TRANSCRIBER'S NOTE: See Transcriber's Endnote for details of this
transcription.
THE
QUARTERLY JOURNAL
OF
SCIENCE,
LITERATURE, AND ART.
[Illustration: Royal Institution of Great Britain Emblem.]
JULY TO DECEMBER, 1827.
LONDON:
HENRY COLBURN, NEW BURLINGTON-STREET.
MDCCCXXVII.
CONTENTS.
_July—Oct._ 1827.
On the Beauties contained in the Ovals and in the elliptic
Curves, both simple and combined, generated from the same
Figure or Disk. By R. R. REINAGLE, Esq., R.A. 1
On the Art of forming Diamonds into Single Lenses for
Microscopes. By Mr. A. PRITCHARD. 15
Analysis of a newly-discovered Spring, at Stanley, near
Wakefield. By Mr. WILLIAM WEST. 21
Observations on the State of Naval Construction in this
Country. 25
On Malaria. No. II. By Dr. MAC CULLOCH, M.D., F.R.S., &c. 39
Dr. TURNER’s _Elements of Chemistry_, reviewed 60
Experiments on Audition. Communicated by Mr. C. WHEATSTONE. 67
On the Petromyzon Marinus 72
Observations upon the Motion of the Leaves of the Sensitive
Plant 76
Experiments on the Nature of LABARRAQUES’ Disinfecting Soda
Liquid. By M. FARADAY, F.R.S., Cor. Mem. Roy. Acad. Sci.
Paris, &c. 84
Hieroglyphical Fragments, with some Remarks on English
Grammar. In a Letter to Baron William Von HUMBOLDT. By a
Correspondent 92
Dr. MAC CULLOCH’s ‘_Malaria; an Essay on the Production and
Propagation of this Poison_,’ reviewed 100
Account of a New Genus of Plants, called _Reevesia_. By J.
LINDLEY, Esq., F.L.S., &c. &c. 109
ASTRONOMICAL AND NAUTICAL COLLECTIONS.
i. FRESNEL on the Undulatory Theory of Light 113
ii. Rule for the Correction of a Lunar Observation. By Mr.
W. WISEMAN, of Hull 135
‘_De l’Influence des Agens Physiques sur la Vie_. Par W. F.
EDWARDS, D.M.’ &c., reviewed 137
Account of Professor CARLINI’s Pendulum Experiments on Mont
Cenis 153
Analysis of ‘_Transactions of the Horticultural Society_.
Vol. vii. Part I.’ 159
_On the Recent Elucidations of Early Egyptian History_ 176
_Proceedings of the Horticultural Society_. 190
MISCELLANEOUS INTELLIGENCE.
