CD
:(7>
= C7>
CD
CO
S(to
C
^ THE
ENGINEERS, MINING SUEVEYOE'S
AND CONTEACTOE'S
FIELD-BOOK.
BT
W. DAVIS HASKOLL,
CTVrL ENGINEER.
SECOND EDITION, MUCH ENLARGED.
CONSISTING OF
A SERIES OF TABLES, WITH RULES,
EXPLANATIONS OF SYSTEMS, AND USE OF THEODOLITE FOR
TRAVERSE SURVEYING
AND PLOTTING THE WORK WITH MINUTE ACCURACY
BT MEANS OF STRAIGHT EDGE AND SET SQUARE ONLY;
LEVELLING WITH THE THEODOLITE,
CASTING OUT AND REDUCING LEVELS TO DATUM,
AND PLOTTING SECTIONS IN THE ORDINARY MANNER;
SETTING OUT CURVES WITH THE THEODOLITE
BY TANGENTIAL ANGLES AND MULTIPLES
WITH RIGHT AND LEFT-HAND READINGS OF THE INSTRUMENT;
SETTING OUT CURVES WITHOUT THEODOLITE
ON THE SYSTEM OF TANGENTIAL ANGLES BY SETS OF
TANGENTS AND OFFSETS ; AND
EARTHWORK TABLES TO 80 FEET DEEPy, ^
CALCULATED FOR EVERY 6 INCHES IN DEPTH. /, ^ 1J y^
LONDON: >^'
LOCKWOOD & CO., 7 STATIONER S'-H ALL COURT.
1866.
I \ u
LONDON
PRINTED BY 8POTTI6WOODE AND CO.
NEW-STHKET 6QUABH
PREFACE
TO
THE SECOND EDITION.
Since the First Edition of the ' Field Book,' the author has
found, through conversation with numerous friends, that it
would be advisable to enter more into detail as to the ap-
plication of the Tables. He has therefore given, in the Intro-
duction to this Second Edition, an explanation of the system
of levelling with the theodolite, by which the student may
perceive how rapidly a network of trial levels may be ob-
tained over a very extensive area through a hilly country ;
and also of the system of traverse surveying and plotting,
more particularly as applicable to the working surveys re-
quired through thickly populated districts, where great ac-
curacy in the plans is necessary.
For those who object to the theodolite, a set of tables has
been given for setting out curves by numerous offsets from one
tangent. The author has besides added, in this Second
Edition, Earthwork Tables for every 6 inches up to 80 feet
deep ; and a Table of Gradients, which will be found to reduce
very considerably the labour of preparing working sections.
a2
INTRODUCTION.
It is not unworthy of remark that, whilst every branch of engineering,
with two exceptions, has, during the last thirty years, been progressing
with giant strides,' the exceptions, land surveying and levelling,
remain exactly where they were ; this, of course, is the general rule only :
there are exceptions, no doubt, numerous. Taking into consideration the
great advantages of the present day, in the shape of ordnance maps,
tithe plans, improved instruments, and the gradients and curves which
we may now adopt, it is doubtful whether, generally speaking, surveyors
know as well now how to pick out a line of railway as the professional
man of a quarter of a century ago. This was about the only reproof
made against the engineer by Lord Eedesdale in his late ' raid ' on rail-
way people generally. His lordship observed that railway plans were
not sufficiently studied ; the observation is not a whit more flattering to
the writer than to his brother professionals, but he submits that it is
true.
It would, of course, be unfair to apply this observation to those cases
where a professional man is sent down at the very last moment, when
there is scarcely time to prepare any plans and sections whatever, after
merely giving a glance at a country, where he can very often barely see
a mile ahead. The condition now more particularly referred to, is
where the engineering surveyor is engaged in actual exploring or trial
levelling for the selection of a line of railway at home or abroad, and
as to the most expeditious method of obtaining sufficient levels to ensure
the best passes, the most favourable starting-points when we are at
liberty to select, and the best points or thereabouts along the line so as
to avoid heavy works. These circumstances necessitate getting over a
wide expanse of ground in a short time, and this can be done only by
adopting suitable means.
The ' good old times ' have passed away, when we laid out railways
through flat and undulating countries ; with very few exceptions, these
territories are all fully occupied, and the engineering surveyor, in pro-
jecting lines of railways at the present time, must make up his mind to
wind along hills and over mountains. Not only the ground is broken
in every direction by chains of lofty hills, but out of these run numerous
INTRODUCTION. V
spurs and valleys which require close study before anything like a
good line can be laid out amongst them, even after a particular general
route of country has been determined on as the best, purely from an
engineering point of view. In such districts as are now referred to, the
hills very commonly rise and fall 50 and 100 feet within very short
distances, such as 100 or 150 yards; not only is it necessary to have
levels over such ground, so as to avoid as much as possible very heavy
works, but the pass has often, and indeed most generally, to be kept in
view, whether it be very high or very low ground ; and not only the
ground rises and falls in numerous places at the rate above mentioned,
for distances of 100 and 150 yards, but often also at the same rate for
ten times such distances.
Again, before the general route above referred to can be determined
upon, the country for a mile or two right and left, and often much
more, requires examination, not merely by the eye, which in really hilly
countries is very likely to deceive, but by some rapid instrumental ex-
ploration ; and it is only when this has been done that the best line
generally can be discovered. The work more particularly referred to
now, is railway work at home, where we have often a severe par-
liamentary ordeal to go through ; this we observe advisedly, for unless
we have opposition, it matters very little, except as regards expense,
what kind of a line is brought forward.
Notwithstanding all these difficulties, however, which have sprung up
naturally, and simply from our having to project our works under cir-
cumstances generally so very different to those of twenty and thirty
years ago, we adhere, with only a few exceptions, to exactly the same
instruments, and the same mode of using them as we did then. The
reserve, however, of a few exceptions has been made, because there are
engineering surveyors who have adopted a totally different method of
going to work, and mostly they are well and profitably employed ; but in
subjects of this kind we cannot refer to exceptions, and we can only deal
with the general state of things as we meet with them.
The only instrument still generally employed for getting explore levels,
even over the most hilly country, is only and simply the level in its ordinary
form ; and, however expert the observer may be, he will not get over a
hundred feet rise in much less than six observations : with the theodolite
this is done at one sight, that is, with five-sixths less trouble and time.
The ordinary mode of using the level for trial levelling, is to begin at
some particular point, and to wind up and down with instrument and
staff along the sidelying ground proposed to be adopted, and so get a
few levels right and left, these being referred to in the level book, and
on a plan by letters or numbers. One trial line having been got over,
another line is tried in the same manner ; but, from the nature of the
instrument in its simple form, the work is slow, and in hilly countries
confined to very narrow limits.
VI INTRODUCTION.
Two or three instances which have occurred within the author's ex-
perience, will perhaps tend to explain the different results that are to
be obtained from trial levelling with the theodolite, and with the level
in its ordinary form.
It is now some years since, that a line of railway was laid out, and
even stumped out, through a mountainous country, and the construction
of which would have involved about 2| miles of tunnel through a very
hard rock, containing large quantities of water ; this was independent of
very heavy cuttings and some lofty viaducts. The works altogether were
so expensive that some thoughts were entertained of abandoning the
whole concern as not likely to pay. Let it be distinctly understood that
the men who had laid out this line were thoroughly able and experienced,
but the only instrument they had used was the level ; for some six or
seven miles of approach to the tunnel, they were confined in the gorges
of hills rising some four or five hundred feet on each side, and they
could not get out of them.
Under the circumstances above mentioned, a new order of things was
established, and the theodolite was brought into operation for trial
levelling. In about three weeks a new line was found ; two short tunnels
were substituted for the long one above referred to, with practicable
works of approach.
On another occasion, of much later occurrence, after about six weeks'
trial levelling, with the level, by a gentleman of first-class experience
and abilities, plans and sections were deposited for a short line, which
showed two tunnels, one of which was upwards of a mile and a half in
length, with very long and heavy embankments on each side, one of
which, for a considerable length, was 80 and 90 feet deep. The deposit
was made, but no further motion was taken in the matter ; and not only
this, but a line between the two places was given up as impracticable.
Under this state of things the subject was taken up by another engineer;
he trial levelled for a line between the two same places, but with the
theodolite, and in a short time he obtained so many levels over an ex-
tensive area, and over totally different ground, that he obtained a line
with only a quarter of a mile of tunnelling, all other works being of
quite an ordinary character.
The writer will mention one more instance to show how easily the
eye, even of a well-practised man, may be deceived in the matter of
levels in a hilly country. A professional man of extensive practice had
been told that in a particular place, through which he was running a
line, he would there have a tunnel; but he was quite satisfied, from
what he could see, that he should only have some 40 feet of cutting.
When, however, the deposit was made, the section showed 300 yards of
tunnelling, with a depth of 110 feet.
The above instances have only been given to demonstrate practically
to those who are not in the habit of using the theodolite for taking trial
INTRODUCTION. VH
levels, that the practical application of the instrument for this particular
purpose has led to most important results ; and it was only because the
writer had had most satisfactory experience on the subject, that he cal-
culated the tables given in this volume, and which are equally applicable
to the best and most accurate style of surveying, that is, surveying by
traverse. This in no way refers to Parliamentary work.
As regards these tables and theodolite levelling, it is now about two
years and a half ago that he had occasion to take some levels through a
valley amongst the chalk hills in the south of England ; besides the
main line there were 37 cross-sections, each of which was about half a
mile long, each falling from 350 to 500 feet, and then rising 500 and
600 feet on the other side ; in a week, thanks to the theodolite, the
work was accomplished, and, with the assistance of the tables, then in
manuscript, it was very rapidly cast out, reduced and plotted, just in
the same way as in the ordinary level book, angles of depression and
elevation being taken, instead of heights in feet, for back and foresights.
To the practised engineer, it must, of course, be needless to explain the
manner in which the levels for a section are taken with the theodolite ;
but the writer having met with many who really had no idea about it,
he will'not apologise for now giving a full explanation, the more so that
such matter is always useful to students, and will in all probability
become more so at some future time, when theodolite levelling will
become common practice.
LEVELLING WITH THE THEODOLITE. CASTING-OUT
LEVELS AND EEDUCING BY THE USE OF THE
TABLES. PLOTTING SECTION.
Let a o b be an angle of elevation of 20 degrees, measured with the
theodolite placed at o, whilst a staff has been held at a ; and let the
distance from o to a measure 100 feet, o a= 100 feet is only the length
measured along the surface of the sloping ground ; b o is the true hori-
zontal distance, and b o is the cosine of the angle of elevation ; and a b
is the difference of level = to the sine of the angle of elevation. By
means of the tables we get the lengths of both these required lines. At
page 64, we find that for the angle of 20 degrees, and for the measured
length 100, the horizontal distance for difference of levels is 93'969 ;
this will be equal to b o ; and at page 65 we find that the difference of
level* for this angle of 20, and measured length of 100 feet, is 34*20 ;
this will be equal to a b, and will give the rise, or height of A
above o.
We will now apply this to the diagram of a section, p. ix. ; 1, 2,
3, 4, 5, 6, are the stations for placing first the levelling staves, and
VU1
INTRODUCTION.
then the theodolite ; for instance, the level of the ground at station 1
having been previously ascertained, the staff was held at station 2, and
the theodolite set up at station 1, paying proper attention, of course, to
the verniers of the vertical limb and to the bubbles. The centre of the
instrument is found to be 4*10 feet above the ground; then the telescope
is directed by vertical motion to 4-10 on the staff held at station 2 ; the
vernier is clamped, &c, and the angle of elevation is read off, 9 50'
entered in the book, and the distance is measured along the sloping
ground, 410 feet. The theodolite is then removed, a staff left behind at
station 1, and the instrument carried to station 2, the staff from which
INTRODUCTION.
** /"^
0*5
\. /'Jr
(m
eoo/e
i !"''
1 /."
' iiif '
' Hi
' jilt i
' Hf 1
6SW
SS'O^
/ lr
ES 09E
/ JM
896
S-6IS
A3
:: 7 ". .:.:::"
to station 3; the t he odol it e is then ptupeil j set up over
i-.i- :~ - : :'-r Lr :_"-: :: :'-r :zr.n~ :-. --' .-: :"_" _":"--: : - is - :~ : : -.- i
to be 6-1 feet; then die telescope is directed to 5*1 on the staff held at
station 1, and die angle at depression on therertical limb should be
found to lead exactly 80 ltf-SO 9 9 50*. The telescope is now
*mwm^A to die staff at 3, the angle of deration read off, entered
in the book, and die distance from station 2 to station 3, equal to
800 leer, is measured and also entered. The instrument is then removed
2, some peg or mark being left dure, in order that the
from station 1 may find dm exact spot The
-; vz-;;z :. :-z : r: : rr'.r f " m; -
the staff from station 1 being now held at station's, and the
of the instrument being 4*15 feet above the ground, die telescope
is directed to 4'15on die staff at 1, and die angle of depression is read
off and entered. The telescope is now turned to the staff held at 4, and
directed to 415 (the height of the instrument above the ground); the
vernier is again damped, &c, &c; the angle of depression is read off
from the limb, and entered in the book, and the distance, 405 feet,
n :>-:- : l.zi 'z, _t- ;z : rr- I \. =.:-.
The theodolite is now removed to station 4, whilst the staff is brought
forward from station 2 to station 3, and the other staff is carried for-
ward to station 5; die instrument being now placed at station 4, we
take the angle of devotion on to the staff held at station 3, and then the
angle of deration to the staff held at station 5, exactly in the manner
already explained, and we ly^i g r w m jw thin , nuimw tn i\u. end of the line.
Let us now refer to the field-book in which the observations am
canoed.
nastiaHi
For Angle
Bsi
Fall
LengBa
-,
Tlpfcet
Dfafc.
Bsaaeej
Lsaf4H
24:: :
Itafc
5000
9-50E
;:
410
si i n
04 5
Mi
80-10D
2-20E
:-::
800
34259
89 1
799
87-40D
10-15D
72-07
4 5
270-52
6603
398
79-45 E
9-15E
90 01
560
380-53
553
80-45 D
2-35 E
**>li
782
395-68
7934
781
87-25 D
7-15 D
:; -M
809
319-33
8534
801
83-45E
It will be observed that the back angle is a complete check upon the
whole of the field-work.
The rise and fall are obtained from the tables of 'Differences of
IXTKODUCTCOX. XI
Levels,' and the reduced lengths from ! Horizontal Distances for Diffe-
rences of Levels,' merely by removing the decimal point to the right
or left.
The levels having been cast out, and reduced in the ordinary manner,
and the reduced lengths added np in the column ' Total Reduced Distance/
the section is plotted in the usual manner.
It will be observed that in the diagram explanatory of the mode of
plotting the levels, only the leading points have been noticed on the
section : small inequalities are quite secondary considerations in taking
trial levels over a hilly country, but there is nothing to prevent inter-
mediate depressions in the ground being noticed on the flypage.
It will also be observed, that besides the angles of depression and
elevation taken along the main line, we may also take observations right
and left, the levels so obtained being quite as valuable for our purposes
as those obtained from the main line. It is indeed the great facility
with which these side levels are obtained by the means of theodolite
levelling which makes the system so valuable ; from the rapidity with
which the work is done, a difference of 200 or 300 feet in levels, or
much more, being obtained at one sight, quite as easily as 8 or 10 feet
with the ordinary level ; and when the instrument is supplied with a
micrometer, the distances are read off rapidly, quite near enough to all
intents and purposes, without chaining. In the diagram and example
of field-book given here, no reference is made to side levelling, in order
that there may be no confusion in the elementary explanation of elevation
and depression, and the corresponding rise and fall, and reduced distance.
what has been just said, it cannot fail to be observed, that for ob-
taining levels over the ridges enclosing large areas of watershed, the
m is very rapid, and equally valuable for taking cross sections in
very sidelying ground, in matters of deviations. It is by these means
that a great number of levels above a given datum are written in on
maps or plans ; and as regards railway engineering, there then remains
but little to do in determining the direction of a line, in ascertaining
pretty accurately the nature and extent of the works, as well as the
gradients and curves to be adopted. "With such documents at hand, it is
easy to avoid sending in ill-studied plans and sections.
But very few engineers, if any, were better acquainted with all the
details of engineering field-work than the late Mr. Gravatt ; and he was
perfectly aware that, even in his working-days, the level by itself was very
limited in its capabilities for trial levels, and to increase its usefulness, for
the purpose of trial levelling and cross sections particularly, he added the
appliances shown in the accompanying diagram, in which it will be seen
that a. and b are two plain sights, which are so contrived that they are
shipped and unshipped with the greatest ease ; a. has a vertical slit and
two horizontal ones : b has a fixed vertical horsehair, and is also pro-
vided with a slide, d, carrying a cross-hair, which intersects the vertical
201
INTRODUCTION.
horsehair higher or lower, according as the slide is moved up or down.
The slide n is also provided with a vernier on each side of the broad
arrow ">, by which the divisions engraved along b are subdivided into
tenths and hundredths. The dotted line, de, shows that this contrivance
affords a most ready means of obtaining the rates of inclination of any
sidelying ground, or, as will be presently seen, any difference of level.
The depth between the horizontal slits of a is made exactly equal to
the whole of the divisions on b, which whole is made by the maker
exactly equal to some decimal fraction of the horizontal distance between
a and b, which in the instrument before us measures exactly 10 inches.
The whole of the divisions of b is equal to 2 inches, or of the dis-
tance ab ; one half, therefore, of the divisions is equal to 1 inch, or i
of the distance ab ; and as this inch, or
equal parts, each subdivision is equal to $
r x 5 of ab, is divided into 10
of ab: two subdivisions
j n , and twenty will be f ; and these
rise or fall per hundred (any unit of
hundredths will give the
measurement) horizontal.
The instrument is used in the following manner. "When an observa-
tion is required to be taken, a staff-holder is sent on to the given spot ;
if an elevation is to be taken, the observer applies the eye to the lower
horizontal slit, and the cross-hair of the slide d is made to coin-
cide with that reading on the staff which is equal to the height of
the instrument above the ground ; there only remains to take off the
reading. In the diagram, the cross-hair intersects above the 12th divi-
sion, and by means of the vernier (the divisions of which are too small
to be shown in the figure), we find the subdivision to be -53 ; then the
whole reading will be 12*53, which means at once that the ground rises
at the rate of 12 - 53 per hundred horizontal as, for example, 12'53 feet
per hundred feet horizontal.
If an angle of depression is to be taken, the eye is of course applied to
the upper horizontal slit. In the figure before us, with the slide still at d,
INTRODUCTION. Xlll
we find the arrow intersects a little below 7 subdivisions, and the excess
we read off by the vernier (the upper side of the arrow) to be *47 ; the
reading will therefore be 7*43, which means that the ground falls 7 '4 3
feet per hundred feet horizontal.
Now, we have observed above, that 'the cross-hair of the slide is
made to coincide with that reading on the staff which is equal
to the height of the instrument above the ground.' It may be added
that, for all ordinary purposes, it is unnecessary to use a levelling- staff;
it will be generally sufficient to send a man to the required spot, where
he may hold up a piece of white paper at the height of his neck, or
thereabouts, according as the instrument is higher or lower above the
ground. For short distances, this will answer all practical purposes,
where rapidity is more requisite than extreme accuracy of fractions of feet.
An approximate level may, however, often be required for some con-
siderable distance. For instance, let us suppose that an elevation has
been read off of 27'47, and that the distance, measured along the sloping
ground, is 460 feet ; required the total rise, and the horizontal distance
from the observer to the point observed. Refer to Table I., and under
the column ' Eise or Fall per Hundred Horizontal,' look for the given
reading 27*47, or the nearest to it; we find this, or 27'42, at page 15,
and it coincides with the angle of 15 20' ; now look for this angle in
Table II., where we shall find it at pages 54 and 55 ; the angle of
15 20' gives for 400 feet, difference of level, 105*77
and for 60 feet 15-86
Total rise or difference of level = 121*63
Similarly we find the horizontal distance :
For 400 feet, horizontal distance, 385*76
For 60 57*86
Total horizontal distance from] _aa<>.g<>
instrument to observed point j
In this instrument of Mr. Grravatt's, as made by Archbutt and Sons,
the plain sights also enable an observer to take a bearing, or horizontal
angle, with considerable accuracy, whilst the divisions on the cap or
sunshade will enable him to take approximate angles of elevation or
depression, which will often be found exceedingly useful.
To the young practitioner and student, and to those generally who
have never taken levels by any of the means here mentioned, it may be
as well to make a few observations as regards the above example.
The rise per hundred feet horizontal wc find to be 27*42, and the
measured distance along the slope is 460 feet ; if 27*42 had been mul-
tiplied by 460, we should have had 126*13 for difference of level, or an
error of about 5 feet. This is mentioned to make it perfectly intelligible
that the readings we get on the scale, are the ratios of rise or fall per
XIV
INTRODUCTION.
hundred feet horizontal ; in the next place we may add, that of course,
in taking the observations, it is necessary that the bubble should be
exactly in the centre of its run, in the same -way as though the observer
were taking ordinary levels.
THE ELEMENTS AND PRACTICE OF TRAVERSE
SURVEYING.
The correct practical principle of working a traverse on the ground
consists of the best method of reading the angles round any regular or
irregular polygon, and measuring the lengths of the sides. From these
angles and lengths certain calculations are made, which enable us, with
no other instruments than a straight-edge and set-square, to lay the
work down on paper with any degree of precision. Table II. gives these
calculations all ready to the surveyor's hand.
Let a o e be a regular octagon, which we propose going round with
the theodolite, starting from a. Let a n be the magnetic north ; zero on
the horizontal limb is made to coincide exactly with thfl needle ;* in tha
next place, the angle nab is taken, which will here be 22 30';
90 22 30' = 67 30' = the angle b a f, to which bf is the sine, o*
departure, and a f the cosine, or latitude, given in Table II., as already
fully explained above. Now, in the regular octagon, each of the angles
at the circumference, that is, a b c, b ce, ceh, is equal to 135 degrees.
The intersecting angles at b, = 360, are made up of abd, = 180,
* In Mr. Hoskold's Transit Theodolite, constructed by Messrs. Archbutt, the
compass is nearly twice the ordinary sue, and quite free and open, so that it can
be read very accurately.
INTRODUCTION.
xr
xvi INTRODUCTION.
plus abc, = 135, and dbc, which will be equal to 45. It will be the
same thing, of course, at c, e, &c, as in the regular octagon given the
angles at the circumference are all equal to each other.
