weighted by a heavy debt, and the surprisingly small £1,920,000,000 of Italy.

The comparison of provinces, as well as nations, is also instructive. Mr. Giffen finds that Ireland has less than a twentieth of the property belonging to the United Kingdom. The property per head in Ireland is less than a third of what it is in England, and not much more than a third of what it is for Scotland. Upon these facts Mr. Giffen remarks:

"Reckoning by wealth, England should have 86 per cent. of the representation of the United Kingdom, or 576 members out of 670; Scotland, by the same rule, should have about 64 only; and Ireland no more than 30. . . .

There should be a representation of forces in Parliament, if we had perfectly just arrangements, and not merely a counting of heads. Nothing can be more absurd to the mind of any student of politics, who knows how forces rule in the long run, than the system now established, as between the metropolitan community of England and its companions in sovereignty, by which one of the companion communities, and that the least entitled to privilege, obtains most disproportionate power."

In the first volume Prof. P. Martin Duncan writes on the Madrepores, and in his concluding remarks calls attention to the remarkable distinctness of the existing acompared with the Miocene corals of the same area Prof. F. Jeffrey Bell's paper on the Holuthuria comes next in order, and is followed by Mr. F. Moore's paper on the Lepidoptera, the collection in the last order containing 208 species of butterflies, and 64 species of moths The Sponges are described by Mr. H. J. Carter, F.R.S., and the Ophiuridae by Prof. Martin Duncan, who contributes also a special paper on the anatomy of Ophiothri: variabilis and Ophiocampsis pellicula. The Polyzoa and Hydroida are taken in hand by the Rev. Thomas Hincks. The Coleoptera have come off badly, if Mr. Bate's de scription of one new species (Brachyonychus anderson, represents the whole of the material collected in this order. We suspect, however, that more will be heard about the Mergui beetles at some future period.

which he regards "merely as a small supplementary contribution" to Messrs. Hume and Davison's labours in the same field. The list chiefly records the distribunos in the outer islands of the archipelago of a few of the species recorded by these last authors. Dr. Hoek, of Leyden, writes on a Cirriped (Dichelaspis pelimads, which does not appear to have been observed since Darwin published his original description in his monograph. The shells-marine, estuarine, freshwater, and terrestrial-form the subject of a paper by Prof. E v. Martens, of Berlin. Mr. Stuart Ridley has been entrusted with the Alcyonaria, and Prof. A. C. Haddon describes two species of Actiniæ. The Annelids are treated of by Mr. Frank E. Beddard, who includes in hus paper an important section on the structure of the eyes in one of the species described. The Pennatulica art

Dr. Anderson himself contributes the list of birds

One of the most legitimate uses to which estimates of national capital can be put, is to ascertain the progress of wealth from age to age. In an historical retrospect, Mr. Giffen reviews the work of his predecessors, rescuing from an undeserved neglect more than one writer who had the courage and sagacity to employ what Colquhoun calls "approximating facts." The succession of estimates, from the age of Petty to the present time, appears to justify the hypothesis of a constant increase of property-treated of by Prof. Milnes Marshall and Dr. G. H a five-fold multiplication per century. Contemplating the long series of records, Englishmen may reflect with pride that the increased estimates are matched by an ncreasing power of handling them, that the growth of material prosperity has not been attended by a decline in statistical genius, and that the work of Petty is continued by one who is worthy to be compared with the founder of Political Arithmetic. F. Y. E.

Fowler, and the Myriopoda by Mr. R. I. Pocock, the being the first list of species recorded from the ar pelago. The Comatulæ are described by Dr. P. Herbert Carpenter, the Echinoidea by Prof. P. Martin Dunca and Mr. W. P. Sladen, and the Asteroidea by this last author. These organisms, when referable to know!. species," show variations which are sufficient to impart a character to the collection as a whole, and to indicate

bladed grasses. Group X., hairy grasses. Group XII., ribless bladed grasses. Groups VI., IX., and XI. are separately dealt with, but those above-mentioned will sufficiently show the principle upon which the classification

is made.

The figures (diagrams, showing the tapering, obtuse, flat, involute, or imbricate character of the herbage, are exceedingly plain and characteristic, and will be of great assistance to the observer in the field. The leaf-blades, stems, ligules, sheaths, &c., are well shown in crosssections, and at length. JOHN WRIGHTSON.

OUR BOOK SHELF.

Facsimile Atlas to the Early History of Cartography, with Reproductions of the most important Maps printed in the Fifteenth and Sixteenth Centuries. By A. E. Nordenskiold. Translated from the Swedish original by J. A. Ekelöf and Clements R. Markham. (Stockholm, 1889.