I. MECHANICAL SCIENCE.
1 On the Combined Action of a Current of Air, and the
Pressure of the Atmosphere 193
2 Considerations relative to Capillary Action 194
3 Novel Use of the Plough 197
4 Discovery of Rocks under the Surface of the Sea 198
5 Paper to resist Humidity _ib._
6 Professor Amici’s Microscopes _ib._
II. CHEMICAL SCIENCE.
1 On the Specific Heat of Gases 200
2 On the Incandescence & Light of Lime 201
3 Evolution of Heat during the Compression of Water _ib._
4 On Electrical Excitation _ib._
5 Magnetic Repulsion 202
6 Diminished Solubility of Substances by Heat _ib._
7 Composition of Cyanic Acid 203
8 Iodous Acid 204
9 Manganesic Acid _ib._
10 Heavy Muriatic Ether, and Chloric Ether _ib._
11 Test for the Presence of Nitric Acid 205
12 Peculiar Formation of Nitre _ib._
13 Experiments on Fluoric Acid and Fluates _ib._
14 Crystallization of Phosphorus 206
15 Solution of Phosphorus in Oils _ib._
16 On the Inflammation of Powder, when struck by Brass 207
17 Cementation of Iron by Cast Iron _ib._
18 On the Preparation of Ferro-prussiate of Potash _ib._
19 Sulphocyanide of Potassium in Saliva 208
20 Decomposition of Sulphate of Copper, by Tartaric Acid
_ib._
21 Separation of Arsenic from Nickel, or Cobalt 209
22 Chemical Researches into Certain Ancient Substances 209
23 Compounds of Gold 210
24 On the Bitter Substance produced by the Actions of Nitric
Acid on Indigo, Silk, and Aloes _ib._
25 On the Existence of Crystals of Oxalate of Lime in Plants
214
26 Fallacy of Infusion of Litmus as a Test _ib._
27 Tests for the Natural Colouring Matter of Wine 215
28 Test of the Presence of Opium _ib._
29 Denarcotized Laudanum _ib._
30 Extraction of Morphia from Dry Poppy Heads 216
31 Preparation of Morphia _ib._
32 Easy Method of Obtaining Meconic Acid 217
33 On a New Vegetable Acid _ib._
34 Altheine, a New Vegetable Principle _ib._
35 Rheine, a New Substance from Rhubarb 218
36 On Dragon’s Blood, and a New Substance which it contains
_ib._
37 Purification of Madder 219
38 On Indigo, and Indigogene 220
39 On the Mutual Action of Ethers, and other Substances 221
40 Faraday’s _Chemical Manipulation_ _ib._
III. NATURAL HISTORY.
1 On the Supposed Influence of the Moon 222
2 Luminous Appearances in the Atmosphere _ib._
3 On the Determination of the Mean Temperature of the Air 223
4 Indelible Writing _ib._
5 Peculiar Crystals of Quartz _ib._
6 Native Iron not Meteoric 224
7 Native Argentiferous Gold 225
8 Prothéeïte, a New Mineral 226
9 Volcanic Bisulphuret of Copper _ib._
10 Fall of the Lake Souwando, in Russia 227
11 Vegetable Torpor in the Root of the Black Mulberry Tree
228
12 Method of increasing the Odour of Roses _ib._
13 Pine Apples _ib._
14 Mode of Condensing Vegetable Substances for Ship’s
Provisions 229
15 Rewards for the Discovery of Quinia, and for Lithotrity
_ib._
16 Upon the Gaseous Exhalations of the Skin 230
17 Effects of Galvanism in Cases of Asphyxia by submersion
_ib._
18 Recovery from Drowning 231
19 Preservation of Cantharides _ib._
20 Chloride of Lime in cases of Burns _ib._
21 Cure of Nasal Polypi 232
22 Bite of the Viper _ib._
23 Experiments on the Poison of the Viper _ib._
24 Destruction of Moles _ib._
25 On growing Salad Herbs at Sea 233
26 Chinese Method of Fattening Fish 234
Meteorological Diary for the Months of June, July,
and August, 1827 236
CONTENTS.
_Oct.–Dec._ 1827.
On the Means generally used with the Intention of curing a
Stoop. By the late Mr. SHAW 237
A Critique on the Aplanatic Object-glasses, for diverging
Rays, of Vincent Chevalier, ainé et fils. By C. R.
GORING, M.D. 248
On the Existence of Chlorine in the Native Black Oxide of
Manganese. By JOHN M’MULLEN, Esq. 258
Modern Improvements of Horticulture 261
FARADAY’s _Chemical Manipulation_, reviewed 275
Statistical Notices suggested by the actual State of the
British Empire, as exhibited in the last Population Census.
Communicated by Mr. MERRITT 283
On the Modern Ornaments of Architecture, &c. 292
_De l’Influence des Agens Physiques sur la Vie_. Par W. F.
EDWARDS, D.M. &c., reviewed 296
Experiments on Thought 308
Hieroglyphical Fragments, illustrative of Inscriptions
preserved in the British Museum, with some remarks on Mr.
Champollion’s opinions. In a letter to the Cav. San Quintino
310
On the Naturalization of Fish. By J. MAC CULLOCH,
M.D., F.R.S., &c. 320
WADD’s _Nugæ Chirurgicæ or, a Biographical
Miscellany_, reviewed 329
_Nugæ Canore, by_ UNUS QUORUM, reviewed _ib._
WADD’s _Mems., Maxims, and Memoirs_, reviewed _ib._
On Tic Douloureux 346
Remarks on some Quadrupeds supposed by Naturalists to be
extinct. By JOHN RANKING, Esq. 350
Description of a cheap and portable Instrument for enabling
Young People to acquire a knowledge of the Stars, or determine
their situation in the Heavens. By S. LEE, Esq. 371
CARUS’s _Introduction to the Comparative Anatomy of
Animals_, reviewed 377
_Comparative Value of the principal Varieties of Fuel, &c.,
by_ MARCUS BULL, reviewed _ib._
DANIELL’s _Meteorological Essays and Observations_,
reviewed _ib._
_Philosophical Transactions of the Royal Society for 1827_,
reviewed _ib._
_Practical Treatise on the use of the Blowpipe, by_ J.
GRIFFIN, reviewed _ib._
_Circle of the Seasons, and Practical Key to the Calendar and
Almanack_, reviewed _ib._
_Conversations on the Animal Economy_—reviewed _ib._
Notice of a New Genus of Plants discovered in the Rocky
Mountains of North America by Mr. DAVID DOUGLAS. By
JOHN LINDLEY, Esq. 383
A Description of the Aurora Borealis seen in London on the
Evening and Night of the 25th of September, 1827, with
Critical Remarks, &c. By E. A. KENDALL, Esq., F.S.A.
385
Proceedings of the Royal Society 424
Proceedings of the Horticultural Society 425
ASTRONOMICAL AND NAUTICAL COLLECTIONS
i. Ephemeris of the periodical Comet for its Return in 1828,
computed with the consideration of a resisting Medium. By
Professor ENCKE 428
ii. Elementary View of the undulatory Theory of Light. By
Mr. FRESNELL 431
iii. Remarks on the action of Corpuscular Forces. In a
letter to Mr. POISSON 448
iv. Calculations of Lunar Phenomena. By THOMAS
HENDERSON, Esq. 450
MISCELLANEOUS INTELLIGENCE.
