the four collections, in each of which it occurs in longer or shorter form.*

Among the few other detached plays, there are, in addition to the Skryvener's play of S. Thomas mentioned above, three preserved among the Digby manuscripts in the Bodleian Library, having for their subjects, with addition of much irrelevant matter, the story of the Conversion of S. Paul, of Mary Magdalene, and the Slaughter of the Innocents. One devil named Mercury enters with thunder and "a fyeryng, comyng in hast, cryeing and rorying," and informs "Belzal," with dismay, of the Apostle's conversion, expressing his opinion that "the devyl's law will now be clene downe layd." The two agree to stir up the Jewish Bishops to interfere in the matter, and then "vanyse away with a fyre flame and a tempest." Mary Magdalene lives in a castle which the Devil, with the aid of the Seven Deadly Sins, besieges, and the history of Mary's fall follows. The handwriting of this manuscript is of the reign of Henry VII.

Among the lost plays, Miss Toulmin Smitht refers to one, perhaps belonging to a series called the "Play of the Lord's Prayer," of which Wyclif, who died in 1384, speaks in his advocacy of the translation of the Bible as the "paternoster in English tongue, as men seyen in the play of York." Is would appear to have been more of the Morality type, certain qualities being personified, and was so popular that a guild of men and women was established for the purpose of keeping it up. Another series of lost plays, based on the Creed, was performed in York every tenth year by the guild of Corpus Christi, and there was also, in the same city, the universally-acted play of S. George, which elsewhere, as at Windsor, was exhibited more as a spectacular pageant or pantomime (i.e. in dumb show) than as a drama, the saint "ridyng and fightyng with the dragon, with his spere in his hand."

THE

NOTES ON MAPPING.

BY RICHARD A. PROCTOR.

(Continued from p. 8.)

THE EQUIDISTANT PROJECTION.

HE equal surface projection dealt with in my last paper on mapping, though useful for special purposes, is of course not suited for general use in atlases. Equality of area can only be obtained at the expense of considerable distortion, even when a portion only of the surface of a globe is presented: when a hemisphere is shown, the distortion is still greater; and it becomes excessive when the whole globe is presented, though this, of course, must be the same with all methods of projection.

I have by no means done with the subject of equalsurface projection. I shall have hereafter, a good deal more to say, even about the special method of equalsurface projection which I dealt with in my last paper. There are other methods of presenting portions of the globe, or the whole globe, correctly as regards area,-as for instance the extension of Flamstead's method, and the cylindrical equal-surface projection, which I devised in

York Mysteries, No. 37, 'Harrowing of Hell." Chester Mysteries, No. 18, "Harrowing of Hell." Coventry Mysteries, No. 33, "The Descent into Hell." Towneley Mysteries, No. 25, “Extractio animarum ab inferno." Cf. also Cursor Mundi, 11. 17,84918,450.

+ York Mysteries, xxix., and see also Appx. II., pp. lxiv.-lxviii. for complete list, as far as known, of places and plays in Great Britain and Ireland.

1867.* These methods are described and illustrated in my "Essays on Astronomy," but as that work is nearly out of print, and no new edition will be issued, I shall shortly take occasion to describe the methods in these

pages.

For the present, I turn from the equal-surface projection, to the equidistant projection, which I take to be on the whole, by far the best projection for all maps of large portions of a globe's surface, and to be theoretically the best also for maps of small portions, though practically, the conical projection, owing to the much greater ease with which it can be drawn, will probably be always preferred for showing small areas, -as countries like England, France, Spain, on the earth, and constellations on the globe.

In reality, neither the equal-surface nor the equidistant methods are projections at all. For, a projection of outlines on a spherical or other curved surface signifies the curve in which straight lines drawn from a fixed point to all points on such outlines, meet some other surface, plane or curved. A projection in mapping is always made on a plane surface. The Gnomonic, Stereographic, and Orthographic projections, are all properly called projections. The equal-surface method described in my last may be conceived as a sort of double projection: for, if the sphere be supposed to rest in a hemisphere of twice its radius, and from the highest point of the sphere, all outlines on the sphere are projected upon the hemisphere: and then from a point at an infinite distance vertically above the hemisphere, the outlines so obtained are projected upon a horizontal plane, the projection thus formed will be the central equal-surface projection described in my last. The so-called equidistant projection is not however a projection even in this sort; but purely a method of construction.

Fig. 1.