We will now return to the theodolite, which we have left all clamped,
and reading 22 20'. The length ab being measured, the instru-
ment is to be removed to station b, and there set up exactly over the
point b, which is done by the shifting of the legs, so as to make the
plumb-bob hang exactly over the right point. The next adjustment is
to bring the bubbles exactly to the centres of their runs ; this places
the instrument in horizontal adjustment, so that the angles taken shall
all be horizontal. This is effected by means of the parallel plate screws,
two of which are shown in the figure at a and b. The instrument being
correctly placed at b, we have now to bring the reading 22 30' to bear
exactly on point a, where, of course, a pole is held up, care, however,
being taken that the intersection of the wires of the diaphragm shall
be exactly on the foot of the pole, whilst the vernier, as last fixed on
the limb, remains perfectly untouched.
To do this, the clamp c is slackened, which allows the whole of the in-
strument to be turned round bodily on its axis, without any portion of
the upper part of the instrument being moved in the least degree. The
theodolite is now to be turned round, whilst the observer looks along the
upper telescope, which he directs towards a, or through the plain sights
s, s ; when the intersection of the wires of the diaphragm* (which, for
the sake of brevity, we shall in future call the sight) pretty nearly
coincides with the station a, the clamp c is tightened, and the
contact of the perfected sight with the foot of the pole at a, by means
of the tangent-screw d, which allows of the most delicate and regular
horizontal motion of the instrument.
This perfect contact being effected, we now release the verniers,
which are shown at e, by slackening the upper clamping-screw f ; the
telescope is now turned round to station c, and when the sight is nearly
in contact with the foot of the pole, screw f is tightened, and, by means
of the tangent- screw, the contact of the sight is perfected. "We can
now take off the reading of the vernier on the limb, reading with perfect
accuracy by means of the magnifier i. The magnifiers in this instru-
ment are, by a particular contrivance, made to move with the greatest
possible convenience, which is a most important thing in getting an
accurate reading on the limb. In the present instance, the reading will
be 247 30'. The length of bc, being measured, the instrument is
now removed to station c, with the reading on the limb (247 30') left
untouched.
* In order to see the wires of the diaphragm clearly and comfortably, it is neces-
sary to draw out the eye-piece G very gradually, until the wires appear sharp and
well defined. This must be done delicately, as even the sixteenth of an inch back-
wards or forwards makes a great deal of difference.
INTRODUCTION. XV11
The theodolite being now set up at c, in the same manner as at a and
b, the clamp-screw c is slackened, the upper telescope is turned on to
pole left at b, clamp-screw c is then tightened, and perfect sight com-
pleted by means of tangent-screw d. Now release clamp-screw r, turn
the telescope on to e, tighten r, and complete the contact of sight by
means of tangent-screw h. The reading on the limb will now be found
to be 112 30'. This operation is completed until we have gone over
the ground from end to end.
Let it now be observed that the reading at b was 247 30'; this,
deducted from 270, leaves 22 30' = to the angle cbl, of which cl is
the sine, or departure, in the tables, and b l the cosine, or the latitude.
The reading at c was 112 -30'; deducting this from 180, leaves
67 30', of which l e is the sine, or departure, and l c the cosine, or
latitude.
General Kule. Where the reading ia less than 90, subtract the
reading from 90, which will leave the angle required ; when the reading
is more than 90, and less than 180, subtract the reading from 180,
which will give the angle required ; when above 180, and less than
270, subtract the reading from 270 ; and similarly, where the reading
is above 270, and less than 360 deduct the reading from 360 : in
each case the remainder will give the angle required.
In the practice of traverse surveying we always make the reading
5', 10', or 15', &c, according to convenience, by moving the poles, or
making our marks on walls, &c, a little to the right or left; this will be
found a great practical advantage, inasmuch as it does away with all
fractions of minutes, and increases the clearness of reading, a matter of
the greatest importance in traverse surveying, for the special purposes
we are now considering.
It is to be observed that in the usual practice of traverse surveying,
we measure the sides and angles round any polygonal figure, regular or
irregular, and that in doing so we go as far north as we do south,
and as far east as we do west, and that consequently the ' southings '
are equal to the 'northings,' and that 'eastings' are equal to the
V westings.'
Now the ' Differences of Latitudes,' or the northings and southings of
any line, are the distances that the ends of lines measured round any
polygon are north or south of the other ends.
The ' eastings ' or ' westings,' or departures of any lines, are the per-
pendicular distances from one end of the lines to a meridian, or line
passing south and north through the other end, the ' meridians ' being
parallel lines supposed to pass through every station on a survey. In
any polygon, regular or irregular, the sum of all the interior angles is
equal to twice as many right-angles as the figure has sides, less four
right-angles.
As observed above, and as may bo seen by referring to the figure at
Xviii INTRODUCTION.
p. xiv., whether we consider the regular octagon or the circle, in going
round the polygon, we go as far north as south, and as far east as west ;
therefore, when we reduce the ' northings ' and ' southings ' of all the
lines from the tables of Difference of Latitude, and similarly when we
reduce the eastings and westings of all the lines from the Tables of De-
partures, we at once have proof of the accuracy of the work, since the
northings will be equal to the southings, and the eastings equal to the
westings, if the chaining has been correctly done.
In the same manner, we shall have proof of the angles having been
correctly measured, because all the interior angles will be equal to twice
as many right-angles as the polygon has sides, less four right-angles, or
180, if the theodolite has been correctly used. There will, however, gene-
rally be some two or three minutes difference, even with the most careful
work, unless some particular plan be adopted, such as that which has
been mentioned above, of making the readings 5', 10', or 15', &c, by
making our marks accordingly. In the description of work to which
we have been more particularly referring to, a difference of two or three
minutes might be of considerable importance ; at least for a working
survey amongst buildings we should object to it, and the more so that
it may be avoided; but in country surveying, or where looking such
minute accuracy would be loss of time, it is usual to divide the difference
or error over the work.
In the example we have given of traverse surveying at p. xxi., it
might be very inconvenient to have to go round ; but the work may be
proved by going over the work a second time, but backwards, so that we
shall still have our northings equal to southings, and our eastings equal
to westings.
It is very possible that to many this going over the lines a second
time may appear fastidious, but in fact it consumes but very little time,
from the work having been already all set out ; and, in the next place,
it removes all doubts from the mind of the surveyor, as well as from
that of the chief for whom he may be working. Where, on the contrary,
the work has not been proved, the surveyor will feel perhaps for months
afterwards uncertainty about his plans ; and if any hitch occurs in the
setting out of the works, he will be sure to feel no small amount of un-
easiness, and attribute the difficulty to some possible error in his work.
As to the degree of accuracy which we have considered necessary in
town lands surveys for the purpose here contemplated, we will only
point out that the mistake of a foot may bo of far greater importance
than a foot error in a cutting or embankment on an ordinary section,
for in this last case it would only involve some difference as to a greater
or less quantity of earthwork ; but serious as such a blunder would be, it
would be trifling compared to the setting out works so that 'any por-
tion of them might fall a foot within instead of outside of a building.
The engineer who has had to set out works through ground thickly
INTRODUCTION. XIX
covered with buildings, knows all the importance of a correct plan for
such purposes.
In the theodolite we are now referring to, it will be observed that there
is a lower telescope, which is so set that its axis perfectly coincides
with that of the upper telescope, when at zero ; there is also a diagonal
eye-piece, so made that when screwed into the telescope, it admits of
its being pointed directly vertical, and of observations being made in
such direction with as much facility as if the glass were pointed hori-
zontally; this is a considerable advantage, as it allows of underground-
works being connected in the most direct manner with the surface.
Further, by the special construction of this instrument, when any
particular point has been found on the surface, there are means of
setting out from such point any angle taken underground, without
making any alteration on the vernier plate : that is to say, that leaving
all screws fast clamped, the instrument may be brought from under-
ground works to any fixed point on the surface, and any particular angle
set out or checked, one or both sides of which shall exactly coincide
with fixed underground lines. The vernier zero being made to coincide
exactly with zero on the limb, and the instrument turned round until
the needle points to its own zero, both telescopes will be in the same
vertical plane ; any angle being now taken may be transferred to the
surface, and the large size of the compass will show the slightest
deviation that may have taken place.
In ranging curves, the addition of the second telescope is important,
inasmuch as it enables the observer to be always satisfied that the zero
of the instrument, during the course of any number of observations, has
not deviated from the direction of the tangent. Any want of check on
such deviation is often a source of error in setting out long curves, and
is often caused by the observer moving about the instrument without
sufficient care, or by his attempting thoughtlessly to move the vernier
plate without having first released its clamping-screw. Such errors are
often carried to the end of the curve, where they become greatly in-
creased ; they are frequently then rectified (!) by what is termed easing
the curve, which simply means that at one end a curve is often of a
radius 5 or 10 chains shorter than it should be.
PLOTTING TOWN SURVEYS BY TRAVERSE
TABLES.
Since the introduction of railway and other great engineering works
into the very centres of large towns as, for instance, of the railways now
constructed or about to be constructed in the parts of London covered
XX INTRODUCTION.
with valuable property the accuracy of working surveys has become of
the very highest importance. Not only is it by these plans that it is
determined whether buildings and parts of buildings lie on the line of
works, but often there are no other means of setting out these works
than by the working plans.
Not only important and expensive working drawings are got out ac-
cording to the plans, and often become of no value if these are wrong,
but the works themselves are frequently set out from the plans only, and
immense difficulties must be the consequence if they are incorrect. Some
considerable length of curve, or straight line, may be laid down on a
plan drawn to a very large scale, and properties are often purchased in
portions only, and not consecutively, and the works are of necessity set
out from the plans and commenced ; and if they have not been correctly
surveyed, and also correctly plotted, very serious consequences may re-
sult : not only may we find that we interfere with buildings we did not
contemplate touching, but the relative position of the centre lines may be
wrong ; and where masses of buildings intervene between works com-
menced in two different places, it is often very difficult to check
satisfactorily the operations of setting out by work done on the
ground. In short, the work is altogether different from ranging curves
and straight lines through fields, or even villages and small country
towns.
The writer believes that, generally, it is the system of 'plotting the
survey which is at fault. If the ground is well traversed with a good
theodolite, and the lines carefully chained, this part of the work can
scarcely be otherwise than satisfactory ; but the means adopted usually
for laying down upon paper long lines (often from 15 to 30 inches and
more) exactly at the angles, the writer considers unsatisfactory. The
instrument used for laying off angles is the protractor, perfect it is
admitted within certain limits, and the same may be said of the large
parallels employed in the next operation of plotting a traverse survey
in the usual manner. For ordinary purposes nothing can be better ; but
an extensive survey, plotted to a large scale (and 20 feet to the inch is
not too large for the purpose we have now in view), requires altogether a
different method in order to attain the accuracy necessary for important
works.
By means of the Traverse Tables, a good survey may be plotted in
the same manner and with the same amount of accuracy as a section, as
the accompanying diagram will explain.
From the Traversing Notes, the Angles 1, 2, 3, &c, on the accom-
panying diagram, are obtained, the lengths a b, b c, c d, &c. being
most carefully chained. To illustrate the method of plotting, it will
be sufficient to give one example, as the work otherwise would be
merely a repetition of what has been said under the head of Levelling
INTRODUCTION.
XXI
with the Theodolite,' pp. vii.-viii. Angle 1 is 33 2 5', and the measured
length up the side of the street is 422 feet ; at page 91 (Table II.) we
Angle 1=33-25
2=50-40
1=58-
4 = 64-
5=45-15
6=47-15
7=26-25
8=49- 5
have Departures ' corresponding to ' Difference of Levels,' and for
33 25' we have for
feet. feet.
400 = 220-29
20= 11-014
2= 1-1014
Horizontal Distances for Dif-
422 = 232-4054
and for ' Latitudes, ' corresponding to
ference of Levels,' we have for
feet. feet.
400 = 333-88
20= 10-694
2 = 1-669
422 = 352-243
Both these results are shown plotted on the diagram for Angle 1, and
similarly for the other angles.
When the first portion of the survey, as from 1 to 8, has been completed,
the smaller areas may be enclosed and plotted in the same manner. It
will be seen that by these means, the most minute accuracy is ensured
for the whole as well as for the details of the survey. When the work has
proceeded thus far, the centre line of the works should be laid down, and
the details of the ' blocks' should then be filled into the width required.
CONTENTS.
PAGE
Pkeface to the Second Edition . . . . . iii
INTRODUCTION.
Laying out Lines of Railways. Importance of Trial Levels as
shown practically in many instances ...... iv vii
Levelling with the Theodolite by means of angles of Elevation or
Depression for the purposes of Trial Levels. Kapidity with
which the comparative Levels over a great extent of country are
ascertained vii viii
Practical explanation of the System. Use of the Theodolite. The
Field-book; Casting out and Reducing Levels from angles of
Elevation and Depression by means of the Tables and Plotting
Sections. Example ix xi
Mr. Gravatt's latest improvements in the 'Dumpy Level,' for
Cross Sections and Trial Levels. Practical examples and use
of the Tables xi xiv
Traverse Surveying; Explanation of the System. Use of the
Theodolite. Importance of Traverse Surveying in preparing
Working Surveys of ground thickly covered with buildings.
Practical examples. Minute accuracy with which the work may
be plotted without instruments and merely with a Straight-edge
and Set-square. Example of the practical use of the Traverse
Tables. General Rules xiv xxi
CONTENTS. XX111
GENERAL EXPLANATION OF TABLES
I. II. AND III. 5-9
TABLE I.
Tabic of Inclinations and Gradients for showing at a glance on
plans the Kise and Fall of Sidelying Ground, either from angles
of Elevation or Depression, or by means of Mr. Gravatt's im-
proved ' Dumpy Level.' Co-efficients for Setting out Slopes of
Cuttings and Embankmenls. Eeduction for Chainage along
Sloping Ground over hilly countries, where more than ordinary
care is required 10 23
TABLE II.
TRAVEESE SURVEYING AND LEVELLING WITH THE
THEODOLITE.
Table for Plotting Traverse Surveying without calculations and
without instruments, by the use of Straight-edge and Set-
square only
For finding at a glance the Differences of Levels, and the Corre-
sponding Horizontal Distances, from angles of Elevation and
Depression
For Casting out Levels, reducing to Datum, and plotting Trial
Sections from angles of Elevation and Depression taken with
the Theodolite 24^-113
TABLE in.
SETTING OUT CURVES WITH THEODOLITE.
Twenty-two Tables of Tangential Angles and Multiples for Set-
ting out Curves without calculations, from 4 chains to 85 chains
Radius, for the 66 feet, 100 feet or Decameter chain, with Eight
and Left-hand readings on the Theodolite for 25 consecutive
angles for each Eadius; Bend of Eails. Bends in 66 and 100
feet for Trimming Foot of Slopes and Side Drains. Super-
elevation of Eails. Tangents and Cotangents . . 114 143
TABLE IV. EAILWAY CEOSSINGS 144
XXIV CONTENTS.
TABLE V.
SETTING OUT CUEVES WITHOUT THEODOLITE.
PAGE
On the Principle of Tangential Angles, by Tangents and Corre-
sponding Offsets, calculated for Field Use from the Sines and
Versines of the Angles at the centre .... 145 146
Practical Explanation of the Principle and Construction of the
Tables, with Examples, illustrated, of Setting out Curves with
the Theodolite and without. Overcoming obstacles on the Line
of Curve on the latter system. Crossing Rivers. Method of
finding a Station on a Curve from which the whole of such
Curve may be set out 146 154
Table for Setting out Curves without Theodolite, on the Principle
of Tangential Angles, by Tangents and Corresponding Offsets,
calculated for Field Use from the Sines and Versines of the
Angles at the centres, from 4 chains to 80 chains Radius, for the
66 feet, 100 feet or Decameter chain, and for 16 consecutive
stumps for each Radius ....... 155 165
CONTRACT EARTHWORK TABLES, AND
MEASURING UP.
Explanation of Tables 166169
TABLE VL
Earthwork Table up to 80 feet deep, for every 6 inches in depth,
and for 10 different Formation widths .... 170 175
TABLE VII.
Earthwork Table up to 80 feet deep, for every 6 inches in depth,
and for 8 different Slopes 176 181
TABLE VIII.
Table of Gradients, giving Rise or Fall, per mile, chain, 5, 10, 20,
30 and 40 chains; and per 100 feet, 500, 1,000, 2,000, and
4,000 feet, to facilitate the preparation of "Working Sections, and
for checking without calculation the accuracy of Parliamentary
Sections. . . . . ' . . 183189
Note to Binder pp. 1 fo 4 are cancelled.
EXPLANATION OF TABLES.
TABLE I.
The first columns of Table I. have been prepared to show at a glance, on
either plans or cross sections, the rise and fall due to the angles of de-
clivity of side-lying ground. As regards earthworks, the importance of
this can hardly be over-estimated when we are laying down a line either
for a railway, road, or canal, because it affords a ready means of ascer-
taining depths of cuttings and embankments, and of making suitable
alterations in the direction of the centre line of works. Generally, the
information which we are desirous of obtaining on this point, is the
difference of the levels right and left of a line at a distance of perhaps
two or three hundred feet ; this is given at a glance by the tabular
numbers, when the angles of acclivity or declivity have been taken ;
thus column 2 gives the rise or fall per cent horizontal, all in yards, feet,
or metres, for every five minutes of every angle of inclination, which an
explorer may at once write down in his note-book without any calcula-
tion whatever, and the surveyor may make the same observations in his
field-book right or left of any of his chain lines, whilst making his survey.
If these lines are laid down on the plot plan, the differences of levels are
easily plotted at the same time, with all sufficient accuracy for the
purpose in hand. In a hilly country, particularly, these notes on a plan
afford the readiest means of avoiding as much as possible heavy cuttings
and embankments.
With the exception of the theodolite, which, however, is much too
cumbrous to be always carried about for taking angles of inclination, the
writer is not acquainted with any practically useful inclinometer, except
that which he has used for many years past.* This consists of a semi-
circular protractor, with a pendulum pointing to zero when the instru-
ment is held horizontal ; it is numbered from zero to ninety degrees
both ways, so that when used in taking an angle of elevation or depression,
the pendulum at once reads off the observed angle, and with much
greater steadiness and accuracy than might at the first glance be expected ;
if the pendulum be sufficiently weighted, say, with about two ounces.
With a six-inch semicircular protractor, with the vernier loaded, no
difficulty will be found in reading off to three or four minutes, and for the
* The writer, however, wishes to guard himself against any imputation of claiming
either discovery or invention in so simple a matter, and is only desirous of making
more generally known a really useful inclinometer for ordinary purposes.
6 EXPLANATION OF TABLE I.
short distances and the purposes for which the inclinometer could be
used, this is abundantly accurate; the instrument is furnished with
plain sights, the axis of which is, of course, made by the manufac-
turer, parallel with the diameter of the instrument. Fig. 1 is a sketch
of the instrument. It reads to twenty-two degrees, and as the line of
sight ab is parallel to the ground line cd, twenty -two degrees is the angle
Figl
of inclination, and the table supplies the amount of rise for every
hundred horizontal. The writer trusts that he may be excused for men-
tioning for the information of the young engineering surveyor, that one-
half of the cardboard protractors sold by our instrument makers may
readily be fixed in a plain glazed flat case, and that with a pendulum
attached it will make a very useful instrument for such purposes. The
great advantage of such an instrument is the readiness and rapidity with
which it supplies, with the assistance of the tables, the rise and fall for
ordinary cross sections.
The second portion of Table I. gives a series of coefficients for setting
out slopes where the cross section is in steeply side-lying ground, of which
the angle of inclination has been 'taken ; the writer considers that where
the ground rises or falls rapidly, this furnishes a better mode of setting
out the slopes of earth-work than the ordinary method by differences
of leveL
Let fig. 2 represent an embankment, 2 to 1 slopes, of 20'2 in depth on
side-lying ground, of which the angle of inclination has been measured.
Column 4 of Table I. gives the rise or fall per unit. Take this tabular
number opposite to the angle of inclination, mvlti'ply it by 20-2, and the
product added, to 20*2 will give the depth due to ab, and a b multiplied by
the major coefficient, for slopes 2 to 1, gives the distance b c. On the
EXPLANATION OF TABLE II. 7
other side the first tabular number- multiplied by 20-2 is deducted instead
of added, to get the depth d e, which, multiplied by the minor coefficient
for slopes 2 to 1, will give the distance fe: observe, that in both cases
the lengths be, and/e, are measured along the sloping surface and not
horizontally, which ensures a much more accurate setting off where the
earthworks are heavy, and the natural surface of the ground considerably
inclined.
TABLE II.
Table II. is a traverse table for every five minutes of the quadrant
which will be found a sufficiently close approximation for all surveying
purposes, as we can always manage to lay out our work to five minutes
and generally even to ten minutes. It is constructed so that the
Latitudes and Departures are given in one page for lengths from 10 to 90,
and of course by the mere removal of the decimal point one figure to the
left, from 1 to 9, and similarly by the removal one point to the right
from 100 to 900, and so on.
Independently of its use for regular traverse surveying it will often
be found useful in the field in getting round obstacles, as for instance
in fig. 3, where a large sheet of water comes across the base line
ab. From a set out any convenient angle bac, equal to, say 22 de-
grees, and measure along ac, until the obstacle is so cleared on the
other side that from a point c we may set out an angle acb of 68
degrees, (22 + 68 being equal to 90). Let AC measure 1250 feet ; re-
quired the length of ab. By table of latitudes we shall have for 22
degrees,
927-181000
185-44 200
46-36 50
1158-981250
oi 1158-98 feet for the length of ab, and if the angles have been properly
8
EXPLANATION OF TABLE II.
set out, cb will measure 468-26, for, by the table of departures we shall
have for 22 degrees,
374-611000
74-92 200
18-73-
50
468-261250
Table II. has been so arranged, that the horizontal distances and dif-
ferences of levels due to inclination are very readily obtained in the same
manner, when the angle of elevation or depression has been taken, and
length along the sloping ground carefully measured. In the last example,
for instance, if the angle of 22 degrees were an angle of elevation, and
the distance 1250 feet, the length measured along the sloping ground,
then we should have 1158-98 for the horizontal distance, and 468-26 feet
for the difference of level.
It will be needless to observe here, that in a case of taking levels by
inclination, we should not recommend such a distance to be taken at one
sight, and we have only done so here in order to show how the use of
this table is applicable in both cases, with regard to surveying and
levelling, and in mountainous countries, when a good theodolite is care-
fully used, a great amount of country is levelled over very rapidly, and
as regards cross sections the inclinometer mentioned above does all that
is required very easily with these tables, as all calculations are avoided.
EXPLANATION OF TABLE IV.
TABLE III.
Table III. has been prepared with a view of avoiding in the field all
the computations of tangential angles in setting out circular curves.