I. MECHANICAL SCIENCE.
1 On the Adhesion of Screws 453
2 Improvement in Steam-engines _ib._
3 Improved Clock 454
4 Method of dividing Glass by Friction _ib._
5 Use of Soapstone in diminishing Friction 455
6 On peculiar Physical Repulsions _ib._
7 On the Magnetic Effects of Metals in Motion 456
8 Duration of the Effects of Light upon the Eye 457
9 On the Measurement of the Intensity of Light _ib._
10 On the apparent Decomposition of White Light by a
Reflecting Body when in Motion 458
11 On the Barometer _ib._
12 Easy method of reducing Barometrical Observations to a
Standard Temperature _ib._
13 Diamond Lenses 459
14 Sapphire Lenses for Single Microscopes _ib._
15 On a Method of securing and Preserving the Rowing Pins in
Boats 460
16 Cold Injection for Anatomical Preparation 461
II. CHEMICAL SCIENCE.
1 Extraordinary Experiments on Heat and Steam 461
2 On the Use of feeble Electric Currents, for effecting the
Combination of numerous Bodies 462
3 Crystallization of Metallic Oxides 465
4 On Bromine _ib._
5 Elementary Nature of Bromine _ib._
6 Quantity of Bromine in Sea-Water 466
7 Sale of Bromine _ib._
8 Preparation of Iodous Acid _ib._
9 On a peculiar Nitric Acid, and Sulphate of Potash 467
10 On certain Properties of Sulphur 468
11 On the Fluidity of Sulphur and Phosphorus at common
temperatures 469
12 Separation of Selenium from Sulphur 470
13 On a new Compound of Selenium and Oxygen—Selenic Acid 471
14 Preparation of Hyposulphuric Acid 473
15 Singular Habitude of Phosphoric Acid with Albumen 473
16 Economical Preparation of Deutoxide of Barium 474
17 Preparation of Aluminum—Chloride of Aluminum _ib._
18 Mutual Action of Lime and Litharge 475
19 New Chloride of Manganese discovered _ib._
20 Preparation of pure Oxide of Zinc 476
21 Deuto-Sulphuret of Cobalt _ib._
22 Separation of Bismuth from Mercury by Potassium _ib._
23 Sulphuret of Arsenic proportionate in Composition to
Arsenic Acid _ib._
24 New Double Chromates 477
25 Dobereiner’s finely divided Platina 477
26 New Metals 478
27 Analysis of Porcelain Pottery, &c. _ib._
28 On the Composition of simple Alimentary Substances 480
29 Preparation of Sulphate of Quinia and Kinic Acid, without
the use of Alcohol 482
30 Pure Narcotine prepared 483
31 Uncertain Nature of Jalapia _ib._
32 Preparation of pure Mellitic Acid
33 On a New Acid existing in Iceland Moss 484
34 Remarks on the Preparation of M. Gautier’s
Ferro-prussiate of Potash, as described in this Journal for
July, 1827 _ib._
III. NATURAL HISTORY.
1 Squalls of Wind on the African Shores 486
2 Destruction of an Oak by Lightning 487
3 Description of a Meteoric Fire-Ball seen at New Haven _ib._
4 Remarkable Meteoric Phenomenon 488
5 Aurora Borealis seen in the Day-time at Cannonmills 489
6 Aurora Borealis in Siberia _ib._
7 On the Presence of Ammonia in Argillaceous Minerals _ib._
8 Composition of Apatite 490
9 Burmese Petroleum Wells _ib._
10 Direction of the Branches of Trees _ib._
11 Effects of Light on Vegetation _ib._
12 Organization and Reproduction of the Trufle 491
13 Alteration of Corn in a subterraneous Repository 492
14 Quick Method of putting Insects to Death 493
15 Destruction of Snails by common Salt _ib._
16 Remarkable Hairy Man _ib._
17 Application of Remedies by Absorption from the Surface
_ib._
18 On the Strix Cunicularia, or Coquimbo Owl 494
19 Naturalization of Fish 496
20 Mode of keeping Apples _ib._
21 On the Cultivation and Forcing of Sea Kale 497
Meteorological Table 500
TO OUR READERS AND CORRESPONDENTS.
The drawings, illustrating the construction of a Blow-pipe, are not
sufficiently accurate to enable us to publish them. Our Correspondent
will observe that we have noticed another part of his letter.
We regret that we are unable to offer our Correspondent, upon the
subject of _Gas Works_, any precise information. There can be no
doubt that an atmosphere tainted by coal gas is injurious to animal
and vegetable life, but much will depend upon the extent of the
contamination, and other causes, of which our limits prevent mention.
To say nothing of danger from fire and from explosion, it has always
been matter of surprise to us that gas-works are tolerated by the
government in close and confined situations—that the Thames is
suffered still to be polluted with their offal, and that they are
sometimes placed close by the road side, (as at Brentford,) to the
nuisance of every one who passes. These matters want looking into.
Q. will find an answer to his question, in the “Gazette of Health”
for last July.
F. R. S. must remain unanswered till after St. Andrew’s Day.
Dr. Heinecken’s paper is disposed of as he desired.
Mr. BRANDE and Mr. FARADAY will commence their Lectures and
Demonstrations in Theoretical and Practical Chemistry, in the
Laboratory of the Royal Institution, _on Tuesday, the 9th of
October_, at Nine in the Morning precisely. Further particulars,
and a Prospectus, may be obtained at the Royal Institution, 21,
Albemarle-street, or by application to the Lecturers.
_In the Press_—A COLLECTION OF CHEMICAL TABLES, for the use of
Students, in Illustration of the Theory of Definite Proportionals, in
which are shewn the Equivalent Numbers of the Elementary Substances,
with the Weights and Volumes in which they combine, together with the
Composition of their most important Compounds, and the Authorities
for their Analysis. By WILLIAM THOMAS BRANDE.
THE
QUARTERLY JOURNAL
OF
SCIENCE, LITERATURE, AND ART.
JULY—OCT. 1827.
_On the Beauties contained in the Oval, and in the Elliptic Curves,
both simple and combined, generated from the same Figure or Disk_.
By R. R. Reinagle, Esq., R.A.
Being the subject of a Discourse delivered at the Royal Institution
of Great Britain.
After an apposite discourse to introduce the subject, the first
course taken, was to demonstrate the advantages of understanding the
right use of geometrical terms in our descriptions of the varieties
of shape, both in nature and art.