It is true a projection called the equidistant and sometimes the globular was suggested long ago, by the French mathematician Lahire, in which a point P (Fig. 1) was taken at such a distance on A O a, a diameter of the sphere, produced, that a straight line PC, to C the bisection of the quadrant A CB, bisected A B in c. But this method does not project all equal arcs along A B into equal lines along O B. Nor has it any practical value whatever. I doubt if even Lahire himself ever thought it worth while to construct a chart on this plan. Delambre suggested the true equidistant construction, which may be defined as a construction in which all points

* It was subsequently re-invented by Professor P. Smyth, and employed to show that the Great Pyramid is the centre of the land-surface of the earth-which is absurd; to such base uses may the best laid plans of men (and mice) be brought!

are represented in their true direction from the centre, and at their true distance as measured on the globe. The meridians and parallels in the maps of hemispheres given in most atlases are not on the true equi-distant construction, though they approximate to it fairly enough. They are obtained by dividing two diameters ED E' and POP' of the circle PE P, Fig. 2, crossing at right angles into eighteen equal parts in a b c &c. each quadrant P E, PE', &c. into which they divide the circle into nine equal arcs in A, B, C, &c. Circular arcs Pap', Pb P' &c., give the meridians and circular arcs. At A', Bs B', &c., give the parallels of latitude. To show that this construction differs appreciably from the true equidistant construction, we need only notice that in the latter the parallels corresponding to At A', Bs B', &c., meet the circumference PEP'E' at right angles, which is obviously far from being the case with the circular arcs At A', B&B', &c.

have radii a b and a k equal to the arcs AB and AK. Hence we see that while the scale does not differ radially in the equidistant construction from the scale on the globe itself, it is larger transversely to the radius, in the same degree that the arc distance on the globe is larger than the sine of the arc.

Of course this is a defect; and if it were possible by any method of construction to get rid of all defects, in the representation of part of a globe upon a plane surface, then we should have to reject the equidistant construction on account of this particular fault. But as this is not possible, we have to inquire whether any other construction is on the whole more suitable, or characterised by smaller defects.

Several authorities, from whom one does not care to differ, consider that the equidistant projection should not be used as it always is-for maps of hemispheres in our atlases, because the projection thus gives different scalevariations in different directions, from no variations at all along a radius, to an increase in the proportion of 15,708 to 10,000 transversely to the radius at the outside of each hemisphere. Professors Hughes and Nichol, and Sir George Airy, have given their verdict in favour of the stereographic projection for the purpose of showing hemispheres. I imagine, however, that they have none of them drawn charts of more than one pair of hemispheres on the stereographic projection. If they had, they would hardly assert, as they do, that the continents are represented of their true shape in this projection; for, Africa or South America, in a stereographic projection, with the south pole as centre presents a very different shape from the same continent on a projection having a point on the equator as centre. It is true that, in the stereographic projection, the scale at any point is greater in the same degree radially and at any angle whatsoever to the radius, than the scale at the centre; and if we were in the habit of measuring short distances on charts of hemispheres, this would be an important advantage. But as we never do this, and as large distances are affected in no such uniform manner, the stereoscopic projection has no advantage over the equidistant in regard to uniformity of scale-variation; while as regards amount of scale-variation it is altogether inferior, the increase at the border of a hemisphere being as 2 to 1, in the stereographic (radially and transversely both) as compared with 1 to 1 radially and 1.57 to 1 transversely, in the equidistant construction.

As to change in area-scale, a much more important point in maps of large portions of the globe, the stereographic projection compares still worse with the equidistant; for while the areas at the border of a hemisphere on the equidistant projection are only larger than those at the centre, as 157 is larger than 100, or not much more than as 1 to 1, they are four times as large in the stereographic projection.

Thus the equidistant construction is much better than the stereographic for maps of hemispheres in ordinary atlases. For sailors' charts, as I shall hereafter show, the stereographic projection is the best of all, and, except for rhumb-sailing, ought long since to have replaced Mercator's. But for atlases, in which the maps of hemispheres are intended to give a good general idea of the positions and (as far as possible) the relative dimensions of different parts of the earth, the equidistant projection is much the best.

The great fault of the maps of hemispheres in our atlases, is that only a pair is given, and this pair always the same. The learner always sees Africa, Canada, and Greenland, Siberia, Australia, and New Zealand distorted

and enlarged in the same way and naturally falls into the mistake of supposing that these false shapes and sizes are correct. Were a different pair of hemispheres introduced, at any rate in the larger atlases, as for instance a northern and a southern map, two maps having Greenwich and its antipodes as centres-the erroneous ideas thus conveyed would be to some degree corrected.