These calculations are simple enough, and yet troublesome in order to en-
sure accuracy, for one error may involve the loss of many hours' field
work ; besides, however rapidly they may be made, the time given to them
will always be more advantageously devoted on the theodolite, and
seeing that the chainmen do their work accurately, for unless the curve
be well chained, there can be no hope of closing the curve satisfactorily.
It will be needless to observe that the table is based upon the formula,
1718*9
-p ,. = Tangential angle for one chord.
It will also be almost as supererogatory to observe that, generally speak-
ing, in setting out curves, the first stump is upon a fraction of a chain. To
make use of these tables with all desirable rapidity, it is only necessary
to set out at first with the fraction of the tangential angle due to the
fraction of chain ; when this has been carefully done, the instrument
may at once be removed, and a considerable length set out from such
station.
For sharp curves it will be observed that the tangential angles have
been given by half instead of whole chains, which will be found to give
more satisfactory results for curves of short radius.
TABLE IV.
Table IV. is a table for railway crossings, which is too explicit to need
any further information on the subject.
A 3
ttotssaidaa
PUB UOTCJ'BAgi^-
30 sojSuv
OviO"iO^O^OW0 1 flO , '>0i0 1 flO l flO^O | flO , oO
m h n nw + ^in'o | M M J) MM + + U1>0 | M
O t* to
co
s
H
ft
ft
a
3
w
Eh
P
O
1
H
g
CO
+3
1
si
t^o h o\oo vo V) + p* w O 00 r^vo +wrt O 0\ t--vo u-> t4- cJ m 00
000000 t^t-~.r-^t^t^i^t-~. r-^vo vo vo vo vo v vo 10 ui 1^ 10 >o >o 10 m +
0>ONC\CSONC7\0\C7NCyNOSONCNOO\0\00\0\C^OsC7NONC7\C>CTNC7\ON
b b b b b b b b b b b b b b b b b b b b b b b b b b b
1
2>"o
"
co m ^vi t-^oo O m co t}-vo m 5\h m ivo 00 r wononO
1 M CJ p> p C* pj P* WmMMMMtl^-+^-^+VHOlO''llO U1VO
poop p p p p p p p p p p p p p p p p p p p p p p p
HW
I 1
*1
2-3
2 <v
<=*
.0
CO O 00 VO + pi O 00 VO tJ-c* O 00 VO t}- p* O 00 VO rj-fj 00 vo rf- p O
pJpJmwmwwOOOOOOnOnOnOn Ovoo 00000000 t^.f-t^t^r~N
P* C* CI M P C* N H N PJ tJ N M M M M M M M W W M M W M M M
mmmmmmm.^mmmmmmmmmmmmmmmmm
si
.5.5
D
00 O Mm n o\N Tj-r^Or* vin O r* J">oo O covo 00 m tJ-vo 0\rt i
t-^00 00000000 0\0\0\CNO O O m m w w pj pj pj rj co co co co **- -<i-
p) p c pi cJ p N p N t fitoMwmmrocicomMMtotoMMM
I-l
3
il
p owo co O I^tJ-moo ii-ifj owo mMM u-icJ On h. + m 60 io co t"^
VO ioui^iOrj-r)-rj-MmtlH < p) N w m m O O O O 0M>0\ O\00
* # "d- _+ rt- <t ."4" ;d> 4- ^ ;<*- ^ * ;dr rh tJ- 'dr -4" ^ ^ ^r .^- .^ to wwmto
#1
hi "i-OO rl >O00 M V> OVMNm rJ-00 n\o O rJ-t^M ioO\WNm ^o
rj- ^t- rj- 10 w> u^vo vo vo t^. r^oo mm o\0\0 O O h m h fi d mmw
u->voi^iu-)iY-iu-)W-iu-)W-)iovr)vriOVow-i OVO vovovovovovovovovovo
ft
3
el
8
-droo mnm t^tJ r-.c* t^t* t^d r-~H t^-H nhoo r}-ov'drOv , <i-C7v^-
toc^tlwi-cOOON O\oo 00 r-- r^vo vo vou-i^J-Ti-rororJ r w ih O O
<5N OS ON Ov C7v ON O\0O oomoooooooooooooooooooooooooooooooooo
u 5
2,'S
^
O
rj-w t^^O t->tOOvO MO* toO N^hM wirt OvOO f> to C7\ t^ <*
t^OO M O\0 O M d NM + ^- o->VO VO t^OO OOOvOOtltOCOtl-vO
O O O O M M M M W M M M W W M W 1-1 l-l * jS _t> ti tJ t< N H t
V t< V< tj n rt *c V V V< V< "d V* V V? V 'm "t "t n cj V< *t V< ti
+3
b f*
ofa-2
?, *"!
c3- a
hi rt rt rj MMM^-iJ-in vovo vo l^t^oooo OvO O * H rt co^-'dj-u^
OOOOOOOOOOOOOOOOOOi-i>-''hi-ii-ihihii-iw
ooooooooooooooooooooooooooo
OOOOOOOOOOOOOOOOOOOOOOOOOOO
P^uozuoh
^iiift'jod
IIbj ao asi'a
t^OO O - to tJ/vO t-^ Ov O S to tJ-vO 00 OS w to t}-vO r^OO Ov O t to u->
11 l-l t> M H N H f MMMWWCltlrJ-T)- + ^<j- + ^lfllO<OlO
p p O O O O O O O O O O O O O O O o o p o p p p p p p
b b b b b b b b b b b b b b b b b b b b b b b b b b o
jo oi^B'a
to Ov m oo On ^d- t c 'd- t* r owo y-> -dj- -^ t^ On t y>oo H vo h vo w
r~- Vi On io *M b oo vb Vl- V "w "onoo *r^.vb u-> Vj- to "rt *r "w b O Ov Ovoo oo
^Wl^^*^MMMWW(lrtf<rtflMtlrtrttMMMM
T^nozuoH
pojpanjj .iod
HBJ JO SSI'S
m n fi ' 'd V) V) "tJ to Vo Vo Vo Vo Vo Vo Vj- V}- Vj- "tJ- t}- t}- ^lo^uiifl
oSBntBqo joj
UOI^OTipO'JI
N H PJ PJ Mt*lMr}-^UN ii-|VO VO t^. r^OO OO ONOvO - i- C< tOxdj-^J-u^
pOOOOOOOOOOOpOOOOpOH.HiMi-.MM wh.
bo bo b
UOISSOldOQ
ptreuo]4BA9ia
jo sai^uy
~b voO voO iflO <nO oo oO w-iO vnO WO vtnO 00 "lO w-iO
m m tl t) row^^-io>0 1 M M tl K MWi-^Wifl I w
VlO ""> vo O w-iO vo O "~>0 vo O vo O "lO vo O vo O "lO "lO vo O vo O vo O vo
n rt t) mm^tJ-vovi I wwHrttocoTj-Tj-vouii h* >* n pi co to -4- -4- vo vo
rj- vo
t*sVO vo -d- pl m o 00 P^vo ** po N -i O OnOO Invo io + M rt m O OnOO t-~.vo iotj-m-
^-rJ-d-^-d-Tj-rj-coporororocorocoplplplplPlplplplPlPl>--i-i'-i>-i'-i-i-"
ON On ON ON ON ON ON ON ON ON On On ON ON ON ON ON ON ON OS ON ON ON _0* ON ON ON ON On On On p\ p\
b b b b b boob b b b b b b b b b b b b b b b b b b b b b b b b
pl ^^NOvO Pl ^- vo t^ On i- po vovo 0O O N tj-vo OO O Pl ^-VO OO Onm m<oNOnn
vo vo vo vo vo t-.r^t^t^-t^ t-^oo ooooooooononononOnOOOOOOm'-im.-iwc*
O O O O O O O O O O O O O O O O O O P P O N N J< M N H M - M ~.
00 VO vo PO M ON In vo rj- pl O 00 VO rj- PO ih ON00 VO t}- CO m ON t-- + pl O C\ N >0 M
nO vo vO VO VO u^ioiOVHOV>^^^j-^-Tj-rowflMMfON pl pl Pl d M >-i w >-c m w
n O povd Ovm +no povo oo h <j-lsO povo O pl vooo w -^-oo >- ^}-t^O Tj-t^o tJ-
tJ- vo vo vo vovo \O*0 NNN InOO 0000ONONO\0 00 0>-'>-'MplplplrococO'd-T+-
>ort O In r}- pl Onvo +moo mhooJ mmoo^O row OsN<jnwm onniomh On
0O00 OO N tv tNVO VO VO VO lOUSUTO^ + Th^-mMMMt) pl pl Pl Pl m ih i- m >-( o
tJ- d- u-i vo iovo vo tN tNoo oooo onOnOnO O i-i >-i d pi mm^^-'o vovo vo in tNoo oo
vp vp VO VO vp vo vo VO vp vp vp VO vo vo vp In tN In In IN IN In JN In N N N In ts ts ts ts ts
O vihvO m N POOO rJ-O vo m N fO0 rJ-OvO f) 00 tj- O VO MOO rJ-OVO CO ON vo w tN
On ONOO 00 tN tNVO VOVO vniri + ^-MMMrt pi m w ii O O On On ONOO OO N n tNVO
oo ^J^|>-f^t^J^tN^^r^t>.tNr-^r~.t>.tNtNrNjN.tNtNtN jnvd vovpvovovovovovo
pi on in vo pi oo vo * oo vort-rj-ri-ri-popopi o onoo tNvo vovoTf-copiMnooooN
VO VO Inoo O\O\0 h h t) n + w-ivo f-OO ON O O <-i H W + vovo tNOO ON O m pl to co
pl pl rl p p p< cococococopococoropoco^^r^^^T^-^' N t-d-T4- T j.i/~iu- 1 i ri , ou - )
p< V H pi pi 'pi pi pi pi pi pi 'pl Vl pi Pi Pi Pi Pi Pi Pi 'pl Vl Pi V* Pi Pi Pi 'pi pi 'pi "pi 'pi cl
vo f^oo 0\0 n m w + vovo oo On O m pl ro t}-vo t^OO On m pl po vovo 00 On ih ri <+
w w pl pl pl d pl pl pl pl pl pl pororotoroporororort-rJ-ri-Tj-^j-^-^j-vou-iio
0000O0OOO0OO00000O0O00OO0000O0OOO
000000000000000000000000000000000
OO H NrtVO M iflO >oo\ d-oo POOO pl t^. Pl VO M vo o
VO 00 ON - pl <4- vo r-~oo On - O rh vo t-^oo O CO rj-VO
vo vo vovo vovovovovovo t^r^r-~r>-t-- t-~oo oo oo oo oo
ooooooooooooooooooooo
vo ON tJ- On pooo ro tN pl tN m vo
t^oo O -" ro rf-vo tN On O Pl ra
OOOO OnOnOnOnOnOnOnO O O.
OOOOOOOOOi-iwhi
ooooooooooooooooooooo
ooooooooo
o o o
vo pi tN po o vo po onvo poo h-Nd ONt-^yiPoooovo
r^. t^vb & *b vovorl-T}-^-Ti-pororopl pl pl pl pl m
^-pi m p^t^yo^'p' n
* * b b b b b b
po Onvo
On Invo
On On On
OOPlt^.plVDl-'VoOvoON -3-0O POOO pl t~~ pl VO w vo O
VO 00 On m pl rj- vo f^OO On pl *j- vo >--00 O >-< po rl-vo
lo vo vovb vbvbvbvbvbvb k K n nn noo oo oo m oo
vo On d- On pooo po f- pl Sm*
inoo O M ro^-vo N 0\0 pl ro
00 00 On On On on On On on b b b
VO t^.00 On O O ih pl PO rj- vovo In On O w Pl po tJ-vO t^oo On w pl po vovo In On O Pl ro
_c _, ih m Pl pl pl pl pl pl pl pl pl pl popopopopocororoto-r)-^-^-^}-.^-.^^j-vovovo
b b b b b
V00vo0vo0o0vo0 v o0vo0 l o0 l o0vo0vo
Hplplcoco-5i-T4-vovo| i-iwplplporo-d-^vovo
OvoOvoOvoOvoO'OOvo
l-l -< Pl Pl COPOTt-T^-volO
jo 83iSuy
o vo o vo o vo o vo o vo o vo o vo o vo O ^0^2.^2^ ^2
7 wmNNCOCO^tI-vovo. wwHrtCOCO^^-voiO M
o onoo r^vo vo * co d hi O Ov r^vo vo rj- co N O Onoo f^vo vo tJ- c
" oo o O o oo o O o onononOnonOnonon onoo oooooooooooo
Sv^ONONOvONONOvONOV ONOO M0OMOOO9 0OMMOO0O0OMMOOM
b b b b b b b b b b b b b b b b b b b b o o o o o o o
co 10 t-^ ON n covo 00 O c* "+NO 00 O C* vo r^ On m t}-vO 00 O MW1NO
c* d N c> MMMM'+'t^-^rhi^viuTo vovo vo vo vo r>- t^ t^ i>.oo
SI
o
O OO Isv^J-mh Onoo iC i^MM m Onoo vo vo co m O On t--vo >t M m
wOOOOOOOnOnononOnon onoo oooooooooooo t^t-^r^r->t--t^
MMMMi-ti-iOOOOOOOOOOOOOOOOOOOO
N h C\t^ m tJ-00 rJ vo ON C< NO ON cl NO <3\ WN O rj-t^i-c r}-00 <-i vo ON
<+ vo to vovo vo vo t t-~ t-^-oo oo oo On 0\ On O O m >-< hi c* d d co co co
^^-^-<i--<i-<4-'fr'+-<i--<i-Ti-Tt-Tt-Ti-Ti-.ri-tovovovovovovovovovovo
f^ vo d 0\N^WH(vO + hi ONt^^H O NiOWOM^O CO hi OMv
O O O On On On On OnOO OO 00 00 f^ r^ r^ t~- t^vo vo vo vo 10^^10 + ^
MMnM(lHflt)f)rttlrtt)t)tlHrttltltltlt(
SB
hs mvo mvo mvo Mt^-N t~^ cooo r}- on o O vo w t^rioo co no H
OnOnO O >-i m c< cJ co co *$- rj- to tovo no f--oo ooONO\OOi-icleco
r~- r~.oo 000000000000000000000000000000000000 onononOnonon
vOvovovOVOVDvOvOvOVOvOvOvOvOVOvOVOVO uhouho
iowvivo
0)
a
OnOnOnOnOnOnOnO O <* m C* CO 3- to vovo 1^00 O r rj- t-~ On M to
rj- tovo t^oo C\ O N CO tJ- vovo I^OO On O <-> r> co tovo t-^OO On m N
u-i vo to vo to tovo vovovovovovovovo t^t--t"^t^t^.t^v^-r-^ t^OO 00
t) ti rt t) rt 'rt ' ' fi 'n rt ft rt el t) ' rt tf d N V
i
g a
o
VOVO 00 O W CO VOVO 00 O C< CO VO t>- ON HI c* tJ-vo 00 O N -sj-vo 00 o H
10 to tovo vo vo vo vo vo t"^ f^ f^ C-- t-- C^OO OOOOOOOO OnOnOnOnOnO O
OOOOOOOOOOOOOOOOOOOOOOOOO'hm
p p p p p p p p p p p p p p p p p p p p p poop
HI VO O VO O ON tJ- ON f 00 COOO CO f*. Cl t^ C* VO hi VO MVO w to O VO
tovo 00 ON ih N CO tovo 00 ON w M tJ- vo r^OO O CO tj-vo f^ On O d co
0000*-ii-'i-iH<i-iwMHclc<c<clcococococococo-^-^-Ti-
b b b b b b b b b b b b b b b b b b b b b b b b b b b
Xb^uoztjoh
uoi}Buipni
jo oi^a
<* to t* m m O On
On on on On onoo oooooooooooooooo i^i^i^r^t^-r-^t^r^t--.t^r^ Kno
TBIuozuoh
pajpung; aod
UBj; jo asiy;
mno o oo iocntJ-on cooo cooo corbel n h vo h vo mvo voo o
yovO OO On w cl co tovo 00 ON >h c4 ^ <o r^OO O CO t^-vO l~^ On O N
O O O O M il in m i-l w m cl N M CJ H C> CO CO CO CO CO CO CO '$ '<$
a&BUlBqO I0J
uoi;onpa'a
U0ISS8.t(fo(I
PUB UOI1T3A0I3
jo S9[3uy
vovo OO ON m CO tJ-vo 00 On m CO vovo 00 O cJ tJ-vO t^ ON m covor^ONM
yo 10 vo vovo vovovovovo r^r^t^c^ r^.00 0000000000 OnOnOnOnOnO
bo b b b b
O voo voO voO voO voO voO voO voO voO voO voO voO voo
i-iMdNcoco'^-'^-vovo MMHSrOM + ^'o'o
o
io O wi lo lo O lo O lo "iO lo "~> O "tO lo
wddcocoT*--<i-LOLO| nwOdcoco-^-Tt-LOLo
On
OloOloOloOloOloOlo
n w N N cocotJ-x^-lou-)
o
d m o onoo f-vo >oo + Mrt m O on Onoo i^-no lo <$-
oooooo r^t^t^r^t^r^t^-r^t^t^ r^vo ^o vo vo vo vo vo
MOOOOMOOOOMMMMMMOOOOMOOOOOOMMOO
b b b b b b b b b b b b b b b b b b b b b
CO d w ii O OnOO t^NO lo LO r}-
NONONONONO UOLOLOLOLOLOLO
oooooooooooooooooooooooo
b b b b b b b b b b b b
(t ^NO\M -+NO oo w co looo O to looo O to looo O
OOOOOOOOCTNONONONOOOOnwiiwddddcO
MM-.-.-i.i-iupJdddddddddddd
cono oo m r}-r^ONrt wh-O co
COCOCOTJ-TJ-ri.4-LOLO LONO NO
Ooovo io + H m On r-.NO uiw O C\ r^-NO +mm O
t--.NO NO no no NO NO u-)W-iu-)U-iu-iu-i0 , ^-^i-'+'T^}-T}-'4 -
p o p p p p p o o p o p p p p p p p p p p
OnOO r-^ lo ^ d n O OnOO f-~ lo
cocococococococod d d d
OOOOOOOOOOOO
wnh vioo n in o\ w n h io o\w tN f *o ^oo d
rh tj- vo u-i vonO 5 N t-^00 00000\ONOO-i*-id
UHiH/HOi^uiwiunnvn^unovi lonO NO NO NO NO NO
t--dNO wloO tJ-On cooo d r-^
d co co ^i- *}- lo lo lovo no r-- t^
NONONONONONONONONONONONO
lo CO w ^NV)Mn cms.u^m- ONOO NO ^J- d OOO NViMf) w ONOO no fr d O 00 NO
^-*i-r}-cococococodddddiiii>iiiOOOOOOONONONONON OnOO OO
d d d d d d d d d d d d d d d d pi d d d d d d d d J* " H JH
Nmc\iah NtnOMonea >^ t)oo lo w oo J-w t^^j-
co rj- tJ- lono no r^r^oo o\ o\ O m d mw 4 "^ lono
On ON ON On ON On OS ON On ON On O O O O O O O O O O
K M M M M M M M W M W "d d d d "M d d "d V* d
woono coooo Lod onno co o
f-. t-.oo ONOOMddco^}-Lo
O O O O _H W J1 _H _M -1 _M
d d d d d d d d d d d d
N'J-nOO tJ-mOO lo f< ON lo d ONNO co o N + mOO lo
NOnOnO vn^iA^-^ + t^mmrt d d CM f w p-c O O
d O t^-st-noo Lotoo t^^ii
O O On On OnOO OO 00 OO t^. t^ t-~
LOLo-^--<4-'J-T}-^-'*-'d-'>4-'^-^-
O co looo w r}-t^-0 tnN m lo on moo d nmvo w no
ionO t^-OO O h f| ^- lono 00 On O d co lono 00 On m d
OC 00 00 OO On On On On On On On On O O O O O O O m w
d d V) d d d V* d d d d d to co Vo Vo co co co to to
M f-COONLOMVO coO t-~coO
^j- u-i ir^oo O d to lo t-^oo O d
MMMMddddddcoco
CO CO CO CO CO co co to to to to CO
>flN 0\m tOVO OO O H WNO\C( t}-NO O d "J- t-. ON d
poooooooooooooooooooo
rh t--- O d ^oo O cono On m tJ-
lo LONO no no no r^ f~- t--- t^oo oo
OOOOOOOOOOOO
O lo O ^-ONTJ-CN-^-ON-d-ON tooo tooo tooo cooo tooo tooo rooo tooo cooo tooo t}- On
LONO OO On O C- CO LONO 00 On h M ^- lo r-.O0 O * CO tJ-nO ts O O M loNO 00 On n d
^-^J-^tI-woioi/^v/^ioio lono nonononono t^r^.t^r^t-^c^ r-^oo oooooooooooo cnOn
ooooooooooooooooooooo
OOOOOOOOOOOO
O cono On co r-v O ^oo m no O lo On cooo m ts f) r^- d r^- cooo coOn^J-O lo m r-^ co On
OnOC r^NO NOLOLorJ-cocoddnOOON 0\00 OO t-- t-^NO no lOVo-^-rJ-Tj-cocod d w
^"'^^^J- v OLOJ-)0-ilov<-i vonD NONONONONO N N N ts N t-> NOO OO OO OO OO OO OO OnOn
cono r^ O d tJ-nO On >i co u-,00 Odw-it^OMrJ-t^ONO'^-t-^OMior^Oco u-iOO m
O O >i -" 11 ii ii d d cJ cJ tococotO'^-^-^j-^T^-vow-i iono nonono r^r^t^c^oo
>oO vno voo wo i>->0 l oO >00 loo loo loo lo
OloOloOloOlooloolo
i w d d coco^J-tJ-lolo
2
U0T3S3ad9(I
puB uoi^BAaia
jo saiSuy
"b UN O >0 un O un O un wiO WO un O
HiHiddcoco^Ti-uNUNi h m ri
S 2
UNO unO ioO unO voO
dcnco^-^-uNUNi m
CO
M
ED
1
E
M
H
P
O
ds
g
i i
H
H
Ed
r-l
B
r 1
si
Si
So
5
co d m o O onoo t--vo vouN^coddniO
oooooooooooooooooooooooooooooooooo
ONOO 00 t-VO <OlOrJ-Mtl
CNCOCOCOCOCOCOCOCOCO
0OO0O0O0O0O0OOO0OO0Q
b b b b b b b b b b b b b b b b b
0000000000
si
am
unoo O covo ON n + l>- O d >o( m +no
VO VO N N N r-oo OO 00 0\C\0\0\0 O O w
COVO ON d UNOO HI T^- t^ O
Hi^HicJddcococOTj-
COCOCOCOCOCOCOCOCOCO
O
il
Is
o
t)-Mm O ON00 t^ un t}- CO hi O ONOO f*. un $
HltdttHHHMHHHMQgQQQ
ooooooooooooooooo
en d hi O 00 c^vo un co d
O O O O ONONONONONON
O O O O ONONONONONON
u 5
&o
o
hi VO M un O uNOUNON^ONrl-ON'ri-O >fl O >0 h D d r^ d 00 M 0\ +
OOOOCvOOOtHMi-iMrJcorori-u-) unvO vo r-~ f--0O 00 on ON O O hi
vo vo vo vo f^rvr-^c^t~-.r^r-^r^t-^t^.t-^r^.r^rN.i-^r^r^.r>-.t->. t--oo oo oo
I-l
-p
il
" o
O
co w ON00 vo +Mh O 00 vo +mm O 00 VO iflMM O ON r> un tJ- d m
ocoo t^-t^t^t--t^f^ r--vo vo vo vo vo vo >rnonio<o>fl^^rh444
-p
03U3
00 VO to M ONVO -^-N OOOVO rl- d m o\oo vo
unvo r^oo ooONO*-iddcoTj- unvo vo t-~oo
dddddddddddddddd'd
un co d hi onoo r-^vo un u-i
ON O hi c d en ^- u-ivo t^
d cococococncococnco
d d d d d d d d d d
"-1
o
Jl
oo vo co O t"- + " ONVO 'd- hi ONVO ^-hoo ion owo ^ m OvNiflMO
vOvOVDvO UNUNUN-d-TJ-^-<J-cocococod d d w m m m o O O O O
."* :* ."*" :* ."*" ."* r*" .^ :* :* t ."* .^ ."* ."* r 1 " r*r*" :* :* :*:<*- :*:<*- r** ^ ."*"
>otOM D\ tNiOrj-tor) m O O O O >- hi d d roONO\M covo O ^
to un t^-oo o d -^-vo oo o d ^vo oo o ^-vo oo o d -<4- r-^ on -^-vo
mt*imjlTj-^-^-^T)-V)iovivo WVO VO *C ^O vO N tv N t^. NSO OO 00
cococococococococococococo^coco'coco'cococo'cocococococo
lid
t-~. O covo On d unoo hi t^- r-. O WNO covo
ooo\o\0\ff\OOOHMHt)NflMwn
wwi-iHiMclddddddddddd
p p p p O p p p p p p p p p p p o
O tovo ON d vo covo O
^J- <4r $ -^ un unvo vo vo t^.
