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Art. IV. A Treatise on the Constructing and Copying (of) all Kinds of
Geographical Maps, &c.' By Thomas Dix, Master of North Walsham Academy. 8vo. pp. 36. price 3s. Scatchard and Letterman, and
Greenhill. “ IT must be obvious to every one,” says the author, “ that
the drawing of geographical Maps will imprint on the mind a more permanent idea of the relative situations and extent of the different kingdoms, seas, rivers, &c. &c. of the world, than any other method.” Hence, in schools where geography is taught, we believe that the practice of copying maps is pretty generally adopted : but there is room to apprehend, that the modes in which it is performed, are usually very inadequate to the advancement of scientific information. Boys may copy maps, as they do landscapes, by the eye; or may trace them through a glass, as Mr. D. informs us they do at Eton College ; without forming any conception of the use of meridian lines, or parallels of Jatitude, the accurate knowledge of which can alone give any just idea of the position of places on the globe. We are, therefore, very glad to see a treatise on this subject, adapted to the use of schools. “ My chief aim," Mr. D. observes, " is, to divest the subject of projection, of its formidable mathematical appearance, and to render it, and the minutiæ of mapping in general, more comprehensible and more pleasing to young students, by removing the difficulties which have hitherto attended them." "He has, accordingly, furnished clear descriptions of the principal methods of projecting maps of the world, hemispheres, and smaller portions of the globe, illustrated them by very neat and accurate diagrams, inserted tables of all the requisite calculations, explained instruments that facilitate the projection of the sphere, and descended to minute directions for the execution and completion of maps.
We heartily wish that this treatise may be introduced into every seminary where geography is taught, and into every family where that science forms a part of private tuition. Hoping that it will obtain an extensive circulation, we subjoin remarks on some passages, which may be improved by revision in future impressions, but require, at present, à degree of explanation or correction. We premise, that they are not of such a nature as to invalidate Mir. D.'s laudable exertions.
Some initiation into mathematical knowledge, is indis. pensable to an acquaintance with the globes ; and still more, (though this perhaps is little suspected) 10 a proper use of maps, which is of much more general importance. Mr. D. has evidently, according to his professed design, endeavoured to simplify the subject; but in some instances he has not accomplished this purpose. Persons who have only a superficial know
ledge of mathematics, will certainly not understand some terms which he has used without defining them. He has sacrificed too much to conciseness.
That his Treatise does not comprehend all kinds of geographical maps, is by no means censurable, otherwise than as it disagrees with the title-page. It is divided into four parts; the first of which relates to the projection of the entire globe, and its hemispheres; the second to that of smaller portions of the globe; the third to instruments useful in projecting the sphere ; the last to the drawing and mounting of maps.
We doubt whether this arrangement might not be more simplified by incorporating the first two divisions. Mercator's projection is just the same for the whole, or for any part of the world: and any portion of the globes, however small, that extends to both sides of the equator, should be delineated in a manner that would suit an entire hemisphere. Hence Mr. D.'s arrangement has rendered his work in some instances tautologous, in others defective.
Beside Mercator's, the only projections of the sphere which our author describes, are the Globular and the Stereographic. To the latter method, we think, he is far from doing justice, when he says, that “ the only advantage it has to boast of, is, that the parallels of latitude, and the meridians, intersect each other at right angles;" and that “ the globular is equal to it in point of facility, and much superior in point of correctness.” p. 6. The stereographic boasts of other advantages, which no different mode of projecting the sphere can claim. 1. It is a real perspective view of the globe, allowing only for the transposition of east and west. 2. It gives very nearly the genuine forms of each distinct country, the latitudes and longitudes being everywhere reciprocally proportionate. In the globular projection, on the contrary, it is only near the central meridian that countries preserve their proper figures: toward the circumference, they are stretched from north to south, to one-half more than their extent, in proportion to their longitude. We cannot therefore agree with the author, as to the comparative correctness of these two methods: and as to facility, we think that the stereographic has some advantage; the radii of its latitudinal circles, being much shorter than those of the globular projection, and consequently admitting of a larger scale for projection. In order, however, at once to avoid so great a disproportion in the size of countries as in the stereographic, and so much distortion of their form as in the globular, we would recommend to geographers a composite method of projection, constituting a medium between these extremes. This may easily be executed, by dividing the same semidiameter of a planisphere according to both the stereographic and the globular projections; and drawing the ineridians, and divisions of
latitude, through points at equal distances between those of the other two methods. That which we propose, will of course partake of the advantages and disadvantages of both the preceding: but it will, on the whole, produce a less distorted figure of the globe than either of them; and therefore we presume, may claim the preference.
Of six methods for projecting maps of particular countries, which are enumerated by Mr. D., the last two are merely partial applications of the general projections above-mentioned : and the first and fourth, which represent the divisions of latitudes, by straight lines, seem to us unworthy of notice. The second is the most accurate, and is easily practicable : we shall therefore quote his illustration of it, omitting his letters of reference.
To project a Map of Europe by this Method. Draw a base linc, in the middle of which erect a perpendicular. Assume a distance for 109. of latitude. Europe extends from 36°. to 72°. N. lat. From (the bottom of the perpendicular) set off six of the assumed distances to the top, which will be the N. pole. Number the distances 40, 50, 60, &c. From the (appermost) point (thus marked) describe arcs passing through the (other) points of division on the (perpendicular) which will be parallels of latitude. Divide the space assumed for 10°. of lat. into 60 parts, (as elsewhere directed.) Look into the table for the number of miles answering to 30°. which is 51, 96, say 52, which take from the scale. Set this distance off on the arc, at 30°, from the centre line both ways. Do the same for 40°. 50". 60°., &e. Through the corresponding divisions on all the arcs, draw curve lines; which wiil represent the meridians, Number the degrees of lat. and long. which will complete the diagram.'