The chief value of the equidistant construction consists, in my opinion, in its suitability for maps of large portions of the globe, celestial or terrestrial, not in its use for hemispheres. It is more useful for these than any other projection; but maps of hemispheres, at least as parts of an atlas, are not nearly so important as maps of continents or of countries.

I illustrate first, however, the use of the equidistant projection for maps of hemispheres; as this point naturally comes first under consideration, this being the use for which the construction was originally suggested. I believe, indeed, that until the publication of my "Constellation Seasons," my "Library Star Atlas," and my

"School Star Atlas," which, (like my "Stars in their Seasons," and the maps of my "First Star Lessons," now appearing in these pages) are equidistant, no maps of regions less than a hemisphere were ever drawn on this construction.

In the accompanying map we have a hemisphere of the earth on the true equidistant construction,-the centre of the map being a point in east longitude 30° and north latitude 38°. The special object aimed at in the construction of this chart, has been to present, as correctly as can be done on a plane, the immense island formed by Europe, Asia, and Africa together. (Following the precedent of those geographers who call Europe and Asia together Eurasia, we may call this great island Eurafrasia.) The Atlantic Ocean is more satisfactorily presented in this map than in any given in our atlases. But a point in longitude 40° W., or 70° further west than the centre of our map, is better suited to show the Atlantic. The student will find it a pleasant and instructive exercise to draw such a chart, using the same

meridian-lines and parallels as in the accompanying map, but taking the central meridian to represent the meridian 40° west of Greenwich.

(To be continued.)

PHOTOGRAPHY AND MEDICAL JURISPRUDENCE.

BY WILLIAM MATHEWS.

II. THE GALTON COMPOSITES IN THEIR RELATION TO THE DETERMINATION OF IDENTITY.

THE

HE achievement of consolidating into a single typical photograph the portraits of six or seven separate sitters has naturally awakened some curiosity. Other and even more remarkable operations may be expected to follow. Little by little, the field of inquiry will extend itself. In the natural course of evolution, possibilities will loom into view that, thus far, are not within the scope and purpose of the experimentalists.

One of the more inevitable of these approaching developments falls so entirely within the pathway of procedure that its investigation cannot be much longer postponed. In this very novel portraiture of the " 'composite order" there are some attendant phenomena that are of a nature at once to challenge observation and to lead in the direction indicated.

At the very threshold it becomes apparent that due attention has not been yet conferred upon the conjointure -certainly under less exacting conditions-of an arranged series of the photographs of the self-same sitter. Of such photographs, it is obvious that their superstructure should be constituted of portraits taken at definite and wellseparated epochs.

The changes which ensue from youth to maturity and from maturity to decadence are clearly amenable to certain physiological limitations. These, by this time, photography might have definitively elucidated. The "Seven Ages" of the dramatist display, we may rest assured, various "points in common which the photo

the outlines are the more perfectly conformable, a broken zone of lighter tinge will skirt the outer shadows, just where the "points in common" the most manifestly approximate.

Here, then, we obtain a glimpse of the conditions under which this effect shall become the most obviously pronounced in its degree. And, in this connection, it must be regarded as already experimentally ascertained that, in the instance of an individual who has reached maturity, the typical form of the face will thenceforward be maintained without manifest or appreciable departure.* It is clear that, under such circumstances, the fiducial lines remain in unison, and that there will arise no difficulties in effecting the absolute super-imposition of the portraits. Meantime, let it be regarded as inevitable, that in the interval between two or more sittings the sitter has become either more plump or more attenuated. Whichever event has happened, the super-imposition will be attended with an identical issue. Interposed between the half-tones of the facial areas and the exterior marginal shadows there will appear narrow belts of lighter tinge, by which the coupled images will be differentiated.

From this vantage-ground, therefore, we betoken the assured attainment of a novel and artistic result in photographic portraiture. This it is for the ingenious to develop. More to our present purpose is the consideration that medical jurisprudence may find here the adjunct of a new and undubitable test of personal identification. Here, if anywhere, we may catch sight of "that function which science asks of photography, and which medical jurisprudence is entitled to ask of both."

Need it be added that this presumed terra incognita has been already practically, if but partially, explored, and that it now awaits only that formal annexation to the ever-extending realms of science which, sooner or later, must inevitably take effect.

HE

THE "GENESTA."

detect and investigate. That the " boy is father to the man" is admitted. But what a portrait will that be in which the boy, the lover, the soldier, and the justice are conjoined into one harmonious photograph! That will be a "modern instance" worthy of the age!