IN this handsome volume there are 142 pages of letterpress in imperial folio, and 51 plates in double folio. It contains reproductions of about 160 of the rarest and most important maps printed before the year 1600. Among these are the maps of Ptolemy, edited by Schweinheim-Buckinck in Rome, 1478 and 1490: maps from Berlinghieri's "Geographia," Firenze, c. 1478; Aeschler's and Chelin's "Ptolemy" of 1513: Reisch Margarita Fhilosophica, of 1503 and 1515; Lafreri's “Atias," Rome, c. 1570; Richard Hakluyt's "Petrus Martyr," Paris, 1587, and "Principal Navigations," London, 1500; maps of the world, by Ruysch, 1508, Bernardus Sylvanus, 1511, Hobmicza, 1512, Apianus, 1520, Laurentius Frisius, 1522, Robert Torne, 1527, Orontius Finacus, 1531, Gry naus, 1532, Mercator, 1538, Girava, 1556, de Judæis, 1593. We find also the first modern printed maps of the northern regions, of the Holy Land, of Central Europe by Nicolas a Cusa, of France, of Spain, of England, of Russia; the first charts for the use of mariners published in print; 82 general maps, or maps referring to the New World: the first modern printed maps of Africa; the first map illus trating the distribution of religious creeds, &c.

As regards the text, chapters L-iii. contain researches relating to the influence of Ptolemy on modern cartography, his merits and defects, and the different editions of his geography. Of the editions enumerated in bibliographical works, 2 sparious ones are neglected. In chapter iv. a review is given of ancient maps other than Ftolemaic, of the portolanos and their influence on modern geography. Chapter v. treats of the extension of Ptolemy's came towards the north and north west. the pre-Columbian maps of Scandinavia and Greenland, the most remarkable of which is one discovered by Nordenskiold himself in a library at Warsaw reproduced on Tab. xxx.) Chapter vi. deals with the first maps of the New World, and the then recently discovered parts of Africa and Asia. Here the author d.aws attention to the hitherto neglected fact that maps from Vasco de Gama's second voyage were printed as early as 1513 reproduced in the letterpress, Figs 8-10. Chapter vil gives an account of early terrestrial globes, and in chapter vien map profection—the author corrects several errors generally adopted in the history of this part of cartography. In chapter n he deals with the end of the early period of cartography, and in chapter x with the transition to, and the beginning of, the modern period He brings out the importance of the work of Jasope Gastad, Talp Span. § Abraham Ortelius, and Gerbürd Mercator, in the develotment of cartogRAN gives besides a catalogue of the maps in Laren's "At`is,' att renew of Creus's celebrated “Catalogus Auc· tomm tabularum geograph param

He also

The work is based on Baron Nordenskiöld's private collection of ancient printed maps. This collection he began to make many years ago, and it is now rich in documents from the periods reviewed in the present "Atlas"

The maps have been excellently copied and printed, and the great care taken by the librarian, Mr. W. E. Dahlgren, has secured the correctness of the citations. All geographers who have a right to an opinion on the subject will agree that the work is indispensable to every library in which there is a department devoted to geography.

Light and Heat. By the Rev. F. W. Aveling, M.A., B.Sc.
Second Edition. (London: Relfe Bros., 1890.
THIS is a new edition of a text-book intended to prepare
candidates for one of the science subjects of the London
matriculation. It has been much improved since its
first appearance, but it still treats the subject in a very
superficial way. Although no one could seriously study
the subject with this as a guide, it is certainly a useful
summary of the main facts, and will probably be found
serviceable by intending candidates. The coloured plate
of spectra has been corrected, but surely this is supertious
in a book which does not even describe an ordinary
student's spectroscope. The author has fallen into the
very common error of stating that the electric arc gives
a continuous spectrum, and he also states that the lines
in the spectra of the fixed stars are different from those
which characterize sunlight; whereas in a great many
cases they are practically identical.

There are numerous diagrams, but they are barely of
a quality equal to those which would be produced by a
student at an examination. The large collection of
questions and answers will be very useful
Warr.n's Table and Formula Book. By the Rev. Isaac
Warren. London: Longmans, Green, and Co., 1889.
WF have in this small work a compact and trustworthy
set of tables, facts, and formula which come within the
scope of an ordinary education. As a reference book, it
should prove most useful, the information it conveys
being concise and to the point. In addition to the usual
tables of weights and measures, &c., we have an account
of the physical and electrical units now in use, followed
by the most important formulæ used in algebra, mensura-
in and trigonometry, and tables of exchange, principal
units of value throughout the world, and comparative
average values of some important coins, the last of which
will doubtless be found useful to those travelling abroad.
Some of the most important business forms, such as
“Form of a joint Promissory Note," "Form of Foreign
B. of Exchange, &c, are printed in full; and the work
concludes with postal and telegraph rates. On the back
of the cover are printed diagrams of a square decimetre
and centimetre and a square inch, together with scales of

centimetres and inches.

LETTERS TO THE EDITOR. [The Eltor does mot hold himself responsible for opinions er pressed by his correspondents. Neither can he undertha to return, or to correspond with the writers ef, revestei MAMUICTISES IMÉEnded for this or any other part of Naturi, N motuit is taken of anonymous communications.]

· Panmixia,"

124 somewhat strained argumentan which Mr. Roa
#A3 p. 511 to my de escr
cessation of sere
Les crne me of the