The words included in parentheses are substituted for Mr. D.'s references to his plates, which, if consulted, will obviate any difficulty that our readers may find in the quotation, except that of drawing curve lines. We presume that the author means straight lines, forming together the appearance of a curve. His mode of expression here affords an instance of that kind to which we alluded above, in our third paragraph.
His third method, is “ when the parallels of lat, are curve lines as in the last method,” that is, segments of concentric circles; “. and the meridians right ones, as in the first.” Of this method, Mr. D. has supplied no farther illustration : but as it is that which is now inost commonly used, a few remarks on it may be acceptable. It is the same that we have formerly nientioned, as the conical projection.
This method, as applied to the plane of the meridian, was communicated to the Royal Society in 1758, by Mr. Murdoch; but it differs only in the extent of the latitudes, from what our author terms “ the globular projection on the plane of the Equator," which was used by Mercator, more than two centuries since. It is inferior in accuracy to the preceding method, proportionally
to the distance of latitude included in the map: but as, for convenience, it is very often adopted, we add, that, when the scale is so large as to render it difficult to sweep the concentric circles, the following inode may be substituted. From one of the higher, and one of the lower divisions of latitude on the central meridian line, raise perpendiculars half the length of a division of longitude in each of those parallels : join the two extremes by a right line; from which, at the points where it meets them, and at angles equal to those which it forms with the perpendiculars to the central line, draw lines equal to a whole division of longitude at each parallel : join the extremities of these; and proceed in the same manner, on each side of the central fine, to the extent of the map. At each intervening division of latitude, draw lines parallel to these. The chords which are thus formed, will be hardly distinguishable from the segments of circles which they would subtend; and are sufficiently accurate for every geographical purpose.
In the stereographic projection, the radii for some of the latitudinal circles are nearly thrice the length of the diameter of the sphere; and in the globular method, about four times the same length. Consequently, a principal difficulty in constructing maps on these projections, is that of procuring compasses large enough to strike the segments that are wanted. Mr. D. in the third part of his treatise, proposes to substitute two instruments for this purpose; which he calls “ the projecting peel and bevil.” “ They may be made," he observes, by any clever workman, if rightly explained to them (him). But those wlio wish it, may have them from the author, at il. each, or at 21. each, if superior workmanship is bestowed on them.” He has furnished descriptions and wooden engravings of these instruments, by which his readers may judge of the expediency of procuring them. For inaps on a large scale, if not very comprehensive, it may suffice, proportionally to enlarge the respective distances from any wellconstructed planisphere, and to bound them by right lines: but it is only when the map'extends to both sides of the equator, that a hemispherical projection can be recommended; and we think the stereographic method the most eligible to be used on such occasions.
Ofthe directions which Mr. D. has given for drawing maps, &c. it is enough to remark, that they are sufficiently clear and particular. It is, however, with a little surprise, that we find a compound colour substituted for the usual wash of verdigris, to distinguish water from land.
On the whole, we strongly recommend the use of this small treatise, to every student, and every teacher, of the science of geography. We conclude our remarks, which, from our opinion of the utility of the subject, have been extended
beyond beyond our usual limits) by suggesting the advantage which pupils may derive from copying maps in different methods of projection from the originals; for instance, transposing new discoveries, from Mercator's, to the stereographical projection. This would impress their minds with precise ideas of the different constructions of maps, and of the real forms of countries; while the drawings thus made on a large scale, might hereafter be rendered more complete, by the insertion of additional discoveries, whenever these were communicated to the public.
Art. VI. Hints towards forming the Character of a Young Princess.
concluded from Page 21. « TOWARD the close of the work,” say the Monthly • Reviewers, “ when treating more immediately on the subject of religion, amid much which we admire, and which we would strongly recommend, we observe some remarks thrown out, which too clearly betray the peculiar notions of the writer.” What these peculiar notions are, may be collected
from what is soon after added: .. " We must be allowed to observe, and we wish to do it without offence, that it is because she has not avowed her rigid religious tenets, and pressed them on her royal. pupil, that we have commended her work upon the whole. We should indeed deeply lament, to see the probable future Sovereign of these realms become the victim of religious enthusiasm, and countenancing principles, already perhaps too widely disseminated, and too powerfully supported.” Vol. 47. p. 187.
Now, for our part, we have perused with particular attention, those portions of Mrs. More's work which treat more immediately on the subject of Religion; and we cordially declare, that we deem every sentiment which she expresses, to be truly rational, as well as truly pious. We are well aware, that the Religion which Mrs. M. inculcates, is essentially different both from that of ancient Pharisees and that of modern philosophers; and to those who are resolved to rest satisfied, either with the dry punctualities of the former, or the baseless morals of the latter, it is most natural, that piety, when described as an inward and spiritual principle, pervading the whole soul, and influencing every part of the conduct, inward as well as outward, should appear rigid and enthusiastic.
That religion should occasionally occupy our thoughts, and that a suitable portion of our time should be allotted to its more immediate duties, would, no doubt, be readily allowed: but the extending it through the whole of life, as if it were to be ever restraining us, and ever keeping us on the stretch, carries with it, in the view of Mrs. M.'s censurers, a gloom, and a severity,