dddddddddd
O p O O O O O O O
IB^uozijoh
IIM ao asiy
^ON^-Os-^-CvioO WO >OOvO hivo wvo
^" UN t^OO O Hi CO VOVO 00 ON hi cl $ vo t--oo
ONOnOnOnOOOOOOOhii-iihww,-,
r* hi h, m js d c< H cJ cl cJ c< N d d cJ c*
o b b b b b b b b b b b b b b b b
M t^d r--d r^doo to ov
O hi cotJ-vo In CT\0 CJ co
dddddddcococo
dddddddddd
b b b b b b b b b b
uoiiBtnpui
jo oi^'be;
d-Hi t-^cooNuiMoo -^-hi r^-^-o t-^T}-Hi r-v.'rj-Hioo u->m onvo toooo
m m o O On on Onoo oo oo S (n r~-vo vo vo ioiown^-tJ-^-cocococopI
re^uozuoH
p9jpunn iad
HBj jo asfa
o\ on on "on b b b b b b b m In m m '
m r-^d f^d Ndoo coon
O _< co rt-vo N Ov O d co
d d "d d d d d co co co
dddddddddd
oSBuiBqo joj
uopoupay;
tJ-vo on d iooo hi Tj-r^O cowiONd vooo w
OOOOOOONONONOOOHliHMHIclcldCO
^- t^ O co n O covo O co
CO CO tJ- TJ- tJ- UN UN UNVO VO
MHiMHiHii-ic^dddddddddd
dddddddddd
U0ISS9Jd9Q[
. pire uox?BAO[a;
jo S9[J5uy
*b "NO W-iO "NO UNO UNO UNO UNO u->o
I HIMC<dCOCO-^--<^-U-)UN| wwcl
hi M
UNO UNO UNO UNO UNO
dcocOT^-^-UNUNi i-i
CO
o O 10 o >oO vo O vo O o O vo O no O o O no O u-iO vr>0 no ""> O o O *o O "">
m d d ww^-t^'o 1 m w tl o w w ^ <( ui vo 1 m m M M tom^+mvi
Th NO
f w O On On r-. f^N ^O u^j- M to H m m O On OnOO t^ t^-NO u-itJ-tJ-co^HmOOOn
MMMH(lH(l(l((((lMld(IHHMNMNNHMHMHMMHO
b b b b b b b b b b b b b b b b b b b b b b b b b b b b b o o o o
^J- r^ O MtsO cono O cono O MNO M fs O *i- t^ O tJ-OO *o on cono O ^00 *' ^
rj- + vo NO NOVO VO* SN t^OO 0O0O OnOnOnO O O m hi w C* ^ f Mt ?IltIv'I
H O OnOO t-~NO *} CO rt hi OnOO t^-NO w^J-MH Hi O ONOO f^NO NO + CO c* hi O OnOO
On onoo oooooooooooooooo r^t>-r>.r^t^.r^t^r^r^ r--NO nCnononononononono no no
OnOnOnOnOnOnONOnOnOnOnOnOn^OnOnOnOnOnOn^PiOnOnOnOn^OnOnOnOnOnON
b b b b b b b b b b b b b b b b b b b b b b b b 6 o b b b b b o o
O no m t^-rjoo rt-O u-iw NMOMnUM tj-o t-> co on o tf oo vocioo *o tf On no c* On
H M CO ro tJ- ^- vy-ivO VO t-~ t-sOO OOOnOOhiiv1c3cocOt}-no novo r~ t^OO On On O hi hi
0000000000000000000000000000 On ON ON On On On 3\ OnOnONOnOnOnOnOnOnO p O
OnOO NO +mh 00 NO ifl ro t) O OnOO * wi^-d m OnOO NO no rj- p* m O OO t-^vo + CO
cocococococococ^c^pJc^cINhimhihihiwhiOOOOOOOOONOnOnOnON
MMHIHIHIHIHIt-IHlHIHlHIHIHIHIHIHIHIHIHIHlHIHIHIHtHIHIHI
><i-cocop*cHiHiOOOOOOOHiclcOri- nonO Ms (> O C< co novo oo O d ^J-NO
OO ^O k d pi* nono NOO 0\0 m d M\j- wiNO N00 On O N CO ^ u-ivO t- On O <-< C*
COrOThr^'^Tl-'^-Tj-rJ- T J-T}-^t-<J^'NW-lU-)VOlOU-iVOVO NOVO NO NO VO NO NO NO NO J>- J"*" J**
V* V< 'n 'n V Vi n V* V* V> 'c4 Vi V V< V* V* V V* n V< c* V* c* V V n m V* V* "h 'h V h
OO no CO O N^ld OOONO tJ- C* O t-s-Tj-M OvNiOMM ONNO -<4- cj OOONO COM ONh- lO
ON ON ON ONOO 00 00 00 t^ t-~ t^ t-> t^NO NONO rNU-|U-|U-|U-i^}--r+- T j-TJ-r}-COCOCOCOc< N f4
00 N NO O W->ONO WOW1WM ONtS^n-^-Tl-T4-T}- NONO NO On H NOOO M VO fl OO tJ- hi OO
OO Hi CONO OO l-l CONO 00 M x^- ts ON C NOOO M t}- t>- O CONO On CONO On cono O MNh t
OO OnOnONOnO O O M M M hi c* p* p MMW^- + ^TJ-mvi nonO *0 NN f^ *
co co co *co co Vj- Vj- '^- ^- Vj- V> Vj- Vj- V* Vi- Vi- Vi- Vi- Vj- V4- Vj- Vj- Vi- Vj- Vj- V* Vi- V^ 'rj- Vi- V}- Vi- Vj-
mno t}-oo hi v">oncjno ONTi-t^Hi mQywNM voonmnm xoONcor^HiNO -^-oo
r-~ t^OO 0O0O OnOnOnO O O hi hi c* c< M cocorJ-Tl-Ti-u-i u-iNO NO no t>- t^OO OO On On On
d N M d d cJ cJ N cocococococococococococorococofocococococococococo
ppppppppppppoooooopppp p p p p p p p p p p
ri-O ^HtNO hi t^c^OO COOntJ-O vohiNO C< ts COOO tJ-OWOmnO C< N M G\ ^- O NO hi
vn t>-oo hi co t^-nd novo d ^-insoo o hi co -j-no inOm d ^- u-, r^oo O d wm
COCOCOri-Ti-T}-rj-ri-'r}- T }-u- ) V^>W-)irNU-i U->NO NO NO NO NO NO NO t^tst^r-.ts l^OO 00 OO 00
d d d d d d d d d d d d d d d d d d d d d d d d jl f) ji rt f< el _e
b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b o
NO M O ts Ti- f< ONNO + M ONNO rj-f< OVN^d OOO ITiCOHl ONt-vU-lCOHl OMMflMM
^^^^^^Tt-rh^^i-cococococococococococococococococococococococo
cococo ri-'ri-^Ti-Tj- r }.Ti-vr)iyNu-)ioNo w-)no no no novo vono t~.t^t^.c^-rs r-^oo oo oo oo
fidddddddddddddddddddddddddddddddd
no O cono O co r-^ O mno ^oo w un on t no O mnm ^oo d* O ->4-oo d wioxw
f Njs t^OO 0000 ONONONO O O hi hi hi tf C* M CO to + rj- ^" NO Y^^P f *? !~^ ^ r^? 3
N c^ d cl c< r< c* c< c< (>! cococococococococococococococococococococococo
mo u-io voo >oO vno noO >oO n<iO i^O "iO >o O w->o >oO voO >oO wo x ^
" d d to to ^- t(- no no | MMddtotorj-<j-voioi MMddtoto^^-ioio
Ti- VO
puB uox^BAOia;
jo saiSuy
o!
O\oo r~- r~.vo 10 u-> rj- co co ft m m O O Ov 0\30 oo r-- t^-vo vo vo $ co ft
OOOOOOOOOOOOOOOCnONCNCNONONCNCNONOnCNON
oooooooooooooooocooooooooooooo t^.i>-r-^r^t^t^t^r^t^t^t--t^
b b b b b b b b b b b b b b b b b b b b b b b b b b b
'
ff\MNM voOO ft VO O 'TOO tHO O "1^ MOO ft VO m vo ON ^-00 co t^
iri^o vo r-- t~- l>~0O OO On ON On O O h m i-i ft ft co co rj- ^ ^ vo iov> vo
T^^^^^r^T^^^^^f-vovovovovovovovovovovovovovovovo
^ o
8
t-~vo vo ^J- co ft
O ONOO t-^vo vo vo * ro ft ft i-i O ONOO t- vo *j- co co
b b b b b b b b b b b b b b b b b b b b b b b b b b b
VO CO O r-- vo ft ON r-~ *}- ft O NiOMM ONVO tJ- ft O (MviO r(- t) hc O
ft co ^ tJ- vovo vo r^OO O\0 O i-i ct co co tJ- vovo r-^ t^OO ON O m ft co
O O O O O O O O O O H MM -. H M M M M M M M M M (4 ft Ct ft
ft 'ft ft rt ft ft ct 'ft fl ' ' rt ft fl tl t< ft r! r) 'rl ft f< fl fl f)
^ i,
a
a
ft O Onoo vo vo rj- rt m o oo t-^vo <j-tift o Cnoo vo vo tJ- co >-< o ooo
on onoo oo oo oo oo oo oo co t^r^-t^t^r^r-- r--vo vo vo vo vo vo vo vo to vo
ooooooooooooooooooooooooooo
ON ft voOO h ^j-NO COVO O -+0O MNH^O MVO WVO MvO.ft00 *J- O
CO vovo ts 0\ O >-i M tj- io t^OO ON m ft rj- vo t^OO Ohm t^-VO N C\ m
n cn n n noo oo oo oo oo oo oo oo on on on on on on O p O O O p O
ft "ft ft ft ft ft ft ft ft ft ft ft ft ft ft ft ft ft ft fnWMMWWfOM
MOOOIO +
OOO vo CO O OO vo + ft m ONOO VO to CO M ON t"~- to sh ft
mnwi-i>-i-ii-i0000O\O\O\o\ onoo oo oo oo oo oo r--r-.r-~t-^r--
cococococococococococoftctrtftftclffftftftftctrtftftrt
m
iovovovovovovoO ^}-oo fHO m O ONOO 1--.VO VO I- VO w VO h VO 00 O
oo ft vo o rj-oo ft t^- >- vo O * on tJ-oo cooo cooo -^ on to O vo w t-~ <$-
oo On ON O O O h >h ft ft cococotJ-^vovovovo t-r--oo on ON O O i
^^T^vovototoiovovovovovovovovotovovovovovovo vovo VO VO
53
ov,e
CO t^. ft VO
v<-i ON rh ON fooo ft r-- ft VO
voovoovoovnovnovo
OOOOOOOOOOOOOOOOOOOOOOOOOOO
XTJ^UOZUOH
t^C-lONVowVO ftOO Tj-ONvnM t^f^ONVow N to 0\"IH rs M C\"ih
VOOOOO ii COtJ-VO h- OO ft -+U1N00 O ft CI vovo OO O i-i fO tJ-VO oo
OOOOOOONONONONONONOOOOOO'-'lHlHMWMftftftftflfl
ft ft ft ft ft ft ft ft ft MfOmMtOMMMtOtOMnfOfnmmmM
b b b b b b b b b b b b b b b b b b "o b b b b b b b b
jo ot^a
fiMfOfotOMMtOfOtOfOMfOfommwmtorom
CO CO CO CO CO
Itj^uozuou
poapuiiH xdd
liv& xo asra
SM 0\"1H >C ftOO T}-0\v/->i-t NP1 0\"1 m N M 0\>0 h f^COONvni-t
VO 00 ON 11 CO r^-VO N 0\0 ft ^ vo J--00 O ft CO vovo 00 O ~ CO ^vo oo
00 00 CO ON ON CN ON ON ON O O O O O O * '<- W ft ft ft ft ft ft
ft ft ft ft ft ft ft ft ft cococococo-cococococococococococococo
uo^onpo)]:
t^ w vo O 'i-oo ft vo O rj-oo wnh wo ^00 co r- ft vo O vo O tJ-oo
OOONONOOO'-lt-lftftftfOCO'<i-^-VOVO VOVO VO N NOO OO ON CN ON
cococo^^^^Vh'^^'^^^^^^^^^^'^-ij-il-^-^-^-Vj-
uoissojcloa;
put! uoi^'BAgig
jo s9;Suy
b voO voO voO voo voO voO voO voO voO voO voO voO voO
1 tHMftftCOCO^-rJ-VOVOl MMftftCOCO^-^-VOVO. f
vo t->. oo
m M O M
Vo0vo0vo0^0vo0vo0vo0vo0vo0"- r >0vo0vo0vo0vo0 u ">
m Tt ^vovo I MMddcoco^-Tj-iovoi Mwddcoco^-rJ-vovo
On O
m d
n m _ o O onoo oo r- t-^vo vovovo-d-cocodd'-i'-iOOON osoo oo r- r-vo *o mio
^C\!>o\ Onoo oooooooooooooooooooooooooooooooooo t-t--. - >.r--r-.i--r-.r^i--r^
O O o
0000000000 boo OOOOOOOOOOOOOOOO
i-. r-oo oo
O vo on rj- r-. cooo cooo cooo cooo cooo cooo cooo tJ- On vo O vo w no d f- d
Ononono O h >-H d d cocorj-Ti-vo vono no r- r^oo ooONOOwwddco
vo vo VONO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO IT^ !>* I s 1* t t t^
d - O
co co co co
On Ov On On
ONOO r^NO O^-rJ-^ M w O O OnOO "--NO votj-rj-cod d >t O On OnOO C--nO
ddddddddddddi-iMi-<wi-iiHMi-iMi-(>-iOOOOO
OnOnOnOnOnOnOnOnOnOnOnOnOnOnOnONOnOnOnOnOnONOnOnOnOnOnOnOn
o o b b b b b b b b b b b b b b b b b b b b b b b b b b b
90 f-ND vo
CO t}- vono
d d d d
d-COd w O OnOnOnOn ONOO 000000000000 ONONO ih d COrl-vo r--oo ON w
t^OO ON O >-< 1H d CO + VONO t>-00 ON O >-< d CO ^-NO t-OO ON O H- d CO d-vo
d d d COCOCOCOCOCOCOCOCOCOCOrj-'d-Tj-'rl-rj-'d-'d-r^-'d-VOVOVOVOVOlO
M rt ti
d d d d d d d d d d d d d d d d d d d d d d d d d d d d d
r^vO vo rj-
VO vo VO vo
O O O
co w o Onoo i>-no r}- co d O Onoo i~~. vo rj- co d ih O Onoo t-NO vo co d w O
vovovo^l-rJ-rJ-Tl-Ti-^-Tl-ri-cococococococococod d d d d d d d d
00000000000000000000000000000
d TJ-VO t>.
CO CO CO CO
vo d On r-. vo co m onoo i-.no no no no no no no f-oo O d >-J-vo On d vooo d no
On ih d --i-NO oo O it covof-ONw covor-ONw covo oo O d '-J- t~- On >h tJ-no
h d d d d d cocococococOTj-'^-'d-TJ-'^-vovovo vovo vo no no no t~- t~- i>-
cococococococococococococococococococococococococococococo
00 NO t}-COW on 1-- vo co d ooo>o -d-d O 00 NO VO CO d O oo vo mw t) O oo vo VO CO
1>-vd vo vo vd <0 vovovovovovo'^-T'-TJ-T}-Ti-cocococococod d d d d d m m w m
d d d d d d d d d d d d d d d d d d d d d d 6> d d d d d d d d d d
d <+vo r- t-^ t-^ t-. r^oo oo oo oo oo oo OO d -^-no m O t) t^O fl + r^oo on m cono
O VO d 00 vo d ONVO CO O OO vo tj- d O ON00 ir-vo vo vo ^J- + ^h vono r-.oo O Cl voOO M
d CJ CO CO ^ vo vono r^oo oo o\ O M rt H W + vonO t^OO ON O hi d CO t$-NO t^oo On m
o vo no >o no vb vb vJo vb vb no no i->. V-. V* V- t-. V Y V> V" i- r-.oo oooooooooooooooc on
vo o ""-
CO CO ^- tJ-
lO vo VO VO
O O O O
O voovo mno m r-doo co>3 tJ-onvomno d r-NCOONVoovo doo tJ-onvo
vo vono NO f- t--00 00 ONONO O i-i w d coco-^-tI-vo vono f- f-00 OO On On O
vovovovovovovovovo voNO NOnONOVONONONOvOVOVOVOvovononONOnO IT^
p p p p p p p p p p p p p p p p p p p p p p p p p p p p p
so <*- no d oo ^-m r-^co onnO d oo vow r- -3- O NmOnO co cnno d on vo d On vo d
Cn h. CO rJ-NO M>n cl rt-vor^ONO d +iO(s OnO d tJ- vo r-.0O O Cl CO vo t^OO O Pi
d cocococococO"5J-'4-tj-tJ- , *}-tJ-vovovovovo vovo nonononono c-.r-r-.c--r r-oo oo
cocococococococococococococococococococococococOcococococococococo
O O
00000000000000000 OO OOOOOOOOOO
cod O Onoo vo vocod O Onoo no vo co d w O On t-.NO v-i tJ- d- m O Onoono vo tJ- co d
p O O ON On ON On On ON OnOO 00 00 00*00 OOOOOO t~-. t-^ f~. t t~- C~-- t r-NO NO no NO no vo NO
co co co Vl d d d d d d d d d d d d d d d d d d d d d d d d d d d d d
. M t^ t^^p r^ p" 1 r ? r 5 * - 1^* 1 r^ f- 5 ^ p 5* +y"No\on -^ vo t-.oo d co vo t-^oo d
d COCOCOCOCOCOTl-Ti-rj-Tj-Tj-TJ-VOVOVOVOVO vono nononovono r-- "f~. t t~~ t~~ t- 00 00
CO CO co^o cococococococococococococococococococococococococococococo
CO00 d r-MND m voo voo + On tJ- On rj-oc cooo cooo cooo cooo cooo cooo -d-00 *}- ON
P w d _d co o d- tJ- vo yo vovo no t>-r-oooo OnOnO O w d d coco^J-tJ-vovo
VOVOVOVOVOVOVOVOVOVOVOVOVOVOVOVOVOVOVOVO VONO NbNbNbNONONOvbNbNbNbNb
vo vo
w d d co
voO voO voO voo voO voO voO voO voO voO voO voO voO voo vo
cotj-^vovoi Mi-tddcoco^-^vovoi Mi-iddcocorJ-^-vovo
ON o
uoissaicfoG
pure uoji'BAaxa;
jo se'iSirv
"bvoOvoOvoOvoOvoOvoOvoOvoOvoOvoQvoOvoovoO
h h ti m to <j- ^ vi >o . mihc1p1cocot4-tJ-vovO|
m d co
pi cl pi
02
I
P
1
P
O
1 (
H
a
s
IS
<+- rj- co po pi rl m m o O On Onoo oo r-s r^vo vo iflo^-^wMWfi pi
b b b b b b b b b b b b b b b b b b b b b b b b b b b
*1
o
OO T+" O VO pi t^ co on >o h vo CO ONVO pi 0\U1 OMA^M VO M OO vo pi
CO -<4- vo vovo VO t^ t^oo OnOnOO-*p1pIco-<+-t}- vovO vo r--oo OO OS O
iNtNtNtvtstNtNNlNtN tsOO OOOOOOOOOOMOOOOOOOOOOMKIOO 0*
o
41
I
o^mrt m o O Onoo oo two vo vo rj- co d m o On On Onoo oo t-.vo vr
O O O O O O O OnOnOnOnOnOnOnONOnONON O\0O OO 00 00 00 00 00 00
ON on ON ON on on onoo oooooooooooooooooooooooooooooooooooooo
b b b b b b b b b b b b b b b b b b b b b b b b b b b
c3!C
o
MiOSOVH rJ-VO OO m COVO 0\0 >0 0\MNm lO Q\ m s h VO m VO Ml
l^OO On O d CO r+- vo r-.0O ON O d CO tJ-vO NO^O h m <^-vo f^ On O C^l
u~i vo vovo vo vo vo vo vo vo vo t^t^t^r-^t^r^ t^-OO OOOOOOOOOOOO OnOI
d d V* d d d d d d d d d V* m d d d d d d rt e V e V< t*
T-l
o
Je
OnOO t~.NO vo <$ CO d m O ONOC t^.VO VO vo tJ- CO d m O OnOO f^vo vo tJ
i_i-immi-imi-iwi-i000000000000\OnOnOnOnO
OOOOOOOOOOOOOOOOOOOOOOnOnOnOnOnO
43
O voO vj-> m t>. co O N + r) O Onoo oo 00 OnO <* co vo f^ ^*-oo co o
On i-i ^vO C\m ^J- r^ On d voOO O COVO On pi NO On N u-iOO Pi vxio pi vr
r-vOOOOOOOO OOnONOnO O O m m m w pi pi pi cococo-^-rJ-^VNV
CO CO CO CO CO CO CO CO CO Vj- ij- Vj- rj. ^4. Vj- r}- r+- Vj- Vj- 'tJ- Vh V+" rj- T+- Vj- T+- Vj
o
go
as
" o
O
p M OnOO VO vn co d O On t^NO tJ-
hihOOOOOOOOnOnOnOn
ttt)HtlSrtt(Nt)HHMM
43
a
n s
ai
" o
a
On On On ^ co co cooo tJ- q u-i o NO
^1- tJ- cooo tJ- o no co i-i onoo oo r^
Cl CO y^Np 00 M CO JOS OO O (S
OnOnOnOnOnOOOOOO'-'i-i
g A a
O
hi nmo vj moo t^-ono coonvnpioo ^m t^-Ti-o f-^-o r^-^-o r*
m m pi co to t}- <+ vono vo f^ t-^-00 OnOnO m p-c pi porOTJ-o-i vovo r~~ t~-
r^r^f-.r^r-Nt^.t^t^.r^t^r^r^r^r-> t^oo oooooooooooooooooooooo
jb^uozuoh
00 vo pi On vo Pi ONVO CO OnVO COO r-~Ti-M00 vopl OnVO CO m 00 vo Pi o
to ioNOO O Pi towi p-00 O Pi rt-vol-^O\0 Pi + >o P> ON m pi ri-vo r-
OOMJMO\0\0\0\0\0\OOOOOOHMMHMM()t)(|(|
to to to to to to to to to to ^ ^ ^- ^- ^ t)- ;t + "t ") ,"t + + + + ^ vt
b b b b b b b b b b b b b b b b b b b b b b b b b b b
uoptsuipui
jo ot^a
O OnOO r-^vo vo + tOM m o oo r-^vo vo t4- co pi m O OnOO t^vo VO vo rt
vo vovovovovovovovovovo^^^^^r+^Tj-^^J-tocototocococ' -
I^tiozuoh
PGJPUTIH 23d
UB& ao asja
00 vo pi On vo pi OnVO co ONVO toO ts + h 00 vod OnVO co m 00 vo pi O
co vo r^oo p pi tovop-oo p el ^jr yo r^ on o pi tj- vo r-^ p\ M pi -<j-vo t^
MMMM b\ ON ON OS ON 5\ O O O O O O m n m m m m fl k t< tt tl
tOtOtOtOtOtOtOtOtOtONi-^rJ-'+^+'tvf^-^+^-rt-Nf^^^
aSBureqo joj
uoipnpa'a;
t}-On^J-0 voOvo ih lv.pl t- COOO tJ-OnvoOvO m I^pIOO t+-Onvoi-ivo
VO VO P-00 OOONONOO-(MPlPltOcOTj-u-i iovO VO tv- r--oo OO ON o O
vbvbvbvbvbvbvb tstv'pNNNtNr-tvtNNNNNtNNNps noo oo
uoissaidaQ
ptre 'uopBAaig;
jo sajSuy
*0 voO voO voO voO voO voO voO voO voO voO voO voO "io
M M (I H tOtO^-^lOlO , M M rt tOtO^tVlVl I M
o ' '
1-1 pi to
M N cl
w O O O On Onoo 00 NN t-^vo vo vovorJ-Tj-Tl-totototl d -> m O O On On OnOO
vo vo vo vo ioio>A>oirnflvnoioiouiio>o>'i>o>^'flwnnvnu - iviinio + ^-^-T
t- r-- t^ t^ t~- r-^ r^ t- r- r-. r-^ r^ r-- i-~ t-^ t^ t-^ r-. t-* r*- t^ t-~ t-~ t-. t-~ r-^ t^ r^ r~ t-^ r*. r-~ t
b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b
onvo to o r*-
D 1-1 d to to
0>O>O\0\O\O\O\O>O\O\0\O\0\0
t) N d t4
ro tl
o
OnOO
t^vo
vo o +
to
rt
O
OnOO
t-- t-vo vo
vo
*
to
n
o
ONOO
l^VO
to VO
On Os On
O\00
oo
00
oo
oo
oo
M
oo
oo
oo
oo
f^ r^
r^
lN
r~-
r-^
r^-
r^
r>.
