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‹Better GutenbergAccount of the Skerryvore LighthouseDiagrams illustrative of the Table, Appendix, No. IV · 20 of 24Contents›

Account of the Skerryvore Lighthouse

by Alan Stevenson

20 of 24 · Contents · Download EPUB

Diagrams illustrative of the Table , Appendix, No. IV.

Fig. 114.

References to table

Fig. 115.

References to table

Fig. 116.

References to table

Fig. 117.

References to table

APPENDIX, No. IV.
TABLE OF THE ELEMENTS OF CATADIOPTRIC ZONES SUITED FOR LIGHTS OF THE FIRST ORDER IN THE SYSTEM OF AUGUSTIN FRESNEL.

Note.—The Six co-ordinates of the Generating Triangle of each Zone in these Tables have the Focus of the Principal Lenses of the System for their origin; it being considered more convenient, in executing the necessary protractions, preparatory to the construction of the grinding apparatus, at once to refer the whole of the grinding machinery to the axis of the apparatus. To prevent the appearance of any inconsistency, however, it is proper to mention, that the radiant points of the series of Zones, do not exactly coincide with the Focus of the Lenses nor with each other; and that to avoid the parallax which the distance of the radiant points from the origin of the co-ordinates would occasion, it is necessary to make some corrections upon the linear dimensions, so as to find the line corresponding to the angles θ, ξ, and the distance Δ. In the Hyperpyral series, which stands above the flame, the Zones have the radiant point 10 millimetres above the Focus of the Lenses, and each y of this series, therefore, requires a reduction of that quantity; while the x remains unchanged. In the Hypopyral series, which stands below the flame, the Focus or radiant points of each Zone, varies its place in the flame, moving upwards as the Zone is lower, so that the line joining the Zones and the Foci, revolves as a radius vector round a point between them. In this way, the x’s remain unaltered; but the y’s will be lengthened successively by the addition of 10, 14, 19, 25, 32, and 40 millimetres. As these Tables contain the dimensions of Zones which are intended as an addition to the apparatus of Fresnel, I have adopted the metric scale, so as to render them at once applicable to the existing protractions of that system. It is only necessary to add, that the conversion of millimetres into imperial inches, is easily effected by adding the log. millimetres to the log. ̅2·59516, the sum being the log. of the equivalent of the first term in imperial inches.
θξBCA,ABC,BAC,BA,BC,AC,Co-ordinates of the Apices of the Generating Triangle, in Millimetres, having the Axis of the System cut by the horizontal plane of the focus of the Annular Lenses, for its origin. (Fig. 116.)Inclination of the Sides of the Generating Triangle to the Vertical Axis of the System. (Fig. 117.)AB, Reflecting Surfaces (convex). (Fig. 115.)AC, Outer Refracting Surfaces (concave).BC, Inner Refracting Surfaces (convex).Δ,
No.
of
Zone.		Inclination
of Ray FC
to the
Vertical
Axis
of the
System.		Incidence
of
Ray FC
on Side
BC of
Zone.		Obtuse
Angle
of the
Generating
Triangle
of the
Zone.		Angle of
Generating
Triangle
of Zone.		Angle of
Generating
Triangle
of Zone.		Reflecting
Side of
Zone in
Millimetres
being
Chord
of the
Arc b A.		Inner
Refracting
Side of
Zone in
Millimetres.		Outer
Refracting
Side of
Zone in
Millimetres.		AyAxByBxCyCxInclination
of AB.		Inclination
of BC.		Inclination
of AC.		Radius of
Curvature
in
Millimetres,
XA or X b.		Horizontal
distance
of centre
of
curvature
X from
the axis
of the
System in
Millimetres
= OX.		Vertical
distance
of centre
of
curvature
X below
the outer arris of the
Zone at A in
Millimetres
= OA.		Inclination
of the
Two Radii
in
A and B.		Inclination
of the
Outer
Radius
in A
to the
Vertex.		Radius of
Curvature
in
Millimetres.		Horizontal
distance
of centre
of
curvature
from the
axis
of the
System in
Millimetres.		Vertical
distance
of centre
of
curvature
above
the outer
arris of the
Zone at A
in
Millimetres.		Inclination
of the
Radii
in A
and C.		Inclination
of the
Outer
Radius
at A to the
Vertex.		Radius
of
Curvature
in
Millimetres.		Horizontal
distance
of centre
of
curvature
from the
axis of
the System
in
Millimetres.		Vertical
distance
of centre
of
curvature
below the
outer arris of the
Zone at A
in
Millimetres.		Inclination
of the
Radii in