Every thing deserving the title of beautiful, and every grand object,
assume an outline of definite character: these are to be found in the
different classes of geometrical figures; the former in undulating
lines of elliptic curves, and grandeur in angular dispositions of
figure. All motion assumes a curved direction[1]. The primary and
leading object of the discourse was to prove the fact of original
beauty: and that a curved line was beautiful in an abstract point
of view, free from all associations. For this purpose there were
designed many diagrams on large black painted boards. [p002]
The explanation commenced with six or more parallel lines at equal
distances, and equal length, in an horizontal position to the eye of
the audience, _Fig._ 1; and another set of the same number of lines
drawn perpendicular, _Fig._ 2: these were demonstrated to possess not
the slightest character or principle of beauty in them, either as
separate lines, or collectively, however many.
[Illustration: _Fig._ 1.]
[Illustration: _Fig._ 2.]
[Illustration: _Fig._ 3.]
[Illustration: _Fig._ 4.]
The next diagram consisted of six or more radiating lines from
a centre, _Fig._ 3, and a corresponding number in an horizontal
direction, but of unequal quantities; they diminished like a flight
of steps, _Fig._ 4. It was then shown that the first means of
combining the six or more lines, which had been first drawn, so as
to please the eye, without creating any geometrical figure, was the
radiating principle. Our eye not only can tolerate that union of
lines, but receive the impression as pleasing in character; while all
lines parallel to each other, being right [p003] lines, and viewed
as a flight of steps, or pile of planks, opposite the observer, are
disagreeable. Upon the former principle it is, that the rays of the
sun, and rays of light generally, are so attractive and beautiful.
It is from this circumstance that right lines drawn in an inclined
position to the plane of the picture, derive an interest from the
angles engendered through the imagination.
[Illustration: _Fig._ 5.]
[Illustration: _Fig._ 6.]
[Illustration: _Fig._ 7.]
[Illustration: _Fig._ 8.]
To follow up the principle by regular steps, and to open a clear
view of the laws of beauty in lines, there were traced some inclined
right lines (_Fig._ 5), with a regular set of right angles upon it,
like the stems of leaves on each side. This exhibited no sort of
beauty, nor any other advantage than mere combinations of formal
angles. The next diagram (_Fig._ 6) was an inclined line as before,
with similar angular projecting stems, to which were added elliptic
curves on the upper side of each branch, that produced the form of a
leaf. _Fig._ 7 was another inclined line, having oval curves upon it.
Both these were shown to possess principles approaching to beauty, by
progressive advances in combination and original structure. _Fig._ 8
was an inclined line with the oval curves upon it; to which a similar
addition of elliptic curves were adjoined to the stems, [p004] as in
_Fig._ 6. This addition made a new advance towards beauty. _Fig._
9 commenced a more perfect principle of beauty, having an elliptic
stem with oval branches rising from it, as in the others. If to this,
the principle of gradation had been given, the eye would prefer it;
I mean, by a scale of increase from the top to the bottom of the
projecting stems: and if there had been superadded the external
contour of a lengthened egg, like the form of a sage leaf, we should,
step by step, advance into the region of beautiful character of
exterior shape. _Fig._ 10 is a retrograde, showing how uncongenial
angular forms are to curved lines, when producing ornament; at
least how little our eye can bear the angular projections from the
elliptic or oval turned stem. _Fig._ 11 was a curve of exactly the
same disk, with the same oval stems, to which a small serpentine
addition was made, expressing a leaf. Of all the last seven diagrams,
this abounded with the greatest portion of beautiful lines, and is
indisputably the most agreeable and beautiful. Combinations are like
numericals; many of these forms, placed together with judgment and
discretion, will attract us from the larger proportion of beauty
that meets the eye at once, like a head of beautiful hair: one hair,
however gracefully bent, cannot impress us like an entire lock of
the hair; nor will this [p005] curl charm us as the whole will on
the human head. We owe to construction and combination all our
pleasurable feelings of beauty: no person is allured by a single
feature of any species of objects: but a thousand, or a million,
arouses our anxious notice. Thus, the last diagram of the elliptic
stem and the foliage upon it, exhibited, by the continuity of curved
lines, the greatest approach to beauty, of all the figures presented
to the notice of the audience.
[Illustration: _Fig._ 9.]
[Illustration: _Fig._ 10.]
[Illustration: _Fig._ 11.]
[Illustration: _Fig._ 12.]
These preliminary designs opened the way for richer combinations; but
the subject affording such an immense field of variety, I confined
myself to the narrowest limits, and to one oval disk of seven inches
transverse diameter, from which seven different designs were shown on
paper. The first had a variety of serpentine lines placed at random,
all produced by the disk of the oval just named, and the confluent
lines of two such, placed side by side, or end to end, _Fig._ 12;
which oval disk was put upon the lines to prove the construction.
These lines, without expressing or forming any sort of figure,
exhibit a set of elegant curves, of varied quantities of convex and
concave, with which our eye will be more pleased than any set of
right lines similarly distributed, as in _Fig._ 13, which follows.
[p006]
[Illustration: _Fig._ 13.]
[Illustration: _Fig._ 14.]
Two other diagrams were placed before the company, each a circle of
12 ovals, from the same disk, revolved upon an axis, resting upon one
end of the transverse diameter, (the length-ways of the oval,) which
figure in the skeleton was a duodecagon. _Fig._ 14 is one of the
diagrams; the ovals folding regularly over each other. By suppressing
the continuity of the oval disk, where the lines would traverse, a
very pleasing figure [p007] is created. It may be easily converted
into foliage, and can be amazingly varied in principle, by having
fewer ovals, and making them revolve upon an arm or continuation of
a line from the transverse diameter. _Fig._ 15 is the same diagram,
with all the oval lines described, which forms a figure of elegant
intricacy; each member, or curvilinear subdivision, assumes a most
agreeable shape: the whole, at the first sight, does not carry the
evidence of being generated from the same disk. These agreeable
figures may be varied to an extraordinary extent: the two that were
presented were mere examples of some of the numerous changes that any
given oval disk may create.