r-
t^.VD
VO
VO V
VO vo
OnOnOnOnOnOnOnONOnONOnOnOnOnOnOnOnOnOnOnOnOnOnOnOnOnOnOnOnOnOnOnOn
O
o
o
O
O
o
O
o
O
O
O
O
O
O O
o
o
o
O
O
O
o
o
o
o
o
o
O O
o
hvo to o r-. -3- fvo +wrt O Onoo iomw
i d to r}- + vovo vo r^OO on *-< m d to t}- <ovo
O O O O O O O O O O O m w ;h m m
d d d d d d d d d d d d d d d d d d d
u^tJ- Mdrt m ON OnOO t-VO vo rj- + to tf "-" m O OnOO r^ t^> !>-VO ) uiifliflrj-
ooooooooooooooo t~st^r^t^-r^r^t^t^t~--r~-t->.f^r^ t-^vo vovovovovovovovovovo
ooooooooocooooooooooooooooooooooooooooooooooocwoooooooooooooooooo
b b b b b b b b b b b b b b b b b on b b b b b b b b b b b b b b b
ro vovo oo o ** to vovo oo
OnOnononOOOOOO
00 vo <* rt O Onoo f^vo mwuno vovo f-oo On
rl d to to to to to>^J-
vo tf onvo vo tj- ^ vovo i>- o msmoo r}- d ooo onO d vo O *}- m oo vo vo t-oo t~-oo
On tovo O t}-0O HVO O + On to t-^ rt VO m^O ft >o O NO h VO rt t^- tooo t}- O VO rt ON vo
;ovo vo t^t^J^OOOO On On On O O i-i * rt rt to to rj- + vo vovo vo t^- t-^OO On On O O
^^^^^^Vj-^^Vt-^vovovovovovovovovovovovovovovovovovo vovb VO VO
+ 1100 rf-HiOO vo rt ONVO tOMOO Wl O OS S + M ONVO "* w ONVO MM ON t^. vo rt OOO
OONONOwwtltOtO^- VOVO VO f^OO OOOVOMh^M^^- VOVO r^ t^OO ON O l-< M
0OO0O OnOnOnOnOnOnOnOnOnOnOnOnOnOnO O O O Q O O O O w w **
DOOOOOOOOOOOOOOOOlHMMWMMMWl-ll-.l-tHIHl-4WI-l
< tototototoT+-'rJ-^}-Tj-T+-rJ-vov<-)vovovo vovo vovovovovo t^-r^t^t^ t^-00 OO OO 00
* ^ .* ."* ."* r*" ."* ."* .+ .* .+ .* ."+ ."* ,"* ."* ."* .^ "+ ."+ ."* ."** .* ."* ."* .^ ."* .* ."* ."* ."* :*" r*"
> o o o b b b b b b b b b b b b b b b b b b b b b b b b b b b b b
o
t<
N
O
ONOO
l--.vo
vo
+ tJ- to rt
O
ONOO OO
f-.vO
vn
+ rt-
ro
N
o
ONOO
t-^vo V
N
rt
N
t
H
M
t)
H
N
t)
o
o
o
o
o
1
r)
N
tl
cl
c)
N
M
H
r!
M
t
rt
t)
tl
t>
tl
H
ri
tl
tl
tl
tl
tl
tl
tl
ti
tl
tl
tl
tl
tl
) tJ--oo votl O f^voti o I^tJ-M O l^rj-tl ooo votow onvo r}-tl Ooovo tort On
* ^ r r*"^ * O m tnyo t^oo p tl tJ-voc^-Onm t4 tJ-vo oo On m to u-> t^oo O c< t}- vo
I tototototo + Tj-T$-T4-^}-U-vovovovnvo vovb vbvbvbvbvb r-~.r^t^t-~. t^oo oo oo oo
i rt-ONvoii l^toONVoovo rtoo rhOvo tl Onvoi-i r^toONVotloo tJ-O r->-to ovo
I tl t* to tJ- rj- vo vovo t-^ f^OO 00 ON O O M >h tl to to rj- tJ- vnvo vo t^-00 OO On On O
J t 00 00 00 00 OO 00 OO 00 00 00 00 00 00 00 ON On ON ON On On ON On ON On On ON On ON On ON On O
OvoOvoOvoOvoOvoOvoO l oOvoOvoOvoOvoO , oOvoOvoOvoO , o
M W^-Tj-mVl | MMCltlCOtO^-^J-volOi M M M d MM^^I^IO
t}- vo
noTSsajdga:
jo safSay
O ioO vo O vo O vo O vo O vo O vo O "lO wiO vo O vo O io O vo <
h rt t) mm't ^uiio | h h m cl coMrj-<j-ov>| j
vo n oo
d el el
02
w
IH
ft
ft
1
I
g
OQ
s
I 1
^ o
o
MSN NVO VO VO irnnui^-^^-Mfm el el i-i w n O O O C\C\C
oooooooooooooooooooooooooo<
+3
a
"E3
US
O
eJ^wwOOOOs Onoo 00000000 OvO i- el eo rj- tJ- u->vo NOO O <
tsco On O i el to m rh vovo tsoo on O d eo -^- io^o tsoo On O co *
m w n cl el el el e el d el el el el m w w m w w w + ^- + <
'el el el el "d d d d d d d d d d d d d d d t< tl t) rt d d d i
11
s
il
^ o
o
<^-coeoeldiiOON OnOO 00 N NVO um^ ^- + m w r) d el m m O <
no vo vo >0 vo vo vo inwuAirnrnAivuni^iounoininiriiounrnni
oooooooooooooooooooooooooo<
si
el vooo m vo o vo o vo m N ^ n 0\sunwm el el el eo vo n On co I
vo oo O eo vooo O eo vooo O covo oo h tj-no covo On el vooo w voo
vo vovo vo vo vo t-~ r-~ s noo ooooooonOnonoooOmmumpj*
m w m w w w m w to w w w en en Vo 'en Vo Vj- rj- '^}- rj- '-^j- '-^- Vj- '^f- Vj- *
III
vo ^J- d O oo vo 3" d Ooo N vo co d Ooo N vo tj- el w Ooo Nvo *t-
W M + in vovO NOO ON On O hi cl m + ^- voVO NOO On O O i el to '
fe^uozuoH
q-iiifl '-tad
HM ao dsx^
N vo ^J- n O*oo vo ^}-el >-> On N vo eo d O On nvo rhtOM o On n vo
N On -> co rj-vo 00 O el ^J-voNOn-h CO vovo 00 O el ^VO OO On m CO >
OOOOONONO\ONONOOOOOOiniii-i.-icldeelelelcoco<
^^^Tj-Ti-Ti-Ti-vovovovovovovovovovovovovovovovovovovoi
b b b b b b b b b b b b b b b b b b b b b b b b b b
uoi^'Biin OTI I
jo op'a:
vori-eoeoel m w o Onoo 00 Nvo vovorj-eoeoel wm O On Onoo N 1
O O O O O O O O On On On On On On On On On On On On On Onoo oo oo OO
IB^uozuoh
pgjpuujj aad
HBj jo asia
t-- vo rj- n onoo VO ^J-M ii ONNVoeoel O On NVO ^ ro m o On N vo -
f^ONM eo^j-vpoo O el tj-vonOnh eovovooo O el r}-vooo Oh eoi
ooc^^^oNONONobbbb.bwwwMcleleleleleleoeo<
^T' : r'^ _, T'4 _ '^-'^-vovovovovovovovovovovovovovovovovovovo
eStmreqo joj
uoiipnpail
eooo vomoo + n N-^i-O Neoovo eoovo eoO NeoO Nrhn n<
m r* co to ^(- vo vovo NNOO OnOnO h m el coco^}-vo vovo N No
b b b b b b b b b b b b b b m '<- ' m L m i- , ^, ;
uoissajdaa;
PUB U0{l'BA9^a
jo saiSuy
OvoOvoO t oO ,J ^OvoOvoOvoOvoOvoOvoOvoOvoOvo
| n h tl d m to >t ^- >ri i^ 1 h h n Mm^-^inv) ,
VO N oo
el m
W0<fl0 l o0>o0o0io0o0^0i0'o0io0>o0'o0>o0 l o0 l fl0 1 fl ',
n h M wm^-^ioio | M M f) t) Cl M Tj- Tj- VO U1 j M M t) H com^^vowi 5
On O
c co
eoooo nn t-.NO no vo no u-iu-iu-i^Tj-'tf-cocococoN c* h m m m *- O O O O On On
c^- J~~- p^- t-~ t~-- t-^ jr^. t^~ j t r-~ j^ t~~. t t^ r-^ t . c t t^- t r~. c^~ c-^ t r^ t-- t t^ t-- r t-^ j-^
o b b b b b b b b b b b b b b b b b b b b b b b b boob b b b b
"-> C-. On 1-1 cono oo O (<ho(J\wnm moo rt) O ^oo N t^ cooo cooo rj- O NWO5
^^5- t 5 s M ^ "<*" ^^ t"- On O O CO tJ-nO NOVO h M tJ-NO Is O\0 d tJ- u-> r^ On O
* * * * 1 1 ^ ^ 1" "^ "^ "^^ VO VO *C VO VO VO N (N ts ts ts tv CsM M OO 00 OO 00 OS
t n n 'n k Vi V *n n ' V c< c* V V "n n Vi 'm V* V "n V V V* V> ' h V* v
ON OnOO 00 1-nvO uivi*+MMfl f< m m O OnOO OO t-. f-VO VO NO inuiu-irj-ri-rj-coco
COOO00OOOO0OOO0O0O0O0OOOO0OCOO0C0000C>OOOOOO00OO000OO0OOOO0OO0
o b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b
M 1/-.0 w-im MflMM OO i-< f* -+00 MVO MM in CO hi H M ifl N f) M rj- O O >i
N m ON d NO Ovm N m ^ OMO N m u-iO tJ- On COOO COOO COOO COOO tJ- On io m ts M ON
CO co co tJ- tj- t}- u-j iovp NO Np tstsOOOO ON p\0\ O O w M d W CO CO ^ tJ- u~>\p vp Jn Jn
t) h O ON00 r-.NO w>T}-Ti-COfJiHwOOON ON'X) 00 S h. I--VO NONONONONONONONDNO
mwt<1MM(fi^^^.^.^-^.^.^.^.^-^.ioioioinvnovnrno vr>NO no no no no no
Mrt m ooo t--vo io t$- co c* <-i hi O Ooo t^vO v> u-i ^j- rj- co cl d m o O On onoo r-.oo
c-. On *h co ^J-vo oo O d ^vo oo O c4 t^NO\M co u-> t>. on m co u~> r~- On O c* -^vo oo
M m rj- ^ t)- + ^ in uno i^ u-iNO NO NO NO NO NO NN NN NOO OO 0O OO OO On On On On On
b b b b b b b b b b b b b b b b b b b b b b b b b b bib b b b b b
O u-> >tn tj- rj- co tf e* m O O On OnOO i> f-v vo its <$- rj- co co c* c m m O Onoc 00 NS
ooooooooooooooooooooo t^t^iNiNtNrNrNrNr-.t^t^tNi^t>.t>.t>. t-.vp no vo vo no
-O M i-i 00 fN.NO WtJ-MM m hi O 000 f-.NO ir> V"> %)- ^ CO c* p* M O On OnOO r-OO
NCnw CO <^-nO OO O M nT'VO 00 O M ^'flNONw MU1NO\M CO vr> t>. ON O c* T^-vO OO
:*> CO Vj- ^}- rj- rj- tJ- u-1 !/-> ii-1 io WINO VOVOVONONO ts (n N ts t-.O0 OO OO 00 00 On On On On On
- 00 u-> cJ OnnO COO N^-mOO ioc O\N + m0O u-,c^ o tNTj-H OnNO -n)- >- OnnO CO w
3NCN0 >i >-c c< M^^- IOVO NO r--00 OOONOww^tOTi-^J- w-i^O >0 r--00 ON p O w W
-4 M "c^ Jq Vl "c> cJ 61 ci cl "cl d *N d C3 dCOCOCOCOCOCOCOCOCOCOCOCOCOCO'<4-r}-'4-
^O l ^0 >oO vnO >o0 u^o *oO w-iO w-io v~> O ioO w-iO >oO >oO "lO "^O o
i S t) mw^^ww | Miic4c4coro'4-<st-vnm| m m n mm^-^-uivi
On O
CJ CO
noissajtclag;
jo saiSay
mo >oO no o wo w->o ""> O <oO >oO wO j-i O >oO vo o <flO
| wMcJtftoto^Tj-ioioi n h wm^^uiui , m
"-i p to
to to to
w
H
ft
1
i
1
O
i
pa
02
o
si
Je
^ o
O
O\00 00 00 00 t^. t~~. t~~ t"^VO VO VO VO lOUH^l^lOTj-'+^-^'MMMfnrt
f4t-)MMNMrlt4trtNNr<^NMNrJNN^NNNNN
b b b b b b b b b b b b b b b b b b b b b b b b b b b
.2,0
Eg
MH60* & n O\0O t^NO U-) t}- to IO00 o t* "+ t^OO 00 ON O O * NO w
r> ^-ion onm pj ^vo oo O "4-vo oo w mioNO\M tovo oo O d ""
ON ON O ON ON O O O O O J- * * el J* c* t* <M to to to to t$- -4- t4;
e> c* eJ d N tototototototototototoiocoto'toeototo'toto"tot<
3
43
si
w o
O
fONdtHMOOON ON00 OO NN t^NO NO J-( V) tj- tJ- CO CO el el t d w
totocococococoelcielclflelelcleieielelcleielcicieieipl
ooooooooooooooooooooooooooo
si
11
" o
O
el 00 tj- O t^ On m CONO iflmwiWMM ON00 u-> CO >-i ON00 t^. t~^ t-^ r}- hi
W m 00 IOM 00*0 CO O OO NO + d 11 o OO t^t^-t^ l"--vO t"-~00 ON O cov
00 On On p h el to ^ ^ novo C^.00 on On P -i p* to rj- nono t^. On O m
u^v/^irivONONONOvONOVONOvONONOvOvO t^t^t^'t^V^V^t^t^t^.OOOO
lis
NNN t^OO OO ononO O m pi to to <$ vono t-^oo ON O * el to wnd
NO t>-00 ON O ** pi to t}-vO 1^00 On i-i pi to rj- vr>\o N 0\ O *< el to ^
no no vo vo r-^t^t^.i>r^r^t--.t^ t-^oo oooooooooooooooo onononono
I^nozuoji
iraffjad
HM ao asitf
00 On On On On OnOO 000000000\00\OOOH()Hrlflt)MThvflW
O N **- NO OO O d 'i-vo 00 O d t}-vo 0\m to vitNO\H rovi N Ovm c
NO NO VO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO NO ^O NO NO NO
b b b b b b b b b b b b b b b b b b b b b b b b b b b
uot^Burpui
}6 o^Ba
NONO >-0 U-> tJ- T$- CO CO d " M O O ONON ONOO OO t-.NO NO NO mi^^+c
OVONOVOVONOVOVDVONONONONO U->NOW-)U-)W->W->NOVNlOU- ) U- ) W-lVOl'
re^uozuog;
pajpunjj agd
IIBJ JO Dsja
oo e>o\CTvc\ onoo oooooooooNONONOOOMdddddeoTj-u-iir
O d ^-^O OO O J) "+NO MOM ^J-vp On m m in N On - phoNOnm c
O O O O O i ii m w m pi pj "pi pi 'pi rotototo'to^J-Vj-Tj-Ti-'r^-loii'
nOnONOnONOnononOnonONOnonONOnonOnOnonONONOnonONOvONONO
aSBuraqo jeoj
uoi;anp3'ji
oono ro-iooNO -+M onno <J-rJ O NwmOoo^o <4-N O Nwmh o
h jo +- >n yivp r--oo oo ono m pj Nf^74-No yo^p t--oo on on o >-i m ci
"+^+ + + "t + + + + l fl>0>fl>'li'lTO>OU1viio'0 U-1VO NO NO NO
uoTSsaidaa:
pire uopBAajg
jo sefSuy
O l 'iO'io v oO vr >O l '^O l ^O , oO l oO l 'iO l 'NO n-iOw~>0*r>c
I M M (i H MM^+IOIO 1 H H d ft MM^-^lOlfl 1
o ! 1 1
H CO
to to to
0^0'0"iO'flOiflOwO>JiO>OviOifl0 1 flO | flOwO l OviOw
O os os os os osoo oo oo oo oo t^r^t--t^t^ t-^o no no
MMNmmmmmOOOO
t>rtrtiNc*rJtJNrtNtf..