In the "Galton composites "it has been noted that, in those that are the most successful, the final outcome is in some particulars more effective and life-like than are the separate portraits of the members of the group. If the question be here mooted, tentatively, Whence comes this curious and unexpected consequence? it is hoped that it may not be deemed waste effort.

It should be recognised that the picture assumes in some degree the aspect of being in relief. The appearance might be fitly called "medalesque." How happens this? In reply, it may be pointed out that, in a kindred branch of art in all such engravings as are designed to assume the appearance of medallion-work or bassorilievo, the artist adopts a given expedient which is readily appreciable. Along the margins, between the half-tones and the darker outlines of the engraved work, there is always interposed a zone of absolute white, representative of the play of light upon the illuminated edges of the design.

Similarly, it will always occur that in the case of superposed portraits, and, à fortiori, in those in which

will be the international yacht race for the America's cup, held under the auspices of the New York Yacht Club. Great interest is being manifested by the yachtsmen and others throughout the whole country in the coming contest, while the patriotic pride of many wealthy men in the race has been aroused to such a pitch that they have ordered several new and costly yachts to be built for the protection of the cup. Even General Butler has dropped politics (and law) long enough to say that he wants to enter the ancient America in the race. England will send two very fast yachts, with the hope that one of them will walk away with the prize. These are the cutters Genesta and Galatea. The former is the favourite, and seems to be most feared by the Yankee yachtsmen.

It is understood that the match is to be three races, best two to win-one a triangle 40 miles, one over the New York Club course, and the third, if necessary, 20 miles and return, starting from Sandy Hook.

The Genesta was built by Messrs. Henderson Bros., at Partick-on-the-Clyde. She is 90 ft. over all, 81 ft. on the water-line, 15 ft. beam, 113 ft. depth of hold, and 131 ft. draught. Although originally she had only 60 tons of lead outside, she now carries 70 tons of lead on her keel.

In the conjointure of a photograph of Mr. Gladstone, of thirty years ante, with one of the present date, this effect is strikingly illustrated. In such case each portrait receives its due modicum of exposure.

She has also been recently coppered and fitted with new and heavier spars. Keelson stringers, frames, and strengthening plates are all of steel, while the planking is teak and elm.

With great accommodations beneath, the cutter's fittings are plain but substantial. The deck fittings present several novelties. The bowsprit comes over the steamhead in the centre of the yacht, with more than the usual difficulties in reefing it. To obviate this difficulty, one of the checks of the steel bits is hinged. This device permits of the bowsprit heel being swung round.

British fleets, and, although not always a winner, she proved herself to be, without doubt, the best "all round" boat in the kingdom.-Scientific American.

ILLUSIONS OF THE SENSES.

BY RICHARD A. PROCTOR.

(Continued from p. 63.).

the mast. The fore scuttle, oval in form, is a steel tube, round which the wire-fall of the bobstay tackle is coiled in easier turns than it would be belayed in the ordinary way. Just before the mast is a second scuttle, which accommodates the steward, and also the crew, on racing days. Behind the mast is a third scuttle, down which canvas can be lowered into the sail-room under the cabin sole.

The Genesta will be without any provisions for screening the weather spray besides a racing cabin. The Genesta has a fine saloon, fitted up lightly and elegantly, a ladies' cabin aft, and spacious accommodations for the crew, steward, and captain. The whole length of the yacht has been utilised, and the space obtained is remarkable. The Genesta is to be in charge of C. Carter, who is well known on the Clyde as a clever yacht sailor. She is owned by Sir Richard Sutton. Our engraving is taken from an instantaneous photograph, representing the Genesta ploughing through the water at full speed; it clearly shows the wave-line, and indicates the ease with which she parts the water. All through the yachting season last year this boat met the best of the

justifying Professor Le Conte's statement that no evidence is more misleading and fallacious than the evidence of the senses. So far from seeing being believing, one recognises that often we see an object wrongly tinted, wrongly illuminated, wrongly shaped, besides that fault of wrong apparent size which we might expect to recognise in the case of a sense like sight (which gives no direct evidence as to distance).

Taking this last defect of sight-evidence first, we note that the eyesight cannot really be said to delude us when it seems to tell us that--for example-the moon is as large as the sun. All that sight really tells us is that the sun and the moon occupy fields of view of the same apparent size. This, of course, is correct information as far as it goes, and the sense of sight cannot go further. But the sense of sight conveys false ideas to the mind sometimes even about apparent size.

Perhaps the most remarkable case of the kind-at any rate the most familiar is the apparent increase of the sun and moon in size as they approach the horizon. Singularly enough, Professor Le Conte does not regard this as an optical illusion; "the visual angle being in