[Illustration: _Fig._ 15.]
[Illustration: _Fig._ 16.]
[Illustration: _Fig._ 17.]
The objects next presented, were three vases of very dissimilar
appearance, all produced from the same diagram of the oval; each in
a separate drawing. The first was like a Greek vase with handles;
its character established by employing certain proportions of
quantities, in seven parts. The body has four parts, the foot or
pedestal one; the neck two. The handles were regulated in the
position and projection by lines drawn from the bottom of the vase,
through the ovals which compose the outline of the two sides; and
passing through the transverse diameter. These handles were made
from an oval that was the length of half the line of the transverse
diameter, _Fig._ 16. The skeleton of angles that [p008] govern the
shape of this vase, is a very pretty figure of itself. The form does
not proceed from any caprice of irregularity, but is consistent
with rational organization, and symmetrical proportions. The figure
of the plate sufficiently describes the mode of making the diagram
without entering into the detail. _Fig._ 17 represents a tazza with
handles: the same disk is apparent, by the dotted lines that made the
first vase. The ovals [p009] are placed right and left of a central
perpendicular line, dividing the cup in two parts; the transverse
diameters meet in one line parallel to the base of the tazza; a
dotted outline expresses the angular position of the handles: the
concave lip of the tazza is made by the same oval disk, whose
transverse diameter leads to the under line of the folding edge of
the cup. The leg of the tazza is produced by the same small disk
that served for the handles of the first vase. The body of the vase
and the leg form two equal parts; the whole upper extent ought to be
seven parts, so that it is seven and two[2]; the width of the base
of the leg measures two parts, and the altitude three, of the seven
parts. These proportions cannot produce any other than agreeable
appearances, apply them as we may.
[Illustration: _Fig._ 18.]
The third vase, exhibited an Hebe cup, with a handle, which presented
a totally different appearance in form to the two previous ones. It
was proportioned by similar principles: the larger disk made the
body, inclined right and left upon the end of the oval. The neck and
the leg were both made from the smaller oval disk; the dotted lines
to the ovals of the leg sufficiently show the fact. The handle and
concave lip of the cup were made by an application of the same disk.
The altitude contained four parts. The body two parts, the leg one
part, and the neck one other part; the handle rises one-eighth above:
every portion of this figure is created by the two disks previously
named. The foliage rises from below and descends from above,
one-fourth of the whole height of the body [p010] to the commencement
of the concavity of the neck, where the beading runs round.
I remarked, that by adhering to regular proportional quantities of 1
and 2, 3 and 5, 2 and 5, 7 and 5, 7 and 2, &c., and using elliptic
disks or curves, very great beauties are derived.
[Illustration: _Fig._ 19.]
[Illustration: _Fig._ 20.]
A skeleton of the tazza in angles was drawn on a black painted board,
together with oval disks placed upon those lines, which clearly
demonstrated the whole system of the construction. The explanation
of these various diagrams necessarily involved a circumstantial
description of each created figure, which were thoroughly analysed.
Quantity and variety were particularly dwelt upon, as absolutely
necessary to the production of perfect beauty; equalities being
unfriendly to that symmetry which accords with nature. Some other
diagrams were drawn, to show the inelegant appearance of radiating
lines from the concave or convex half of an oval or an ellipse,
_Fig._ 19: but by drawing another convex half of an oval, and placing
those lines as tangents, greater beauty was formed by the alternate
changes and varieties of inclination of each tangent, _Fig._ 20. This
was capable of an immediate adaptation to elegant vegetation; [p011]
a few convex and concave elliptic curves added to each tangent,
produced an ear of barley, or an ear of rye, the elegant construction
of which, is rarely noticed in our remarks on nature, _Fig._ 21.
[Illustration: _Fig._ 21.]
The discussion on these various designs being concluded, some
important compositions of three great and renowned painters were
produced, to corroborate what had been advanced in support of the
native beauty of the oval and ellipse. Raphael’s grand composition of
the dispute on the Sacrament is in three grand oval curves.
The Doctors of the Church on the ground plan are ranged in an oval
convex line; and the heavenly Choirs engage two concave oval shapes
of the same proportion, but of unequal quantities. This is also a
proof of a composition of parts, bearing two to one.
The facility of expressing such a composition, by being geometrical,
is extremely easy.
The second illustration was the Aurora, by Guido, of the Aldobrandini
palace. This was pointed out to depend upon an oval curve, and
continued curvilinear details: the striking beauty of this fine
composition is owing to its great and simple elliptic curve, which
includes the whole group; the attendant hours have the principle of
radiating to a centre of the oval: thus harmonizing and uniting forms
congenial both to principle and nature.
The third grand composition was by Rubens, the Coronation ceremony of
Mary de Medicis, one of the grand Luxemburg pictures.
This very fine composition is contained in an oval concave [p012]
curve, and the figures in several points radiate to a centre. Some
of the group pass the great leading line, but only to the degree
and with the licence that a genius can effect, which destroys the
too great, and the too palpable construction of the composition.
The allegorical figures of Fame and Genius hovering over the royal
personage, establish a centre to the oval, which prevents a void that
would have been weak in the composition.
Three designs were next produced from Etruscan vases, to carry
the evidence further, and to show the original source of the
demonstrations of beauty in Grecian art. One was a charioteer driving
a pair of magnificent horses of the highest spirit, _Fig._ 22. The
composition is elliptic, and serpentine within.