J~ J^~ r-- t-~ j>- r c^ r^. t^ r-. t~- t-~ r^ r~- r-- r^- t-~ c-^ t-~ c^- t- t^- r~- j>~ t~^ r~~ t t~~ t^ r-~ j i>~ t
ooooooooooooooooooooooooooooooooo
* NO MM rj- Os *> >h no o-> r}- co t* w O
r->. o n vin o n u-ioo o cono o\ t* vooo .,
sj- i/s u-, u-> u-,vp so vo vo t^. ^ ( f^oo oo oo On On On O O O >- "- 1 c e* c to to ^r y- ft"
W M M M M M M M M M M CO M M M M M W ^ ^ ^ V + ^ ^ ^ ^ "+ + + ^ ^
d-NO 00 O e* t~~ tooo cooo rj- to CO C* M o
3- t-~ O rht-^O Tj- t>> ^OO M NO O &<
-* r* co to rj- ^J-
WOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOCOOOOOOOO
o o o b b b b b b b '0 b b b b b b b b b b b
u-> tf o -+00 pj
m ^1- t^ c^ r^ co
rt ?}- y->v> ou on m
do do do do do on
NO O WNN OVM COt}-u-iO ^}-00 ClNO OS
OO rj- OnOO t-~ t^.NO wN-^-ONCor-^cJNO O
N T |^ N O m couir^ONN + N OS H
on os bs bs bs b b b b w m i- m V*
(>Oft+iflMOH+OSOfl "d-vo OO
ONO OO ON O w C4 CO VINO t^OO Q\H H CO ^j- U-|
CnOnOnOnOOOOOOOOOhimhi- <-i
3 . m r r* r 1 f r* f f f r* r* r* r* r* r* r" y*
l-l CO 1000
t^OO ON
w -. w c*
H rl H
O to lOOO W CONO 00 f* U-100
N CO tJ- IO t^.00 ON O H ri r}-
t) tl O (I fl MMMM
Nc4c4clNMc<NN^H
o r--oo o O N c* >* w-i r^.oo on m ei co ion soso t)
m r\ on n +^o oo o o -^-nooo O ii ^ M> m co iaoo O
io uo u-ino vo vo vo t-^ t^. t~- r> r-^oo oooooooo ononOnonO
OnOnonOnOnonONONOnOnOvonononONOnOnOnOnOnO t~~
o o b b b b b b boob b b b b b b b b b b
3-vO t-. Os w CO
N ^}-NO OO 11 CO
O O O O HI
t^. t-^ t^ t^ t^ t-^
b b b b b b
u-i r-N Os hi co
w-i t^ os co tj-
m m m H
t-~ t^. t^ t-^ r^
b b b b b
CO N N M M o
VN VO >-0 u-i W-N ly-| lO
os osoo 00 t^ t^NO no so vn u-i
.^ ^ ^ Ti- -^ Ti- ^" -^ ^ ^ Ti-
+ +tOMt)r)tlHHOO
.* ."* ."* ."* r 4 * .^** ."* .* :* ."* ."*
OS OS OSOO
CO CO CO to
O t^oo O O m fi h <j-vi f^oo On w d co WIND r~- On O r -<i-NO f^ On hi woNO\h co
to t>- ON <S ^}"0 OO O M ^-sp OO O COvot^ONw co u-iOO O C* ^NO 00 w CO vo t-~ On CO *$
u-i u-i uimd no vo so "r^ r^ t^ r^. r^do 00 do do do on on on on b b b b b "- 1 l_l M n f*
ononononono*ovononononovononovo^onovonono t^.t^.t^r>.r^t^.t~.t^r^t~.t^r^
t^.u-)CO>M ONt^vocoH O OO NO *3-tf O Ost^u-iCOM OOO t>.vn'4-N O On f^vO rj- co w
CO -*j- U-i^O NOt>.00 0\0'-lclCOTj-U-i UNVO t>-0O OnO O "-" C<COtJ-u-i U-iNO J^-OO ON O
OvONONOVONOvbOD tNNtsNNNNNt>t>t> NOO 0O00000O00000O0O0000M ON
HH M m M M M M M M M M M M M M M l-l M * - M M M M M M l-l HI M M
M N co CO ^ <4-
O vn.O 1^0 10O 10O >oO <oO vriO
vouii h m H C) wm^-ri-ioio |
CO CO
u->0 "SO <flO voO ntno vn
hi hi H N coco^ti-u-ivrN
24
TABLE II.
Latitudes, or Hori-
ntal Distances for
Difference of Levels
Cosines
ooooo
ooooo
99999
99999
99999
99999
99999
99999
99999
99999
"99999
99999
"99999
99999
99999
99999
99999
"99999
99999
99998
99998
99998
99998
99997
99997
'99997
99997
99997
99996
99996
99996
99996
99995
99995
99995
99994
99994
99994
99993
99993
'99993
99992
99992
99992
99991
99991
99991
99990
99990
99989
99989
99988
99987
99987
99986
99985
99985
Sines
1
0-89
Departures, or
Difference of Levels
De &-
Latitudes, or Horizontal Dis-
tances for Difference of Levels
la
*o O >oO mo *oO o O "OO
o
OOOOC5030300QON10
OlQOOCiQQOQOQOOOQO
OOOOOOOOOOOOO
OOOOOOOOOOOOO
OOOOOOOOOOOOOCO
OOOOOOOOOOOOOOO
00001000505000
OOOOOOOOOOOOO
OOGOOOOOOOQOQOOOOOCXJOOGOQO
OOOOOOOOOOJHOOO
000
OOC5
OQOOOtMHO
C50C5000009
999
QCQOCG
.. O O O O
99090909009
000000O000000
oooooooooo^ticoc^
0000000000000
99999 ( ?5 1 9999? 3 9
0000000000000
^7* ^1 tji Tp "^H TjH T^ t^H ^s^ ^ ^H ^1 ^$4
OOOOOOOOOOOOOOO
OOOOOOOOOOOOO
OOOOOOOOOOOOO
cococococococococococococo
OOOOOt^COiO
OOOOOOOOOOOOO
OOOOOOOOOOOOr b-
OOOOOOOOOOOOO
99900900003999
OOOOOOOOOOOOO
00000000000000
999.
OOOOOOOOOOOOO
89 **
Departures, or Difference of
Levels
TABLE II.
26
Departures, or
Difference of Levels
o d
i
ooooo
00029
ooo?8
00087
001 1 6
00145
00174
00204
00233
00262
00291
00320
00349
00378
00407
00436
00465
00494
00524
00553
00582
0061 1
00640
00669
00727
00756
00785
00814
00843
00873
00902
00931
00960
00989
01018
01047
01076
01 105
01134
01 163
01193
01222
01251
01280
01309
01338
01367
01396
01425
01454
01483
01512
01542
01571
01600
01629
01658
01687
01716
01745
Cosines
0-89
Latitudes, or Hori-
zontal Distances for
Difference of Levels
7>eg.
Departures, or Difference of
Levels
2|
It
O <oO *o O "1 o u->o oo *^o
^O >fliO^^ wwti m 11
XOr-<C0(Mt^C0a0C0C>-*QO
TPOMOOiMNHOOiOO'*
ooooooohhhhhh
OOW^tJI^OONOOOOH
r^CNCOipCpl^GSOrHCO^lO
OOOOOOOOrHrHrHrHrH
OCOOfflNOO^ONCOOO
HMt)(OCOHWt)<OQO
OrHcqcp^tiipcpoOGiprHcrqas
OOOOOOOOOrHrHrHrH
QOOOOOr- 1 H H H H (M (M
OH(NiHOONOOOOH^
OOOOOOOOOOrHrHrH
1 b~ lO <M O CO "tf
C0>0ON
CO **
W l.'- W UN <*4 W ^T T I l-*J t> UN ' ' l"-
OOONO^WfMHOQONOrH
OOrH^CO^lOCD^NQOOO
666666666666h
_ CO
tOlMQN
OCHOqff-lCO^lOiOCONQOOO
66g6666666666
06
66066666666
OilSHiOOOINWOWOO^
OOOHH(M(NWOOC5^iiiO
666666666666 6
OOJOOSOUJiO^MiMHOO
OtNiOOOHTHhOCOOON^
OOOOHHHinff)(M(MC0
6666666666666
f^O^GO^t^dCOi-liOO'*
H(^T)(>ON00OHC0Ttl'Ot>
OOOOOOHHHHHH
6666666666666
*o ""> Q ^O w-i o ^ o *"i O ""> O
It
89
Beg,
Latitudes, or Horizontal Dis-
tances for Difference of Levels.
2G
TABLE II.
Latitudes, or
Eori-
zontal Distances for
Difference of Levels
Cosines
1 n'
99985
6o'
I
99984
59
2
.99984
58
'99983
5 l
'99983
56
5
99982
55
6
99981
54
7
8
99981
53
99980
52.
9
99980
5i
IO
'99979
5o
ii
99979
49
12,
99978
48
13
*5
99977
'99977
%
99976
45
16
'99975
44
*7
99975
43
18
99974
42
T 9
99974
4i
20
"99973
40
21
99972
39
22
99971
38
2 3
99971
l l
*4
99970
36
*5
99970
35
26
99969
34
27
99968
33
28
99967
32
29
99966
3i
30
99966
30
31
99965
29
3*
99964
28
33
99963
27
34
99963
26
35
99962
25
3*
99961
24
37
99960
23
38
"99959
22
39
99958
21
40
99958
20
4 1
'99957
19
42
99956
18
43
99955
*z
44
99954
16
45
99953
15
46
99952
14
47
99951
13
48
99951
12
49
99950
II
So
99949
IO
5i
99948
9
52
99947
8
53
99946
7
54
99945
6
55
99944
5
56
99943
4
57
99942
3
*8
99941
2
59
99940
1
60
99939
0*88
1 Sines
Departures, or
Difference of Levels
Latitudes, or Horizontal Dis-
es ' tances for Difference of Levels
>oO **> O ^0 "> O o O *o O
GOOOt^t^t^t^COCO )L OiO-^-^00
6666666606666
OOO05OOOOOOOOO
O ** r lOOOODOOOC^GO^OiO
OOGOOOt^t^t^OOOiOiOiO^
OOOOOOQONNNNCDOiOiOiO
OOOOOOOOOOOOG5
6606666666606
ON>005HQiomON^HN
GOOOOOGOOOt^t^tr-t^OOOiO
OOOOOOOOOOOOO
0000000000000
HONO-^(MONlO(MaiOW
OOOCOCOaOOOt^t^t^t^OOO
CiOJCiOCiCSOQOOQGiQ
666666666666
(Mr- lOOOOlOCqr- 1 Ol O i< (M
oooocoooooooaot^t^t^b-o
OOOOOOOOOOOOO
666666666666
^ "^ TJI "^ T^ XT' '^ *^ T^ T^ **^ Tf T^i
T)iC0(MOCiQ0iOT)(lHO00O
OOOC5CX)OOOOOOOOQOOONN
000000000505050103
6006006066666
cccocococooococococococqco
10>0"*MCTHOONOK5N
ooooooococooooooooo
0000000000000
6666060666066
NOOiQiO^CO(M(MHOOQO
oooooooooooooco
0000000000000
6666666666666
OOOOOOOONNNOOOiOT)<^
0000000000000
00000000000005
6666666666666
8H
88
_ Departures, or Difference of
Des ' Levels
TABLE II.
27
Departures, or
Difference of Levels
Sines
01745
01774
01803
*Ol8j2
01862
01 891
01919
01949
01978
02007
02036
02065
02094
02123
02152
02181
0221 1
02240
02269
'O2298
O2327
02356
02385
02414
02443
O2472
02501
02530
02559
02589
026l8
O2647
02676
02705
O2734
C2763
02792
02821
O2850
O2879
02908
02937
02967
O2996
03025
O3054
O3083
03I 12
03 141
O317O
O3I99
03228
03257
O3286
O3315
03345
3374
03403
03432
03461
03490
Cosines
Latitudes, or Hori-
zontal Distances for
Difference of Levels
1_ Departures, or Difference of
Des ' ^ Levels
K5 1 ICO. ll>.<NaOCOCO'*t<G5'<#
t^qpOrHCp^cpt^opTT-icp^
rHrHC3<^Cq<jq<J3<NCNcbo3cb<>
H(M(MCO^lOONOOOQOH
NOMOCSIMIOOOH^NH^
iOt-cpOjpcqcp-^cpt>.qpprH
OCOCilOHQOTfONiWOlOfN
oooob-Gpcip^cp^ipcpt^
rHrHrHrHrHrH(fl<Jq<fq(fq<N<fl(fq
ft
(^^lONOOtM^OQOOHM
qqcp^ippi^cpppr^^cp-^
rHrHrHrHiHrHrHrHC^fN^i^cfq
<*C5(MOOOpNiO^COHOCJ
OHqqMM^ipoNopopo
rHrHrHi^rHrHrHrHr^rHrHCNCN
GOpPPrHCqCOCp^lppcpt^
OOrHrHrHrHrHrHrHrHpHrHrH
C0Ot)<(MHN1OM(MO00O
OiOHNMOO^OOCMOOWOi
pt>.OpcpOipprHrH(?C|(yiCOC0
OOOOOOHHHHHriH
lOiaOOCONNQOOOOOOO
6666666666OHH
^NOWCOOWiOQOH^OO)
6666666666666
^ci^oocot^cqcOT-noo-^o
NOOOHCO^ONfflONM^
1 lrH(M(N(MCq(N(NC^COCOCOCO
6666666666666
15
88
Latitudes, or Horizontal Dis-
es " tances for Difference of Levels
__
28
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
m
J
p
>
P
P
p
P
tf
O
m
W
1
to
1 1
P
P
1
O
to
H
g
g
P3
c
H
P
E
H
) (
H
P
(\ Latitudes, or Horizontal Dis-
<v es " tances for Difference of Levels
2 o'
2
3
4
5
6
7
8
9
io
ii
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
3i
32
33
34
35
36
37
38
39
40
4*
42
43
44
45
46
. 47
48
49
50
5i
52
53
54
55
56
57
58
60
Cosines
99939
99938
99937
99936
99935
'99934
'99933
99932
99931
99930
99928
99927
99926
99925
99924
99923
99922
99921
99920
99918
99917
99916
99915
99913
99912
9991 1
99910
99909
99907
99906
99905
99903
99902
99901
99900
99898
99897
99896
99894
99893
99892
99890
99889
99888
99886
99885
99883
99882
99881
99879
99878
99876
99875
99873
99872
99870
99869
99866
99864
99863
60'
59
58
?
55
54
53
52
5i
5o
49
48
46
45
44
43
42
4i
40
39
38
36
35
34
33
32
3i
30
29
28
26
25
24
23
22
21
20
l 9
18
\l
15
13
12
11
10
9
8
I
5
4
3
2
0-87
O 10O <oO n-> O vr>0 oO 10O
O
00
-O 03
is
m
P
1
p
Q
I
B
p
1
p
H
P
9
p
p
qj^oocoi>-T-iiooocqooooco
W05(?q(NHHOOO00t>NO
OOSOSOJGSCiOQOQOaOOpGOGO
M
ON
IOHIOp- (VOO^OOCOCDi I CO CD
^Tj(nW(M(MHOOOOOON
OOOOQOOOGOQOOOQOOOOOQOOOOO
O
ON
00
!-Ht^<MOO^CS-*GO-<*aO<MCDO
OiOJOOSOiCiOioqiOOcpqp
O
00
iOIOIO^-^OOCO^IMHHOO
NO
e0ON^ONC0Q0iOHN(M00
NO
QN"^HGO>OCTOWO>OH
ooooq66 6c6
"^ "^ "^ *^ T^l "^H t}H t^ tJ4 "^ ^H Tt^ '^
3.
ococococooococqcococococo
%
CO
(MOQONOCCHCiNiOCOHO
OOCONNNNNOCDOCOOlO
CO
ooNioeoCTHOQON-^o:
CCaOOOCOOOCOOOaOt^t^t^t^l^
t)(M00(M(MHOOO0000NCD
OOOOffiOOffiOOQOCOOOOO
O
l"fil
II
O *o n O *n O oO ^ O oo
M HI C* M tfl W ij- <^ IO J")NO
Departures, or
Difference of Levels
8
4 De &" Levels
ace c
ji
TABLE II.
29
Departures, or
Difference of Levels
OQ
1
9
O
m
S
M
gj
p
tf
aT
8
P
H
I
H
P
Deir Departures, or Difference of
<w "' Levels
2 o'
2
3
4
5
6
7
8
9
io
II
12
*3
14
*5
16
17
18
19
20
21
22
*3
24
2 5
26
*7
28
29
30
31
32
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
5
5i
54
53
54
55
56
57
58
60
Sines
03490
03519
03548
03577
03606
03635
03664
03693
03722
03751
03781
03810
03839
03868
03897
03926
03955
03984
04013
04042
04071
04100
04129
04158
04187
04216
04246
04275
04304
04333
04362
04391
04420
04449
04478
04507
04536
04565
04594
04623
04652
04682
0471 1
04740
04769
04798
04827
04856
04885
04914
04943
04972
05001
05030
05059
05088
05117
05146
05175
05204
05234
C sines
60'
59
58
56
55
54
53
5*
5i
50
49
48
46
45
44
43
42
4i
40
39
38
36
35
34
33
3a
31
30
29
28
26
*5
24
*J
22
21
20
19
18
\l
15
14
13
12
11
10
9
8
I
5
4
3
2
1
0-87
*o *o o oO 10O oo >oo
00
If
w
O
Q
3
1
i 1
P
gg
Q
P
O
S3
t (
O
w
go"
P
B
H
t 1
H
3
OihOhN(MSH0005(tD
MOOlNNHOOOQrHQOM
CO CO CO CO *^ "^ "^ "^ "^ "^ "^ lO 10
O
O
on
HHiMMT)<lOOCDCDQOCi050
^NOCOOOCTiOQOH^SH
1 icq-^iQcot-^oOi ico^^t*-
Mcbcbcbcbcbcb^^^-^^^
O
ON
00
(MQO^HS^OCOHQO^ON
ON^ONOO(MMIONOO
t^05prHOqcp^t<Cpt>00020i 1
cq(^cbcbcbcbcbcbcbcbcb-^Tt<
00
co^cDcpo^coiob-oocqco
^lpcpb-opqsorHC^cp^ipo
<?qCTcq<^cq<^cbcbcbcbcbcbcb
TPHOQlOOOONrffHOiCDCOO
05Q03or)(05HOONO0^
OHNW^ipOb-NQpaOH
CN<f^c^<^<N<?^oqc^oqcqffqcbcb
lOSOCOCDOOHMOQH-^N
t(IHOOOQOOiMOM>^H
t^OpOOOiOrHrHCMCpcp^tlipCp
%
Ot|((NOOONOMHC5S0 05
lOHNCTOO-^OOHNMOJ
COTHiOipOONCOQpOOOp
i^rHrHrHrHrHrHrHrHrHrHCqcfq
en
NO^QOHiOQONOOMOO
^QCOIXMOOiOOMQOINN
PprHrHCqC^CpcpCp-rJH^ipjp
rHrHrHrHrHpHrHrHrHrHrHrHrH
eo
O
OONOlO^MCTHOOOQON
ONNNQOOOQOOOOOOO
6666666666OHH
O
el
O
OiCOGOCOt^CTCOi-H^OO^OSCp
^ONOOtMCOiQCOOOOCl
cocococp^^-^^r^^^oip
OOOOOOOOOOOOO
O
If
"0 100 voO o O *i-iO ^o >00
w 11 el el ww + '+'o *ovo
O
Latitudes, or Hori-
zontal Distances for
Difference of Levels
qw Latitudes, or Horizon
O De *' tances for Difference
tal Dis-
: Levels
30
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
Cosines
3 o'
99863
60'
i
9986!
59
2
99860
58
3
99858
H
4
99857
56
5
99855
55
6
99854
54
7
99852
53
8
99850
52
9
99849
5i
io
99847
50
II
99846
49
12
99844
48
*3
99842
47
H
99841
46
*5
99839
45
16
99837
44
7
99836
43
18
99834
42
19
99832
4i
20
99831
40 '
21
99829
39
22
99827
38
23
99826
37
24
99824
36
25
99822
35
26
99820
34
27
99819
33
28
99817
32
29
99815
3*
30
99813
3
3i
"99812
29
3a
99810
28
33
99808
27
34
99806
26
35
99804
25
36
99803
24
37
99801
23
38
'99799
22
39
99797
21
40
99795
20
4i
'99793
19
42
'99792
18
43
99790
l l
44
99788
16
45
99786
15
46
99784
14
47
99782
13
4
99780
12
49
99778
11
5o
99776
10
5i
"99774
9
52
99772
8
53
99770
7
54
99768
6
55
99766
5
56
99764
4
57
99762
3
5
99760
2
59
99758
1
60
99756
Sines
o-86
Departures, or
Difference of Levels
o
o
a
S
&
P
P4
o
Ph
og
o
H
OQ
8
Latitudes, or Horizontal Dis-
es ' tances for Difference of Levels
O >oO *o O oO >oO mo *<"> O
vo >o io + ^ m m e* w m
o
CO*O^COM(^iHOOia)NCD0
cpqpGpqOGpcpqDGCl^b-t-r^-l^
OOOOOOOOOOOOO
COCSCTlOOOOtM^lONOOOO
NOOTj(Tt(o:^HOOQOQO
cpqpaDqDqpqpqpcpqpqpr^t^t^
OOOOOOQOOCOOQOQOOOQOOOCOOO
OTflQOHiOOOOCOOOHCOiO
OOOt>-I^C>iOO-tfCO<M<MT lO
qccpqpqoapqpcpqDCpqpqpqpqO
0000000000000
i>>t>ifc>.i>.i>.l>i>.t>.t>.i>.r>.i>.i>
OOOQ000NCO>0>Ot)(C0(M
OcpcpccpqpGpqOGpQpQpqpGp
OOCOGOCOOCOOOOlb-CqCDOCO
HHOCOJOOOOONNOCiO
HNMOlOHOfMNCOOOCOOO
CO(N(MHHHOOOJOOOOON
6oooc3o6o66c56
T4I ^ji "^}i TJ1 tji ^ji ^H ^^H ^^ ^^ ^^ ^^ ^J4
lO(MOffl(MffiO!MCO^OOCq
tj^coo:w(M(M(mhhhoo
9999909990999
OOOOOOOOOOOOO
cococococococococococococo
ic >o >o 10 <* -+ <* -f CO CO CO CO (M
9999999999999
O O O
O* O* CM
OOOOOOOOGOOOOOCOt^t^t^t>.t^
OOOOOOOOOOOOO
It
o o
2^
"o "> O >oO o O o O o O oO
M W M tl C*! CO tJ- rj- *0 iovo
COi lOOOCD^COi lOl^iQCOr-l
009905039090990
ooooooocibooooo
86 De *-
Departures, or Difference of
Levels.
TABLE II.
31
Departures, or
Difference of Levels
30 o>
2
3
4
5
6
7
8
9
10
11
12
*3
14
15
16
17
18
19
Sines
05234
05263
05292
05321
05350
05379
05408
05437
05466
05495
05524
05553
05582
0561 1
05640
05669
05698
05727
05756
05785
05814
05843
05872
05902
05931
05960
05989
06018
06047
06076
06105
'?I 4
06163
06192
06221
06250
06279
06308
06366
06395
06424
06453
06482
065 1 1
06540
06569
06598
06627
06656
06685
06714
06743
06772
06801
06830
06859
06889
06918
06946
06976
Cosines
o-86
Latitudes, or Hori-
zontal Distances for
Difference of Levels
3 De &'
Departures, or Difference of
Levels
r-; =
2^
O oo 10O o O o O >oO 10O
VO >o io + + w to c* 11 11
o
CONNOH
(^wipptpprHc^ooippcpp
ibiQiib)Oibcb666666
ioo>ooioocd
Oi ICqC^C0T^T^iOCDC0t>'t^00
HTjlNOMOO(MX5Q0HTitN
I^CpOrHCNCp^Cpt>GpprH<^
^^^101010x01010x0666
T^^TtH^-^-^-^iOiboibib
C0*Ct^00O<M0lOl>0CO.-<C0
COCONNNNNN000000
Cpb-qpOiOrH<?qcpTt<pCpl>.00
ONt^HOOCOON^HQOW
^(MHOQONCDIOMIMHQQO
rH^Cp^^ipspt^GOCSpOrH
l>C5(?q^t^OCMlOOOOCOXOOO
hoocomoqo0(Non^hqo
Cpcp^GCpqiprHrHG<JCO"TH-^l
o
OS
COONN
O-^t---l^00i-HiO00G^OCiC0
NHiOO^QOWNHOO^a
ipppt^t^C^cOGpppppp
rHrHpHrHrHrHrHfHrHrHCNCqiq
Tjt>OWOO(MiONOMOOi
OOHHHH(M(M(MCOCOWCO
OOODNNHOOlOO^QOeSOO
(MMiOOOOCiHfMWiOCDOOO
iO00OiOiOOCOOCOCOCOCD
6660660006606
86 De &-
Latitudes, or Horizontal Dis-
tances for Difference of Levels
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
Cosines
4 o'
99756
60'
i
99754
59
2
99752
58
3
99750
s l
4
99748
56
5
99746
55
6
'99744
54
7
99742
53
8
99740
52
9
99738
5i
IO
99736
50
ii
"99734
49
12
99731
48
J
99729
4 ?
