Fig. 117.

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

Note.—TheSix co-ordinates of the Generating Triangle of each Zone in these Tables have the Focus of the Principal Lenses of the Systemfor their origin; it being considered more convenient, in executing the necessary protractions, preparatory to theconstruction of the grinding apparatus, at once to refer the whole of the grinding machinery to the axis of theapparatus. To prevent the appearance of any inconsistency, however, it is proper to mention, that the radiant pointsof the series of Zones, do not exactly coincide with the Focus of the Lenses nor with each other; and that to avoidthe parallax which the distance of the radiant points from the origin of the co-ordinates would occasion, it is necessary tomake some corrections upon the linear dimensions, so as to find the line corresponding to the angles θ, ξ, and thedistance Δ. In the Hyperpyral series, which stands abovethe flame, the Zones have the radiant point 10 millimetres above the Focus of the Lenses, and each y of thisseries, therefore, requires a reduction of that quantity; while the xremains unchanged. In the Hypopyral series, which stands belowthe flame, the Focus or radiant points of each Zone, varies its place in the flame, moving upwards as the Zone islower, so that the line joining the Zones and the Foci, revolves as a radius vector round a point between them. Inthis way, the x’s remain unaltered; but the y’s will be lengthened successivelyby the addition of 10, 14, 19, 25, 32, and 40 millimetres. As these Tables contain the dimensions of Zones whichare 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 millimetresinto imperial inches, is easily effected by adding the log. millimetres to the log. ̅2·59516, the sum being the log. ofthe 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 VerticalAxis 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 outerarris 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
arrisof 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 arrisof 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.		 - 16045384406091172640314810304510160·33192·37995·209 593·369986·260 551·481831·497 525·000920·0007451197320314406098750·193194·768466·88102591438114000·003825·312817·77121504512564000·002021·193777·07119241558471054·34 1
 25655384128101160042323201312717155·43090·24993·011 663·063957·410 617·423808·832 593·369895·8167255277432324128108253·903306·807909·9410445163211...3923·652683·5511956475152...1918·373797·40117341448411069·02 2
 35305383848291143120331730321110151·55188·72991·434 734·313926·908 684·958783·619 663·063869·6057059397542513848297850·303411·757446·6710622182711...4015·062542·3111834503214...1813·603815·77116161339011087·52 3
 44915383607091125840340436325644148·58087·76890·424 807·357894·222 754·267755·451 734·313840·9206903537651313607097527·083514·227056·3910751202211...4098·542394·2311742531400...1707·553831·95115261230461109·85 4
 54525383324191112300345307334353146·44487·33289·947 882·445858·858 825·547723·921 807·357809·3376708127758413324197275·233617·566730·6610912221711...4173·082239·6411718555702...1599·723846·04115041123471136·14 5
 64135383040051094432354257343231145·08787·40389·986 959·847820·325 899·011688·608 882·445774·4266512367904273040057082·173723·816459·6311025241211...4237·702078·8211720584115...1489·623858·14115081017591166·57 6
 73745382754341080330363401352229144·48187·97790·5361039·852778·108 974·899649·051 959·847735·7306317038008562754346944·093835·236234·9311131260711...4291·451912·1811748612632...1376·713868·3011536 913161201·46 7
 83355382507521062006372611361343144·60989·06091·6041122·784731·6451053·471604·7301039·852692·7426121358112142507526857·033954·676052·3611230280211...4333·301740·1211844641246...1260·383876·5911632 809301241·16 8
 93005382220071043436381923370601145·47690·67193·2091209·000680·3221135·025555·0591122·784644·9005926088214292220076817·874081·705902·5311320295711...4362·261563·1012006665950...1139·943883·0311756 706331286·15 9
102615381931251024712391327375921147·08992·84395·3841298·900623·4331219·892499·3541209·000591·5565730468315471931256824·464226·675795·6811405315211...4377·241381·6312158694736...1014·673887·6611948 604191336·9910
112225381641541005810400714385436145·36193·00095·4131390·290559·3781308·183439·4281288·900531·9635536308416161641546880·524385·635718·5211237334711...4376·721194·9412200723706... 884·953893·0011956 503461394·3611
12184202135626 991050405953394917143·36293·00095·2711482·755490·1691398·007374·5381390·290467·2175345438514241356266980·894558·835672·6411036353859...4360·701009·4112112752258... 752·783897·3211956 405381457·2212
13150603111604 972607415103404249141·37993·00095·1271576·048415·9911488·972304·6111482·755397·4035158538610021116047123·054747·245654·9210815372659...4329·31 828·1912146780302... 618·373901·1011956 310001525·4313
°′″°′″°′″°′″°′″ °′″°′″°′″ °′″°′″ °′″°′″ °′″°′″
HYPO-
PYRAL
SERIES.		 - 15949164327361170556315837305527159·36992·00094·806 593·815985·212 550·915831·725 525·000920·0007423037338204327368674·743243·488375·64103091505224000·003855·832785·60121284551404000·002002·523781·9111904154208—— 1
 25548554042011153507324443314009158·05192·00094·783 682·731981·810 634·862831·183 610·872920·0007222107453064042018419·603456·448047·7210431170532...3983·212644·1612128483715...1918·553801·5111904142722—— 2
 35148333754321140031332816322713156·59292·00094·719 779·464978·917 726·831830·694 704·730920·0007021457605593754328278·823685·417823·6810501190513...4104·842494·8212124512446...1836·223818·9311904131429—— 3
 44751113507321122353342023331544155·08392·00094·619 885·046974·441 827·926830·261 807·657920·0006823167716213507328252·953941·897701·0010436210424...4218·562340·0212120541148...1756·333834·2011904120407—— 4
 54359403223061104632350823340505153·48992·00094·4881000·663970·608 939·385829·882 920·871920·0006628117823263223068335·864228·067673·0510318230010...4322·952182·1712112565618...1679·853847·3811904105702—— 5
 64016342943191091004355537345418151·86392·00094·3341127·665966·7711062·591829·5571045·740920·0006437377926452943198522·644549·977732·8010115245143...4416·912023·9912104593609...1607·393858·5611904 95343—— 6

APPENDIX, No. V.
NOTICE TO MARINERS.—SKERRYVORE LIGHTHOUSE.

The Commissioners of the Northern Lighthouses hereby give notice, that a Lighthouse has been erected upon the Skerryvore Rock, which lies off the Island of Tyree, in the county of Argyll, the Light of which will be exhibited on the Night of the 1st February 1844, and every Night thereafter, from sunset to sunrise.

A [specification] of the bearings of the Lighthouse and character of the Light will be found on the next page.

And the Commissioners hereby further give notice, that by virtue of a Warrant from the Queen in Council, of date the 13th December 1843, the following Tolls will be levied for voyages in respect of which benefit will be derived from this Light, viz., from every British Vessel (the same not belonging to Her Majesty, or being navigated wholly in ballast), and for every Foreign Vessel which, by any Act of Parliament, Order in Council, Convention, or Treaty, shall be privileged to enter the Ports of the United Kingdom of Great Britain and Ireland, upon paying the same duties of tonnage as are paid by British Vessels (the same not being navigated wholly in ballast), the Toll of One Penny per Ton of the Burden of every such Vessel; and for every Foreign Vessel not so privileged, the Toll of Two Pence per Ton.

By Order of the Commissioners,

(Signed)C. Cuningham,
(Signed)Alex. Cuningham,