[Illustration: _Fig._ 22.]
The youthful conductor of the steeds is in a crescent or boat-shaped
car, and his form is elegantly bent to meet the action and motion;
his mantle flows behind in curved and serpentine folds, expressing
the wind occasioned by the velocity of action. A more graceful or
beautiful group and composition cannot be imagined.
The next design was a female in an elegant and very gentle serpentine
action of the figure. Every portion of the outlines was elegant,
from the varied succession of convexity and concavity; not a single
angle could be traced throughout the whole [p013] of this beautiful
creature. She held in her left arm a very handsome oval vase; and in
the other a sort of scarf with ribands, all serpentine in form. By
her side is placed a young man selected from another Etruscan design.
[Illustration: _Fig._ 23.]
The line of this figure was the outline of an ellipse; it is
perfection in every respect; and the grace was shown to depend upon
gentle curved lines of convex and concave, alternately blended, and
confluent. The motion of ships at sea is described in gentle elliptic
curves; the wings and plumage of birds assume the oval and elliptic
curves; all the fibres of their feathers have that form; some
flattened, others more rounded: the pine-apple and numberless fruits
have all an oval character of outline.
Many take the character of eggs, pointed at one end, and large and
blunt at the other extremity. The leaves of trees [p014] have the
oval shape more than any other; the bend of the branches, and the
whole external form of many trees is oval.
There is no form of created things which may not be found to
correspond in all its dependent shapes to ovals and ellipses of
various disks, even objects which at first sight seem to contradict
the possibility of meeting this system.
The lecture was closed by some extracts and quotations from Lomazzo,
Dryden, Hogarth, Du Fresnoy, and the Abbé du Bos; the tendency
of which was to show that lines had been mentioned, and had been
written upon without any explanation given that could lead to certain
conclusions. That all these authors attributed to supreme genius
alone, and something of the divinely inspired character in artists,
the power to produce those indescribable lines that affect the human
eye so strongly. These lines I described as belonging to the oval and
the ellipsis, and the confluent lines by conjunction and combination;
that these indescribable lines, which from Plato to Dryden had never
been detected or obtained a name; that puzzled all equally alike, are
those alone I attempted, and I believe proved in this lecture, to be
the elliptic combinations.
I stated that the great Greek artists confined themselves to certain
rules and principles of unerring consequences in the production
of beauty, grace, or grandeur in their figures; that all their
compositions depended upon the same species of rule and order. I
pointed out, that fashion is in all countries the destroyer of
taste, that it unfits the mind for fixed principles; that where it
dominates, _there_ taste will be always fluttering and never settle,
nor have a sure dominion. The Greeks, having no such vile tormentor
to divert them from a pure course in their progress, arrived at the
summit of perfection in every scientific pursuit, by following sure
principles as their guides, and by never abandoning a path traced by
nature, and matured by the most sublime philosophy.
FOOTNOTES:
[1] A great number of geometrical diagrams were exhibited, from a
single line, to angles, squares, oblongs, circles, ovals, cones,
cylinders, spiral lines, and various serpentine lines, &c.
[2] The whole extent of the tazza, including the projection of the
handles, should be seven parts; and the height of the vase two of
such seven parts.
[p015]
_On the Art of forming Diamonds into single Lenses for
Microscopes_.—By Mr. A. Pritchard.
[Communicated by Dr. GORING.]
Of the various improvements in Microscopes originated by Dr. Goring,
that which he conceives to be the most important is the construction
of single magnifiers from adamant. The details relative to this novel
class of instruments, I have been induced to lay before the public.
Single microscopes naturally aplanatic, or at least sufficiently so
for practical purposes, possess an incontestable superiority over
all others, and must be recognised by the scientific as verging
towards the ultimatum of improvement in magnifying glasses. The
advantages obtained by the most improved compound engiscopes over
single microscopes resolve themselves into _the attainment of vision
without aberration with considerable angles of aperture_; but against
this must be set the never-to-be-forgotten fact, that they only show
us a _picture of an object instead of nature itself_; now a Diamond
Lens shows us our real object without any sensible aberration like
that produced by glass lenses; and we are entitled, I think, to
expect new discoveries in miscrosopic science, even at this late
period, _from very deep single lenses of adamant_[3]. I shall not
fatigue my [p016] readers by describing the difficulties which were
encountered in the prosecution of the design of making diamond
lenses. Nature does not seem to permit us to produce any thing of
surpassing excellence without proportional effort, and I shall simply
say, that in its infancy the project of grinding and polishing the
refractory substance of Adamant was far more hopeless than that of
making achromatic glass lenses of 0.2 of an inch focus. I conceive it
just to state that Messrs. Rundell and Bridge, of Ludgate-hill, had,
at the time of the commencement of my labours, many Dutch diamond
cutters at work, and that the foreman, Mr. Levi, with all his men,
assured me, that it was impossible to work diamonds into spherical
curves; the same opinion was also expressed by several others who
were considered of standard authority in such matters.
Notwithstanding this discouragement, in the summer of the year 1824,
I was instigated by Dr. Goring (at his expense) to undertake the
task of working a diamond lens: (being then under the tuition of Mr.