H
99727
46
15
99725
45
16
99723
44
17
99721
43
18
99718
42
'9
99716
4i
20
99714
40
21
99712
39
22
99710
38
23
99707
H
24
99705
36
25
99703
35
26
99701
34
27
99698
33
28
99696
32
29
99694
31
30
99692
30
31
99689
29
32
99687
28
33
99685
27
34
99682
26
35
99680
25
36
99678
24
37
99675
23
38
99673
22
39
99671
21
40
99668
20
4i
99666
19
42
99664
18
43
99661
17
44
99659
16
45
9.9656
15
46
99654
14
47
99652
13
48
99649
12
49
99647
11
50
99644
10
5i
99642
9
52
99639
8
53
99637
7
54
99634
6
55
99632
5
56
99629
4
57
99627
3
5
99624
2
59
99622
1
60
99619
Sines
0*85
Departures, or
Differ
euoc of I
..evels
4 Degr.
Latitudes, or Horizontal Dis-
tances for Difference of Levels
>o tji co (M h o G 00 O 10 -r c: h
- 1>.CDOOOCO
7s a a a
0ffi050iOC50
OOOQOOQOO
OHfMjqMWWtMHOOOiN
CONOiO^(NHOCiOOiO
b~b~t^b~t^t~t^t^j^CDOO
aOGOaoaoaoaoaoooooaoooooao
OQXOONCHO^CC^HOO
CiCiCiCiCiCiCiCidiCiCiCiCi
ffl(NiONO(M'r|iOQOOH(MCO
Cq<MHOOOOONOiOiO^M
cpGpqpGpGpb-^b-t>t-.i^t^b,
OCDOOOCOOCOOCO
COOO^lOOOCqiOOOrH^CCO^H
iOt)(-*COCTCTHOOOOONN
opcpopopapcpapqpqpb~t^t^l>.
00 CO 00 <N b-
opcpcpopopqoopopqcopopqpop
^1 TJ^ "^1 "^i TJ1 ^1 **^ '^1 "^1 TJ1 "^1 ^^ ^^
<MOO-*OiOrHt-Cqt^CqOQCOOO
caciCiaoaot^t^cDcoioiOT*
OscpqpcpqpopqpqpqpcpqpcpGp
cococococococococococococo
N-^ON^HQOilONCOOO
(MCTWHHHOOOQO500
ClOSCiCiOiCiCiCiOopcpopop
IHOJNlOeOHODO^r-'OOTtf
10 3 ^ 3 3 ^) <F5 CO CO 00 W <N cq
|6oOCiOOOOOOOffiC3
a a
^ CO Ol
,000
0005C5Ci01CiCiC5CiCiO
6qq666 6q66qc;q
O er _ Departures, or Difference of
OO De *' 'Levels
TABLE II.
33
Departures, or
Difference of Levels
i
2
3
4
5
6
7
Sines
06976
07005
07034
07063
07092
07121
07150
07179
07208
07266
07295
07324
073 S3
07382
0741 1
07440
07469
07498
07527
07556
07585
07614
07643
07672
07701
07730
07759
07788
07817
07846
07875
07904
07933
07962
07991
08020
08049
08078
08107
08136
08165
08194
08223
08252
08281
08310
08339
08368
08397
08426
08455
08484
08513
08542
08571
'08600
08629
08716
Cosines
4
3
2
1
0-85
Latitudes, or Hori-
zontal Distances for
Difference of Levels
Dep.
Departures, or Difference of
Levels
O "iO inO >oO ""> O >o O w-io
vo >o vo ^ ^ w w tf m M
OOOHOHOHCDHOHCD
N^OHIOO^OCCOOJINH
<t>t>t>t>t^t>t>a><x><XiaDob
QOOOOOOHH(M(MCOa3^^
WiiiOOQOOOHCO'tiONCIO
OOOOONNNNNNN
lOOOOOOHNWipONCOO
CO^OQOOH(M^>ONOOOH
OOQOCOOOOOOOOOOiOOO
^^ib*b*bobib*abiboo
iO(MONMHNOHOiOMO
rHC^O^-rtiipcpi^t^GppprHO^
oooMioooonioaoowiooo
TjHOONNOOCiOOTHNWc:
oooo^^oooo^moooo
O^OONOOWQiOHNtMQO
r^CppCSpprHrH(>lCpO?'*-rJ(
cqcqcMcq^cMcqcM^cjqcqcqc^
O (M iO 00 H * O O ^1 O CO h t}(
CO * "* T 'O O O O S O N N
Q0(MOHOOOQ^00C0N^
O rH (M -) 10 1^ X C5 ^ (N ^ >0 N
0000000000000
If
0*00^0
N co w + ^>o *ovo
q t Latitudes, or Horizontal Dis-
OO Deir ' tances for Difference of Levels
i~3
34
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
W
I
O
8
P
g
m
<
Eh
O
N
1 i
O
l-H
H- (
O
of
p
H
1 (
H
K Latitudes, or Horizontal Dis-
O *' tances for Difference of Levels
5 o'
2
3
4
5
6
7
8
9
IO
ii
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
50
5i
52
53
54
55
56
57
58
I 9
60
Cosines
99619
99617
99614
99612
99609
99607
99604
.99601
99599
99596
99594
99591
99588
99586
99583
99580
99578
99575
99572
99570
99567
99564
99562
"99559
99556
99553
99551
99548
"99545
99542
99540
'99537
99534
99531
99528
99525
99523
99520
99517
99514
995 1 1
99508
99505
99503
99500
'99497
99494
99491
99488
99485
99482
99479
99476
99473
99470
99467
99464
99461
'99458
99455
99452
Sines
60'
59
58
U
55
54
53
52
5i
50
49
48
46
45
44
43
42
4i
40
39
38
11
35
34
33
32
3i
3
29
28
3
25
24
23
22
21
20
19
18
\l
15
14
13
12
11
10
9
8
I
5
4
3
2
1
0-84
"0 <oO <O0 woo o O >oO >oo
VD l^lO^-^-MMrt H HI HI
+
00
"8 M
!5
w
Ph
O
H
&5
S
1
P
O
P
0*00000000000
<3\
Ni0(MOO10(MONt)ION
C * CO !M h O 00 N O t)i W (M O
cp:pocpcpcpipipipipipipip
0066666606666
aoaoooaoxccGOQOGOoGacaoao
O
00
OLOuO'fTtiiMHOOODO^H
OODNOiO-*(MCOXNO
6666666666666
t>- t> t> 1^ i> t^ - i>- b- b- b- 1>. t^
00
O
OTOCCNNNNODOONNS
(MHCOCONOiOi'KWH
060OOO0666666
CCOOOOOOOOCwO
O
H'toaowcoiocopooH
NCiC^^^^HOOOOXN
6666666666666
O
oNonoO(MjacHno
OCOOKNCCO'f'+COlM
X X^b-b-.b-b-b-b-b-t^t^t^
6066666666666
Tji ^1 "^t -rgi ^ji ^j^ t^ ^^ ^^ ^^ -^^ ^^ -v-j^
O
10
5-
XJlOCfMNHOO'fOWNH
*t^K(N(MHHOOO00 0C
ccccccac>occccccooD~t>.t^t>-
6 6 6 6 6 6 6 6 6 6 6 6 6
ctcocooocococococococococo
5-
O
CMX-*00(MS0001000
XODNNNOCOlOrP'f-t<CO
X X X X X X X X x cp op X X
6 6 6 6 6 6 6 6 6 6 6 6 6
<m cm cm cm cm cm cm cm cm cm cm cm cm
O
19-924
10021
19919
19-916
19-913
19911
19-908
19-905
19-902
19-899
19-896
19-893
19-890
O
O
(NHOOCNIO^IMHOOONIO
CO CO 10 ia 10 10 10 O 10 o ^h rf H
OOOOOOOOOOOOO
6 666666666666
O
O v-> O *oO 10O u-iO o O oO
w hi ^ pj roto5T-i-w-) iovo
O
10
&
I Departures, or Difference of
C egr ' Levels
Dei
Dtffew
art u res,
nee of L
or
evels
TABLE II.
35
Departures, or
Difference of Levels
1
O
P.
M
of
B
P
H
M
<5
Fh
P
er ^ Departures, or Difference of
5 * Levels
Jo'
2
3
4
5
6
7
8
9
10
ii
12
IJ
14
IS
16
*7
IS
19
20
21
22
23
24
*5
26
27
28
29
30
3i
31
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
5o
Si
Si
53
54
55
56
57
58
60
Sines
08716
08744
08773
08802
08831
08860
08889
08918
08947
08976
09005
09034
09063
09092
09121
09150
09179
09208
' 92 1I
09266
09295
09324
09353
09382
0941 1
09440
09467
09498
09527
09556
09585
09613
09642
0967 1
09700
09729
09758
09787
09816
09845
09874
09903
09932
09961
09990
10019
10048
10077
10106
10135
10164
10192
10221
10250
10279
10308
10337
10366
10395
10424
10453
Cosines
6o'
59
58
s
55
54
53
5*
51
50
49
48
46
45
44
43
42
4i
40
39
38
11
35
34
33
32
3
30
29
28
11
25
24
23
22
21
20
11
\l
IS
14
13
12
11
10
9
8
I
5
4
3
2
1
0-84
O o 100 w->o oO >oO oO
VO V) V) ^ ^" M W H t M HI
00
If
il
1
p
to
a
r
&
p
g
no
w
Q
H
p
Eh
B
g
p
p
H
M
P
M
CDOiOOvOOiOO-^OiCOOOCO
HOOi0O-tG0(NNHOO>0
d)(X)6666666666
r-H 1 1 r 1 1 1
O
o>
T)ir)ilOiOiOO'OONNNNOO
^NOMOONiOQOH^NO
CGirH(^JCp^tCpb-OpprH(jq^
ON
O
WOO^OO(MOOOOiOHO^
NQOONCOlOOOOQHCOTttCO
Pp(^C0^ipCpb-0pprH(7qCp
00
O
H^tHiOOOOOOCTMt)(ON
OOOOOOOt IHHHHr- 1
HCNW^tpCpNCpOpHOTep
cobcbcbcbcbQbocbt~t^-t>'t>
O
VO
a>ocoot^-<*rHoo^-HT-tooiorrq
(MHOONOiOntNHOOON
(N OO f f C CO N CC O O O H CT
lbibibibicibioibiboooo
VO
O
00 00 10 t- <m *a b- a oi *
OKON^^OOMOCOOiM
CpT^OiOONNOOOOOHfN
OD'tOOHNmOiOOOCTOO
-^OOONNODCpOOpHH
oowwobocboocbcbrt<Tj<Ttt^
9-
to
10 co w 10 co w 01 w
HiOO^COMNHCDOiOW
OCONNNCpcCOOOOOH
CO
O
MOHOOCONOOtPM(MO
rfNOWlOOOH'tNOMOO
SNOOQOCCOOOqjQOOOO
O
(MOOOOiCOOONCTOHiO
nooohct4ionqoohm^
GOOOCiOppppppppp
OOOOOOOOOi IrHr-lrH
% 2 1
W?\ O voO *oO "OO o O *f> O ^ O
1 8 1
Lati
zont
Diffe
budes, or
il Distan
rence of
Hori-
3esfor
Levels
y| Latitudes, or Horizon
C$41: De8r ' tances for Difference
tal Dis-
f Levels
36
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
m
>
O
3
I
ti
P
g
m
O
H
m
1 1
P
a
E
I
i
O
H
Q
P
H
M
H
<!
h3
r% Latitudes, or Horizontal Dis-
O ee * tances for Difference of Levels
6o'
i
2
3
4
5
6
7
8
9
IO
ii
12
n
4
15
16
\l
18
19
20
21
22
13
24
25
26
27
28
29
30
31
3*
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
50
5i
52
53
54
55
56
57
58
60
Cosines
99452
99449
99446
99443
99440
99437
99434
99431
99428
99424
99421
99418
99415
99412
99409
99406
99402
99399
99396
99393
99390
99386
99383
99380
99377
99373
99370
99367
99364
99360
99357
99354
'9935'
'99347
99344
99341
99337
99334
99331
99327
99324
99320
99317
99314
99310
99307
99303
99300
99297
99293
99290
99286
99283
99279
99276
99272
99269
99265
99262
99258
99253
6d
59
58
56
55
54
53
5^
5i
50
49
48
46
45
44
43
42
4i
40
39
38
11
35
34
33
31
3i
30
29
28
26
25
24
23
22
21
20
l 9
18
\l
15
14
13
12
11
10
9
8
I
S
4
3
2
1
0-83
O oO ^ O voo o O o O oO
"OlO^^MMH tt H M
CO
00
u
if
m
P
>
O
55
P
ti
of
P
H
<
Ph
H
P
(NNHOOCONH-^NOCTIO
lOWJlOCJNiOTlKNOON'O
OCJNOiOKtNOONO^IM
aOQOOOOOOOGOOOOOOOQOOOOOOO
ON
00
HONO(MQ0OWiO(M00^
OiOKiMpHCiaJNiO^WHO
O
00
OOiO^OOH003NiO000
o 10 10 10 10 10 o rf< -t
O
SO
n o ^ j: im h a X- n c 1?
O
VO
000050000(MMiOON
(M h H O O CO N N O O ^ CC (M
NNNNOOOOOO999
^i 'TJi ^H *^i ^i '^i "^ji "^i "^H "^^ ^^ "^4 T^
O
HO00(NOOWOOWOO(N
ooNOoo^^ooKtMHoo
oocococococococooococococo
5-
CO
C0MN(NHHOOO0300XiN
qpcpqpapqpopcpqpt>b~t^b-t>.
C5 O C' O 6 6 ' Q 35 ffi O O O
O
CO
ii
etc
u
ON^HOO-^HQOlOHOO^H
OXXXNNNOCOOiOiO
qoqpqcX'Xqpqpqpqoqpqpooao
Och>cbC5CiCiOOClGiCichiO
*0 w-)0 >flO w-iO *o O ^ O *o O
hi m N N CO CO j- rfr- "") vovo
^0
De
Diffi'j
partures, or
-ence of Levels
Si
y _ jjepartures, or uinere
3 Deff - * Levels
nee
01
TABLE II.
M
Departures, or
Difference of Levels
Sines
6 d
io453
M
i
10482
59
2
10511
58
3
10540
57
4
10568
56
5
10597
55
6
10626
54
7
10655
53
8
10684
S*
9
10713
5i
IO
10742
50
ii
10771
49
12
10800
48
13
10829
H
14
10858
46
15
10887
45
16
10916
44
7
10944
43
18
10973
42
19
11002
41
20
11031
40
21
11060
39
22
1 1089
38
23
11118
3 Z
H
1 "47
36
*S
11176
35
26
1 1205
34
*7
11234
33
28
1 1262
32
29
11291
31
3o
11320
30
3i
'"349
29
32
11378
28
33
11407
27
34
11436
26
35
1 1465
25
36
'"494
24
37
11523
23
38
"551
22
39
11580
21
40
1 1609
20
4i
11638
19
42
1 1667
18
43
11696
l l
44
"7*4
16
45
'"754
15
46
11783
14
47
11811
13
48
49
1 1840
1 1869
12
11
5o
1 1898
10
?l
I 1927
9
5*
11956
8
53
1 1985
7
54
12014
6
55
12043
5
56
12071
4
57
12100
3
58
12129
2
5 9
12158
1
60
12187
Cosines
0*83
Latitudes, or Hori-
zontal Distances for
Difference of Levels
6 <>*.
Departures, or Difference of
Levels
"o "->0 'oO iflO voO ^ O >oO
no >o>o + ^m M M
MN(MSHOOiOC5^00N
^lONCppHMrJiONQOOH
OOOOHHHHHHHJKN
Goooooooooooooaoopoooooooo
666303666666666
ONCSOOl^iONCOOHM^
cp^tiipt^qpCsprHcq^ipcpt-
doaoa)d)aooo6666666
SQ003H5qM"i*>0CXC3OH
H H H (N (M <M Ol ^1 (M (N (M CO 03
COfiOONOOOJOHNCp^lO
x^t>t>t>t>t>t>cbaododbc>bdo
eqaoocqc3iooqC3
Cr)OCOOOOOI>NNI>
OOHWOWONION03HM
(^c^cp-^ipippt^cpcpppp
ibbooiboibbb)o*c66
HON0(MOQ00i*HONi0
C0C003i0HN(M00^OOHN
Huqcqco^^ooONNoooo
OC3WOC3C0003WOC3MO
CO N iM CO O >0 O CO (M O h O
rHrHC<jCqCOCpcp^^ipppp
wcbcbcbcbcbcbwwwobwcb
OOiOONOO^COCqHOOON
qh^noc: s r. "m o qo o co
OHHH(N^^wcpcpcpi , -i'
<^(Ncfq<fq<jqcn^(?qG^o^cf^^cq
iOO**OCOCO(MOHOO^O
iiONQ0OHC0^ONC3Oi-
OOOOrHr-irH. Ii IHH(N(M
83 De *-
Latitudes, or Horizontal Dis-
tances for Difference of Levels
38
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
Cosines
99255
99251
99247
99244
99240
99237
99233
99229
99226
99222
99219
99215
9921 1
99208
99204
99200
99197
99193
99189
"99180
99182
99178
99175
99171
99167
99163
99160
99156
99152
99148
99144
99141
99*37
99133
99129
99125
99122
991 18
99114
991 10
99106
99102
99098
99094
99090
'99086
99083
99079
99075
99071
99067
99063
99059
99055
99051
99047
99043
99039
58 -99035
59 *99?i
60 '99027
Sines
6d
59
58
%
55
54
53
5*
5i
50
49
48
46
45
44
43
42
41
40
39
38
36
35
34
33
3*
31
3
29
28
26
25
24
*3
I
5
4
3
2
1
0-82
Departures, or
Difference of Levels
\M _j Latitudes, or Horizontal Dis-
e ' tances for Difference of Levels
O >oO *o O wi o O o O o O
vo 10 >o rj- + ^ to n w w
O
00
If
lOt^OOCMCO"^iOCOCDt>.b~l>-
lOCOHOOOCD-'iKMOOO'*^
WNWNHHHHHpOpO
6666606606666
OOOOOOOOOOOOO
ON
01CONO^t>0(M>ONO(M^
O)HC00O^C0HONO-*(N
M(NCTN(^01NHHHHH
0O0OCXDOOO0QO0OO0OOOOOOO0QO
o\
00
"*OiOOOOOOK5^00(M
00
m
3
>
O
O
125
W
S
of
p-1
D
H
P
1^
OOOnON^HN^OSWO
NOiO^^IHOQONO^WH
66o66oQOOQ6oC3
cdooooooooooo
vo
COCTHOOOOOiOt)<(MOQOO
O^M(MOO(NOiO^(MH
6606666666600
VO
N00OQHH(M(MC0MC0
(MHOOOXNOO^COiMH
666666666 6 6 66
^^ "^^ *^ "'^ "*^ *^^ t^ "^^ **^ ^^ "^ ^^ *^i^
I-
(MlOQOOOOiOCOON-fNOH
OOQOQONCOiOO^MCTHH
6666666666660
cooocococococfocooococococo
5-
O
CO
OHOOWOWNfMOO^CO
6600606606606
CM CM CM CM CM CM CM CM CM CM CM CM CM
CO
HN^O(MO>OHNWOO
cpopccccccpccqoGpcpa)
6600666666606
O
O
lO^fMOOOO^KMHONlOM
(M(MW(NHHHHHOOOO
000000000 OO OO
6606666666660
"o o >oo >oo u-> j->o <^o
m m cj c4 ro to ^ ^- 10 >o\o
O
8S
> Departures, or DifFere
* es ' Levels
nee
af
TABLE II.
'3'J
Departures, or
Difference of Levels
2187
2216
2245
2274
2302
2331
2360
2389
2418
2447
2476
2504
*533
2562
2591
2620
2649
2678
2706
2764
2793
2822
2851
2880
2908
2937
2966
2995
3024
353
3081
3110
3139
3168
3197
3226
3*54
3283
3312
3341
3370
3398
34*7
3456
3485
35H
3543
3S7I
3600
3629
3658
3687
3716
3744
3773
3802
3831
3860
3917
Cosines
4
3
2
1
0-82
Latitudes, or Hori-
zontal Distances for
Difference of Levels
Deff.
Departures, or Difference of
Levels
if
l>.rHCDOT*OOOOr>.rHll5C5eO>-
" 00 (M l> H
"* O t^ G>
cV>i c^ cm cm cm cb cb cb cb cb cb cb
OrHrHi^rHrHrHrHCqCMCMCMCM
05VOOOHN(NNWQOMTt(
^OOOHfMiliONQOOHW
t^OOpO CM CO^ippr^pOrH
660566666666HH
HiMCOTjtioONOOOOOH^
00 CO CO CO CO CO CO CO CO "<f "<# TJH "*
tppt^GpClprHCqCp^kCCOt^
cbcbcbcbcbciciCiCsociCid)
(N0ilCM00*OCM00OrHI>Tjt
HOOONiO^KHOClNOiO
C0M-^ipipN0p9OH(N00
i^t^t^t>t>^t>t>cbooGbcGb
MiOOOOW^OOOOffHOOO
QOOH 00 ta C< C5 t^ T* r- 1 00 *o
O rH CM CO CO x)H l IO p *> GO CO O
6666666666066
0(MO00O05HOOTf(!MON
NnCfOCtMNWOiOOO
GpOppiTHrHOlC^CpCp^iOiO
ri<Ti<Tt(ibibuoibibibibu3ibib
OOWOO(MOC5(MkOO(MiO
iOO-^00(MNHiOO^a)CON
OON^QpffiCiOpOOHH
ot)cbcbcb6o'D6cb-^i^TtiTtHT^
N O O ^ o: (M o O 00 N o o CO
M O O W iO OD -( o: CD O iM O 00
-* rji rji o o c 0999N w
cm cm cm cq cm cm cm cm cm cm cm cm cm
O0pfflO'-n5O'^Q0N(M
HC3^CNOOiMmT|ONQ
CM CM CM CI CM CJ CO CO CO CO CO CO CO
82
Latitudes, or Horizontal Dis-
es tances for Difference of Levels
40
TABLE II.