C and B.		Inclination
of the
Outer
Radius
in C to
the Vertex.		Distance
of C
from the
Focus for
the Zones,
in
Millimetres
= FC.		No.
of
Zone.
(Fig. 114.)(Fig. 114.)(Fig. 114.)(Fig. 114.)(Fig. 114.)(Fig. 115.)(Fig. 115.)(Fig. 115.)(Fig. 114.)
°′″°′″°′″°′″°′″°′″°′″°′″°′″°′″°′″°′″°′″°′″
HYPER-
PYRAL
SERIES
OF
ZONES.		-16045384406091172640314810304510160·33192·37995·209593·369986·260551·481831·497525·000920·0007451197320314406098750·193194·768466·88102591438114000·003825·312817·77121504512564000·002021·193777·07119241558471054·341
25655384128101160042323201312717155·43090·24993·011663·063957·410617·423808·832593·369895·8167255277432324128108253·903306·807909·9410445163211...3923·652683·5511956475152...1918·373797·40117341448411069·022
35305383848291143120331730321110151·55188·72991·434734·313926·908684·958783·619663·063869·6057059397542513848297850·303411·757446·6710622182711...4015·062542·3111834503214...1813·603815·77116161339011087·523
44915383607091125840340436325644148·58087·76890·424807·357894·222754·267755·451734·313840·9206903537651313607097527·083514·227056·3910751202211...4098·542394·2311742531400...1707·553831·95115261230461109·854
54525383324191112300345307334353146·44487·33289·947882·445858·858825·547723·921807·357809·3376708127758413324197275·233617·566730·6610912221711...4173·082239·6411718555702...1599·723846·04115041123471136·145
64135383040051094432354257343231145·08787·40389·986959·847820·325899·011688·608882·445774·4266512367904273040057082·173723·816459·6311025241211...4237·702078·8211720584115...1489·623858·14115081017591166·576
73745382754341080330363401352229144·48187·97790·5361039·852778·108974·899649·051959·847735·7306317038008562754346944·093835·236234·9311131260711...4291·451912·1811748612632...1376·713868·3011536913161201·467
83355382507521062006372611361343144·60989·06091·6041122·784731·6451053·471604·7301039·852692·7426121358112142507526857·033954·676052·3611230280211...4333·301740·1211844641246...1260·383876·5911632809301241·168
93005382220071043436381923370601145·47690·67193·2091209·000680·3221135·025555·0591122·784644·9005926088214292220076817·874081·705902·5311320295711...4362·261563·1012006665950...1139·943883·0311756706331286·159
102615381931251024712391327375921147·08992·84395·3841298·900623·4331219·892499·3541209·000591·5565730468315471931256824·464226·675795·6811405315211...4377·241381·6312158694736...1014·673887·6611948604191336·9910
112225381641541005810400714385436145·36193·00095·4131390·290559·3781308·183439·4281288·900531·9635536308416161641546880·524385·635718·5211237334711...4376·721194·9412200723706...884·953893·0011956503461394·3611
12184202135626991050405953394917143·36293·00095·2711482·755490·1691398·007374·5381390·290467·2175345438514241356266980·894558·835672·6411036353859...4360·701009·4112112752258...752·783897·3211956405381457·2212
13150603111604972607415103404249141·37993·00095·1271576·048415·9911488·972304·6111482·755397·4035158538610021116047123·054747·245654·9210815372659...4329·31828·1912146780302...618·373901·1011956310001525·4313
°′″°′″°′″°′″°′″°′″°′″°′″°′″°′″°′″°′″°′″°′″
HYPO-
PYRAL
SERIES.		-15949164327361170556315837305527159·36992·00094·806593·815985·212550·915831·725525·000920·0007423037338204327368674·743243·488375·64103091505224000·003855·832785·60121284551404000·002002·523781·9111904154208——1
25548554042011153507324443314009158·05192·00094·783682·731981·810634·862831·183610·872920·0007222107453064042018419·603456·448047·7210431170532...3983·212644·1612128483715...1918·553801·5111904142722——2
35148333754321140031332816322713156·59292·00094·719779·464978·917726·831830·694704·730920·0007021457605593754328278·823685·417823·6810501190513...4104·842494·8212124512446...1836·223818·9311904131429——3
44751113507321122353342023331544155·08392·00094·619885·046974·441827·926830·261807·657920·0006823167716213507328252·953941·897701·0010436210424...4218·562340·0212120541148...1756·333834·2011904120407——4
54359403223061104632350823340505153·48992·00094·4881000·663970·608939·385829·882920·871920·0006628117823263223068335·864228·067673·0510318230010...4322·952182·1712112565618...1679·853847·3811904105702——5
64016342943191091004355537345418151·86392·00094·3341127·665966·7711062·591829·5571045·740920·0006437377926452943198522·644549·977732·8010115245143...4416·912023·9912104593609...1607·393858·561190495343——6

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