C. Varley, who was however at that time absent.) For this purpose,
Dr. G. forwarded to me a brilliant diamond, which, contrary to the
expectation of many, was at length ground into a spherical [p017]
figure, and examined by Mr. Levi, who expressed great astonishment
at it, and added that he was not acquainted with any means by which
that figure could have been effected: unfortunately this stone was
irrecoverably lost. Mr. Varley having returned from the country,
becoming now thoroughly heated with the project, permitted me to
complete another diamond, which had been presented to me by Dr. G.:
this is a plano-convex of about the 1/20th of an inch focus: it was
not thought advisable to polish it more than sufficed to enable us
to see objects through it, because several flaws, before invisible,
made their appearance in the process of polishing. In spite of all
its imperfections, it plainly convinced us of the superiority which
a _perfect diamond lens_ would possess by its style of performance,
both as a single magnifier and as the object lens of a compound
microscope. After the completion of my articles with Mr. V., being
entirely under my own command, I devoted some time to the formation
of a perfect diamond lens, and have at length succeeded in completing
a double convex of equal radii of about 1/25th of an inch focus,
bearing an aperture of 1/30th of an inch with distinctness on opaque
objects, and its entire diameter on transparent ones; it was finished
at the conclusion of last year. The date of its final completion
has by many been considered a remarkable epoch in the history of
the microscope, being the first perfect one ever _made_ or thought
of in any part of the world[4]. I think it sufficient to say of
this adamantine lens that it gives vision with a trifling chromatic
aberration, but in other respects exceedingly like that of Dr. G.’s
Amician reflector, but without its darkness: for it is quite evident
that its light must be superior to that of any compound microscope
whatever, acting with the same power and the same angle of aperture.
The advantage of seeing an object _without aberration_ by [p018]
the interposition of but a single magnifier, instead of looking at
a picture of it (however perfect) with an eye-glass, must surely be
duly appreciated by every person endowed with ordinary reason. It
requires little knowledge of optics to be convinced that the simple
unadulterated view of an object must enable us to look farther into
its real texture, than we can see by any artificial arrangement
whatever; it is like seeing an action performed instead of a scenic
representation of it, or being informed of its occurrence by the most
indisputable and accurate testimony.
Previous to grinding a diamond into a spherical figure, it is
absolutely necessary that it should be ground flat, and parallel
on both sides (if not a Laske or plate diamond), so that we may be
enabled to see through it, and try it as opticians try a piece of
flint glass: without this preparatory step, it will be extremely
dangerous to commence the process of grinding, for many diamonds
give a double, or even a species of triple refraction, forming
two or three images of an object; this polarization of the light,
arising from the primitive form of the crystal, of course totally
unfits them for making lenses[5]. I need not observe, that it must
be chosen of the finest water, and free from all visible flaws when
examined by a deep magnifier. It was extremely fortunate for diamond
lenses that the first made was free from the defect of double vision,
otherwise diamonds _en masse_ might at once have been abandoned as
unfit for optical purposes. The cause why some stones give single
vision, and others several peculiar refractions, may also arise
from different degrees of density or hardness occurring in the same
stone. Diamond-cutters are in the habit of designating stones male
and female, sometimes a _he_ and _she_ (as they have it) are united
in the same gem,—their _he_ means merely a hard stone, and their
_she_ a soft one. When a diamond which will give several refractions
is ground into a spherical figure and partially polished, it is seen
by the microscope to exhibit a [p019] peculiar appearance of an
aggregation of minute shivery cristallized flaws, sometimes radiated
and sometimes in one direction, which can never be polished out:
I believe I could disstinguish with certainty a bad lens from a
good one by this phenomenon without looking through it[6]. Precious
stones, from their crystalized texture, are liable to the same
defects for optical purposes as diamonds.
Having ascertained the goodness of a stone it must next be prepared
for grinding; it will in many cases be advisable to make diamond
lenses plano-convex, both because this figure gives a very low
aberration, and because it saves the trouble of grinding one side
of the stone. It must never be forgotten, that it may be possible
to neutralize the naturally low spherical aberration of a diamond
lens by giving it an improper figure, or by the injudicious position
of its sides in relation to the radiant. When the lens is to be
plano-convex, cause the flat side to be polished as truly plane as
possible, without ribs or scratches; for this purpose the diamond
should be so set as to possess the capability of being turned round,
that the proper direction with respect to the laminæ may be obtained:
when the flat side is completed, let the other side be worked against
another diamond, so as to be brought into a spherical figure by the
abrasion of its surface. When this is accomplished, a concave tool of
cast iron must be formed of the required curve in a lathe, having a
small mandril of about 2/10ths of an inch in diameter, and a velocity
of about 60 revolutions per second! The diamond must now be fixed
by a strong hard cement (made of equal parts of the best shell lac
and pumice-stone powder, carefully melted together without burning)
to a short handle, and held by the fingers against the concave tool
while revolving. This tool must be paved by diamond powder, hammered
into it by an hardened steel convex punch: when the lens is uniformly
ground all over, very fine sifted diamond-dust carefully washed in
oil must be applied to another iron concave tool (I may here remark,
that of all the metals which I have used for this purpose soft cast
iron is decidedly to be preferred): this tool must [p020] be supplied
with the finest washed powder till the lens is completely polished.
During the process of grinding, the stone should be examined by a
magnifying lens, to ascertain whether the figure is truly spherical;
for it sometimes will occur that the edges are ground quicker than
the centre, and hence it will assume the form of a colloid, and thus
be rendered unfit for microscopic purposes.
The spherical aberration of a diamond lens is extremely small, and
when compared with that of a glass lens the difference is rendered
strikingly apparent. This diminution of error in the diamond arises
from the enormous refractive power possessed by this brilliant
substance, and the consequent increase of amplification, with _very
shallow curves_. The longitudinal aberration of a plano-convex
diamond lens is only 0.955; while that of a glass one of the same
figure is 1.166; both numbers being enumerated in terms of their
thickness, and their convex surfaces exposed to parallel rays. But
the indistinctness produced by lenses, arises chiefly from every
mathematical point on the surface of an object being spread out into
a small circle; these circles, intermixing with each other, occasion
a confused view of the object. Now this error must necessarily
be in the ratio of the areas of these small circles, which being
respectively as the squares of their diameters, the lateral error
produced by a diamond lens will be 0.912; while that of a glass lens
of like curvature is 2.775; but the magnifying power of the diamond
lens will be to that of the glass as 8 to 3, their curves being
similar; (or, in other words, the superficial amplification of an
object; with the perfect diamond lens before mentioned, is 22500
times, while a similar magnifier, made of glass, amplifies only 3136
times, reckoning 6 inches as the standard of distinct vision:) thus
the diamond will enable us to gain more power than it is possible to
procure by lenses of glass, for the focal distance of the smallest
glass lens which can be well made is about the 1/80th of an inch,
while that of a diamond, worked in the same tools, would be only the
1/200th of an inch.
If we wish to compare the aberrations of the two lenses when of equal
power, the curvature of the glass must be increased; and as it is
well known the lateral aberration increases inversely as the square
of the radius, (the aperture and position remaining [p021] the same,)
the aberration of the diamond lens will only be about 1/20th of that
produced by the glass one, even when their thickness is the same; but
as the curvature of the diamond is less, the thickness may be greatly
diminished.
The chromatic dispersion of the adamant being nearly as low as that
of water, its effects in small lenses can barely be appreciated by
the eye, even in the examination of that valuable class of test
objects, which require enormous angles of aperture to be rendered
visible, which it is evident must be of easier attainment by diamond
magnifiers than by any other sort of microscope.
A mathematical investigation of the spherical aberration of the
diamond when formed into lenses, I hope to lay before the public at
a future opportunity. The comparative numbers here taken from the
longitudinal aberration are, I believe, sufficiently accurate for
practical purposes.
_18, Picket-Street, Strand_.
FOOTNOTES:
[3] It seems generally admitted that, within a certain range of
power not exceeding that of a lens of 1/20th of an inch focus,
the beauty and truth of the vision given by the new compound
microscopes cannot be equalled by that of any single instrument,
at least of glass. It is no less true, however, that the _picture_
of the compounds, however perfect, is not like a real object, will
not admit of amplification beyond a certain point with advantage.
Under the action of very deep eye-glasses, the image of opaque
objects especially, first loses its strong, well-determined
outline—then grows soft and nebulous, and finally melts away in
shadowy confusion. Let the experiment be made of raising the power
of a compound up to that of a 1/60th inch lens—then try it against
the single microscope of that power (having, of course, the utmost
opening the nature of the object viewed will permit). The observer,
if open to conviction, will soon be taught the superior efficacy
of the latter—for it will show the lines on the dust of Menelaus
with such force and vivacity, that they will always be apparent
_without any particular management of the light—nor can their image
be extinguished by causing the illumination to be directed truly
through the axis of the lens (as it always may in the compounds)_.
A due consideration of the teeth and inequalities on the surface
of a human hair, together with the _transverse connecting fibres
between the lines on the scales of the curculio imperialis_, viewed
as opaque objects, will suffice to complete the illustration of
the subject; though the last object is not to be well seen by that
kind of light which is given by silver cups—and a single lens of
1/60th inch focus can of course have no other. The effectiveness and
penetrating faculties of simple magnifiers are invariably increased
by an accession of power however great—that of compounds seems to
be deteriorated beyond certain limits. An opinion may be hazarded
that the achromatics and reflectors yet made _do not really surpass
the efficacy of equivalent single lenses, even of glass, when
their power exceeds that of a_ 1/20th lens, from 1/20th to 1/40th
the vision may be about equal—but from 1/40th upwards infinitely
inferior.
The superior light of the single refraction can need no comment—and
it is evident that there must be a degree of power at which that
of the compounds will become too dim and feeble for vision,—while
that of the single instrument will still retain a due intensity.
For these reasons it is conceived that the close and penetrating
scrutiny of lenses of diamond of perhaps only the 1/200th inch
focus, and an equal aperture (which their very low aberration would
easily admit of,) must enable us to see further into the arcana of
nature than we have yet been empowered to do. Glass globules of
1/200th inch focus and indeed much deeper have been executed; but
the testimony of _lenses_ of diamond would certainly be far more
respectable, and is at least worthy of trial and examination.—C.R.G.
[4] In Dr. Brewster’s treatise on new Philosophical instruments,
Book 5, chap. 2, Page 403—Account of a new compound Microscope for
objects of Natural History—is the following passage: “We cannot
therefore expect any essential improvement in the single microscope,
unless from the discovery of some transparent substance, which like
the diamond combines a high refractive with a low dispersive power.”
From which it seems certain that the Doctor never contemplated the
possibility of working upon the substance of the diamond, though he
must have been aware of its valuable properties.
[5] There are fourteen different crystalline forms of the diamond,
and of this number, from the laws which govern the polarization of
light, the octohedron and truncated cube are probably the only ones
that will give single vision. It is unfortunately very difficult
to procure rough diamonds in this country, so we are compelled to
use stones already cut, and to subject them to trial in the way
mentioned in the text.
[6] As many amateurs of science might take an interest in the
inspection of the peculiar effect these lenses have on transmitted
_light_, I shall be happy to exhibit them, as also the perfect lens.
_Analysis of a newly-discovered Spring, at Stanley, near
Wakefield_.—By Mr. William West.