Latitudes, or
Hori-
zontal Distances for
Difference of Levels
C
Cosines
8 d
99027
60'
i
99023
59
z
99019
58
I
99015
s l
4
9901 1
56
5
99006
55
6
99002
54
7
98998
53
8
98994
S*
9
98990
51
10
98986
50
ii
98982
49
12
98978
48
*3
98973
47
14
98969
46
15
98965
45
16
98961
44
7
98957
43
18
98953
42
19
98948
4i
20
98944
40
21
98940
39
22
98936
38
*3
98931
? z
24
98927
36
*s
98923
35
26
98919
34
27
98914
33
28
98910
32
29
98906
3i
30
98902
30
31
98897
29
32
98893
28
33
98889
27
34
98884
26
35
98880
25
36
98876
24
37
98871
2.3
38
98867
22
39
98862
21
40
98858
20
4i
98854
19
42
98849
18
43
98845
17
44
98841
16
45
98836
15
46
98832
H
47
98827
13
48
98823
12
49
98818
11
5
98814
10
5i
98809
9
5*
98805
8
53
98800
7
54
98796
6
55
98791
5
56
98787
4
57
98782
3
58
98778
2
59
98773
1
60
98769
Sines
o-8i
1
I
Depa
rtures, or
Differet
ce of I
..evels
8 De e.
Latitudes, or Horizontal Dis-
tances for Difference of Levels
CO
CTOOOO^(MOCOOWHOCO
ppqigsqsgsoGpqpcpqpb-b-
66cbcbcc<aDcbccbcdbao
G5C50G3GiOSC3C5ClG5G50i01
Tji5S00OHH(M(NWC0(M(M
(MOOOOOCOHOMOCOHO
6666666<cc#<doao
goooooooqooooooooooooooooo
(MOOONiOOTWOOOOiOCOH
(NWHHHHHHOOOOO
^OiOHCDHOHiOO^QO
HOCJNO-^WHOOONiOTO
cooooooooocooo
o^wcico^oooiacqooiOH
HCONOO^tMHOQONO
MC0M(M'MHOO0500NOil
HOONOiO^(MHOOCO
H(Mt)(O0COO(MC0t)(OO00
hooconoolo^moiho
o o 10 lO LO o o 10 lO 10 o 10 10
00CTOffiMNOT)il>HT(fNH
OOOOOOONNCOOiO^oOCO
610666666663366
lOHNOOOiOOCMNrooOif
O O Ci C3 QO GO QO N N O O C O
6666666666606
__i _ _-j J < . , __< _-d I
WH00Or|(iyiO00OT)(HON
OOOOiOCJfflOOOOQOGONN
GiGicpopcpGpGpa)opGpGpqpGp
6666666666666
>h 1-1 cl c* ro c"> ^ ^ <-o <j~ivO
(9 <D O
S^ CO
81
__ , Departures, or Difference of
Deff - Levels
TABLE II.
41
Departures, or
Difference of Levels
3
P
i
n
O
3
S
m
a?
3
1
ft
O ^ Departures, or Difference of
O Be * * 'Levels
8 o'
i
i
3
4
5
6
7
8
9
10
ii
12
J
14
15
16
17
18
19
20
21
22
23
24
25
26
2 7
28
29
30
3i
32
33
34
35
36
37
38
39
40
<M
42
43
44
45
46
47
48
49
50
5i
5i
53
54
55
56
57
58
60
Sines
13917
13946
13975
14004
14032
14061
14090
14"9
14H7
14176
14205
14234
14263
14292
14320
14349
14378
14407
14436
14464
14493
14522
14551
14579
14608
14637
14666
14694
14723
14752
14781
14810
14838
14867
14896
14925
'14953
14982
15011
15040
15069
15097
15126
15155
15184
15212
15241
15270
15298
15327
15356
15385
15414
15442
15471
15500
15528
15557
15586
15615
15643
Cosines
60'
59
58
%
55
54
53
5*
51
5o
49
48
46
45
44
43
42
41
40
39
38
11
35
34
33
3*
31
30
29
28
11
*5
24
*3
22
21
20
19
18
3
15
14
13
12
11
10
9
8
I
5
4
3
2
1
o-8i
WO WO WO WO WO WO
NO W W + tj- to to ts N m ii
00
11
8 5
0Q
P
P
1
A
g
m
Eh
Ul
JH
P
|
O
CS3
H
3
O
w
m
Q
p
M
EH
*
NHioawNHioocqoow
HfflO"*OCOQOOHiOO-t<
O
505WJ'*rHMMN(SHOOC)
(NiOOOHiNOKCCriUN
ipOtsOOHWfWCCpQO
ON
O
^o^oiTfoiooiooiooo
W^ONOHlM'tlONQOOH
HNWilipNOCOOHCqrtfO
rHrHrHrHrHrHrHrH(fqCq(fqCqOq
1 Ii IHHHr- 1 1 IHHr- IrHi Ii 1
09
O
N00030HCTC3^OONOOO
666666666666
t (i 1 i IHr- Ii ii It- 1 H r- (
O
OSCOOOCTOOUJHS^OO
lOMNHfflQOCO'iKMHOQO
M^ipCONqpC59H(jqMcp
tc(ao(X)dba)6o66666
VO
O
HlONaON^OCOON
KJCCONiiHOCieOONiOtM
OHHtMMW^ipOCONOp
W
NiKNONOfMONXSNON
CD (M 00 ^ OS iO lN(N00*tO0
lpooNNcpooooHqqtN
CO
lOQOfMiOOOH^NH^NOCO
O
CO(MHOONOlO^HO
QOHiiNSNOXH^NON
NqoxcpooqiOCiOOOHrH
O
(MOOOOTtia)(MNHOO^
O(MK'+ONO(MC0i0O
CO"^'*'^^'*'*'^lOiOiO)OiO
3?. v o WO ^O WO ^O WO WO
2 2r MMtfrtcoco^-^w wvo
I
Latit
zonta
Diffei
ides, or Hori-
Distances for
ence of Levels
Q1 n Latitudes, or Horizon
Ox e8 "* tanees for Difference
tall
FLe
)is-
vels
42
T
ABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
1
1
h- i
P
O
0Q
O
H
m
hH
P
S3
M
8
a?
P
S
d
h3
q Latitudes, or Horizontal Dis-
t/ ^ tances for Difference of Levels
9 d
z
3
4
5
6
7
8
9
IO
ii
12
IJ
H
1 S
16
17
18
19
20
ZI
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
50
5i
52
53
54
55
56
57
58
60
Cosines
98769
98764
98760
98755
98751
98746
98741
98737
98732
98727
98723
98718
98714
98709
98704
98700
98695
98690
98686
98681
98676
98671
98667
98662
98657
"98652
98648
98643
98638
98633
98629
98624
98619
98614
98609
98604
98600
98595
98590
98585
98580
98575
98570
98565
98560
98556
98551
98546
98541
98536
98531
98526
98521
98516
9851 1
98506
98501
98496
98491
98486
98481
Sines
60'
59
58
%
55
54
53
5*
5i
50
49
48
46
45
44
43
42
4i
40
39
38
36
35
34
33
31
31
30
29
28
26
IS
24
23
22
21
20
19
18
3
15
13
12
11
10
9
8
I
5
4
3
2
o-8o
O o O o O >oO 100 00 >oO
VO ^1 >o ^ + W !^ M M Hi M
O
O
00
II
m
1
Pn
O
pq
1
p
of
3
p
H
1
P
OOCOOOCTOO^OOHOH
O^(MONO(MOC00C0O00
aDCDooccaoaoocaoaocoaOGOao
CiGiOidOiCiCiCiCiCiOiCiGi
H
on
(MHOOOONiO^tMOOOON
qpooqpqpopt^l^t^l^t^ocoo
636060606060606060100606060
00000000000000000000000000
O
ON
00
ioNoooHoqcqcoT)too>oo
posqiqiqiCiqicpcpooooooi^.
Oiobobcbobobobobobobobobdb
00
b
OONOOMOOMOfflNitN
C0(MOOiNO^(MO00Nk0C0
71HHO9OOOOC1OQQ
oioioiosoioodiooboboodb
O
NO
rHOO^OCDr-ll>.CqOOC005^Ci
CO^COGvJOOit^O^CO^IOOO
CN^C^<^<NrHpHrHrHrHpHrHO
O
NO
O
Tticoi-iooocD-^(?qoaoocoo
Wcpcpcpcpcpcpcp<^GN<>ic<i03
O
I
Q00005OOHHH(M(N(M(M(N
OOQCOONOiOjjCOCTHOQ
10 "^ ""^ "^r "^ "^ "^ -r T ^ "^ "^ ^ co
co co co co co co co co co co co co co
O
1 i-^t^OCOCOOOrH^r^Cid^
CCKMHrHOOiQOCONOiOiO'^
to
O
T(iOiOO>OOOHOHOH
lO'^'^i'COCOlNfflHHOO
0C50 0OiOC5 05 0501
O
t<
O
NiOiNOCOlOCOOOOOCOHQO
opopopqpopqpopopqpopopopop
O
11
w HI t* t* ci co ^- <$ v/-> vovo
o\
Departures, or
Difference of Levels
8f
/ De * Levels
TABLE II.
Departures, or
Difference of Levels
Sines
9 d
15643
60'
i
15672
59
2
15701
58
3
15730
5 7
4
15758
56
5
15787
55
6
15816
54
7
15844
53
8
15873
52
9
15902
5i
io
15931
50
ii
15959
49
12
15988
48
IJ
16017
47
14
16045
46
5
16074
45
16
16103
44
"7
16132
43
18
16160
42
19
16189
4i
2
16218
40
21
16246
39
22
16275
38
*3
16304
3 Z
24
16333
36
*S
16361
35
26
16390
34
27
16419
33
28
16447
3a
29
16476
3i
30
16505
30
31
16533
29
32
16562
28
33
16591
*7
34
16619
26
35
16648
25
36
16677
24
37
16706
*3
3
16734
22
39
16763
21
40
16792
20
4i
16S20
19
42
16849
18
41
16878
l %
44
16906
16
45
16935
15
46
16964
H
47
16992
13
48
17021
12
49
17050
11
50
17078
10
5i
17107
9
52
17136
8
53
17164
I
54
17J93
6
55
17222
5
56
17250
4
57
17279
3
5
17307
2
59
17336
1
60
17365
Cosines
o*8o
Latitudes, or Hori-
zontal Distances for
Differ
ence of 1
_.eve!s j
9 De 8T
Departures, or Difference of
Levels
oO o O w>o "> O o O >oo
>0 >0 + t)- M W N rt It II
O
o
If
%3
^oocot-r-tcoo-rjio -.
ibibib6666666t>-b-b~
0100QONOiOTt<M(MHOCiOO
NOCOOC^LOCOH'tNOW
iOO-^O-^O^OOCOGOCOt^ffl
ipOt^qpOpfNCO-^ipcpt^qp
<f^(fqci(N(?^cocb(Wcbcbcbcbo2
OHHfNtMOOKTtt-^^iOlOiO
OOHI^WTttipONqDCiOH
OrHr^rHrHrHr^rHrHrHrHCqcn
C^OOtPHNMOIOHNCOO
QOt>lO'*COHOOONO'fOTH
C0"^^Ot>-00CiCSprH(?C|Cp^
666666cj666666
(NOOCOOQOOCTOOCOHOO
OOCXJOOrHrTHCqCpSp^ipcpCp
66666666666 6 6
WOOfM'OOOH'llNOMOO
OWb-^lCOOiOOMOOfMOO
CONlNQCOOOOOOOHHCT
CMlOOOHTfNOMiOQOH^N
wwwcbcb6 6cbcb6cba36
THOCON(MOOOOi*a)(MCO
ONOOWCOONOOWOJ
O o O
too voO o O *>"> O w-> O
80
Latitudes, or Horizontal Di3-
De8r * tances for Difference of Levels
44
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
CO
1
fc
3
g
I
M
Ph
co
W
H
CO
3
3
g
O
i
w
w
Q
p
H
4A Latitudes, or Horizontal Dis-
lv eff * tances for Difference of Levels
Cosines
98481
98476
98471
98466
98461
98455
98450
98445
98440
98435
98430
'98425
98420
98414
98409
98404
98399
98394
98388
98383
98378
98373
98368
98362
98357
98352
98347
98341
98336
98331
98325
98320
98315
98310
98304
98299
98293
98288
98283
98277
98272
98267
98261
98256
98250
98245
98240
98234
'98229
98223
98218
98212
98207
98201
98196
98190
98185
98179
98174
98168
98163
Sines
60'
59
58
56
55
54
53
52
5i
SO
49
48
46
45
44
43
42
4i
40
39
38
36
35
34
33
32
3i
30
29
28
2
25
24
23
22
21
20
19
18
2
15
14
13
12
11
10
9
8
I
5
4
3
2
079
io d
2
3
4
S
6
7
8
9
IO
ii
12
13
14
IS
16
17
18
*9
20
21
22
23
24
*5
26
27
28
29
30
3i
32
33
34
3S
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
5o
5i
52
S3
54
55
56
57
58
I 9
60
O *nO v*io ^o >oO *0 O *o
VO vi IO ^- TJ- M tfl C< M M
O
Ox
U
11
CO
>1
H
Pn
O
O
i
B
P^
M
Q
M
co"
s
5
l
W
P
HlOO^OOWOOWVOOOOCO
Q00WONO(MONTt<HOO
OffiCJCJCiOOOOQOJCiOl
ON
nOt>"*ON(MOOOOHN
cpcpoooip^^--*^cpcpe:>
co6o6occ6d6occooccqo6d6ooo
oooooooooogoooqoooqoooqooo
ON
00
10^t)<C0(NHOOQ0O^iMO
OOCOi<(NOQOOMHC5NiOCO
t^t>l> t;-l>CpCpCpcpipiO*pip
ccbdo<&c#doc<cc<x>aDa)
O
00
NOOHMiOONOOHCOCO^
WHOXlOiKMOONiONH
q50}0qpqpcpqoq0b-t't~t^l>.
oDODaoacxiaoccaoooaofhcCGO
ococooooooo
VO
QM00(NSHlO05N.r- 1^00
OO9OOOffl0iOqjqD
CiOOod>C5ccdoaoooooao
VO
OMO(NOOIMOO(MO>OH
^^HO00NO^W<MOOQ0
<^C<li^C^rHrHrHrHrHrHrHpp
OOCOOOC30000C50
*
(M(N(M(MHHOOQOONOiO
OOONOO'tMCTOCiOONO
cococococococococococococo
*
CO
^COOirHCOCDI>.OC<icoiOl>-Oi
ii(N(MHOOOa)NOOT((
6o6ci6o6oo66
CO
OHHCDOiOOt)*0^qoo:
OCJQOOONNCOOiO^^COM
oooooooooocooco
OOiOCOOQOK5GqOt^^CClCiCO
cqpqoqpcpQpGpopqpGpqpGpcp
1ft
*b 00 o O ^o >oO o 10 O
W M fj d M M + tJ- >o lOVO
Ti Ti'XV
Departures, or
Difference of Levels
7
9 De *- * Levels
jnce
..
TABLE II.
46
Departures, or
Difference of Levels
ioo'
I
2
3
4
5
6
Sines
17365
17393
17422
17451
17479
17508
I7S37
17565
17594
17623
17651
17680
17708
17766
17794
17823
17852
17880
17909
17937
17966
17995
18023
18052
18080
18109
18138
18166
18195
18224
18252
18281
18309
18338
18366
1839S
18424
18452
18481
18509
18538
18567
18595
18624
18652
18681
18710
18738
18767
'i 8795
18823
18852
18881
18909
18938
18967
18995
19024
19052
19081
Cosines
079
Latitudes, or Hori-
zontal Distances for
Difference of Levels
xn
10 Be &-
Departures, or Difference of
Levels
v> o >o o
lOOOH-tSOM^
C O C CJ W X' f) o o o o -.
COiOCNQOWMtOCONC:
Ci <n *o 00
t^t^i^i^t^docboooboooDaoo
(MiOOOHTj(|>owiOOOHTt*N
Cpt^GpOrHCvl'rJHlOOt^CiOrH
s-
(MOHIOO^OCOOXMOOO
OOfMOTiOONCONKiOO
QOOHNM^iOOOOOOHCq
lOOCDOOOONSNNNN
10 u: o iQ o o o o o io o o
rHC^Op'TtiipCp^QpqSprHtTqOp
T}(ppON00CiOHH(MW
OOOOOOOrHrHr^rHrH
(M^ONCiOlMCOiOCOOOO
00OC<1CSO^^-IGOIO(MC1CO-*
Cpt^qpopqiOrHrHGqcpCp^O
OCOOQOVO(MON^HOOON
opprHpHcrqcNcp^^ipipcp
(MlOOOi-H^t-OCOCOOOrH^
O>0OC0C0(MOHOQC000(M
OOtNOONCOlOCOtMOOOOO
^ipipipippcpcpt^b-b-b-qp
5DHUJC3^00(MNHOO^QO
CQiOONOOtNMiOONOO
l>t^t^t^t^Q0O000000000OOC5
11
I!
S3
79 *>egr.
Latitudes, or Horizontal Dis-
tances for Difference of Levels
46
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
CO
1
>
m
O
P
O
CO
m
H
co
M
P
N
O
P*
O
w
P
P
H
1 1
H
3
"11 n Latitudes, or Horizontal Dis-
JLL eff * tances for Difference of Levels
11 o'
i
2
3
4
5
6
7
8
9
IO
ii
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
50
5i
52
53
54
5
57
58 ,
60
Cosines
98163
98157
98152
98146
'98140
98135
98129
98124
981 18
981 12
98107
98 1 01
98095
98090
98084
98078
98072
98067
98061
98056
98050
98044
98039
98033
98027
98021
98016
98009
98004
97998
97992
97987
97981
'97975
97969
97963
97957
97952
97946
97940
'97934
97928
97922
97916
-97910
97904
97899
97893
97887
97881
97875
07869
97863
97857
97851
97845
97839
97833
97827
97821
97815
Sines
60'
59
58
u
55
54
53
52
5i
5
49
48
%
45
44
43
42
4i
40
39
38
1*
35
34
33
32
31
30
29
28
26
25
24
23
22
21
20
'9
18
s
15
14
13
12
11
10
9
8
I
5
4
3
2
1
078
O m O >oO oO *oO m O <oO
vo >o >Oij- ^- CI M C* M w
00
1
Sf
a3
1
CO
h3
>
a
ft
Pw
P^
P^
M
P
P4
O
co"
p
H
P3
P
COCOOMOtMOOCOON^H
rHrHrHpppCiCiCiCiqpcpqp
obobobdbdbabt^t^t^t^t^t^b-
I NHOO"OOMNOiH>0
O WW(M!M(M(NHHHHOOO
^ aoocoooooDooaoaDaoaoGO^oo
00000000000000000000000000
00
OQOOIMONtPONMOOIM
abobobooobobobabobabocabob
00
is
HOMOCOHON>OWHON
t^cpcpcpppipipipipip^^
obobabebabobobobabobabobob
i^jCOOOOCCOOOOOOCO
OOt l^r^OCOiOOOQC^lOJ^O
opopopqpqocpb~i^t>b~i>-t^p
obobobobobabobobabobobobob
HNWOOOOHN(NN(MN
QOOOCOWHOQOOiOCCfMO
0000000009^^
66o666a)iaco5(
lO-^WHOOONlO'^HOOOO
OiOt)(CO(MOOOONOM(M
CN<NCN<NCN<NT7lrHrHr-lrHrHrH
OOOOOOOOOOOOO
cococootcococococococococo
O
*
CO
OOOOOOOOOOOOO
OqcNCM<MCMOq(MOqC<l(^(M(MG^
O
CO
KNHOO^QOMNHIOOM
MNlMHHOOOaiODNOO
cpcppcpppipipipoipiLpip
OOOOOOOOOOOOO
1 1 1 It 1 i IHHr IHHr IHHH
O
O
M
OOJHOOIOCMOOCOON^H
HHHOOOC5OOC3 00 00Q0
apopceGpqpqpt-t^b-l>t>-t^i>-
OOOOOOOOOOOOO
O
ft
Si
O 10O m O >oO mo m O *oO
hi it el c* co co tJ- >sj- o o<3
ruir
Departures, or
Difference of Levels
7f
) s " Levels
1
TABLE II.
17
Departures, or
Difference of Levels
Sines
3 o'
19081
I
19109
2
19138
I
19166
4
19195
5
19224
6
19252
7
19281
8
19309
9
19338
10
19366
II
19395
12
19423
13
19452
14
19480
15
19509
16
19538
*7
19566
18
19595
19
19623
20
19652
21
19680
22
19709
2?
19737
24
19766
25
19794
26
19823
27
19851
28
19880
*9
19908
3
19937
3i
19965
32
19994
33
20022
34
20051
35
20079
36
20108
37
20136
38
20165
39
20193
40
20222
4i
20250
42
20279
43
20307
4-!
20336
45
20364
46
20393
47
20421
48
"20450
49
20478
$0
20506
51
20535
5*
20563
53
20592
54
20620
ss
20649
56
20677
57
20706
58
20734
59
20763
60
20791
Cosines
Latitudes, or Hori-
zontal Distances for
Difference of Levels
11 e&.
Departures, or Difference of
Levels
O w->o v>o *oo *> o ^0 wiO
o
QONOOiOOCON(MOOitQ
ONMiOONOOCqWOCSN
OOOiOOOOOOOOOO
r li li-Hi li lr-lrHC<JC<JG^(?q(N<M
MHOOOOiOHOQOOt)((M
NCMiOTOH^NO^iOQOH
HCO^iOOOOOOfNCOTltiON
t^r^t>t^^r^t^<QOooaDao<X)
n
%*
_ t- o o
WWTJiONCOOiOHfM^kpO
w*ooimx)oohws:^io
oo^oiOHOcqaoMoo^oio
<*i>5(MONO^OOHOQON
r|<OONl>0pffi9HCTCCW*
^r-tOOiOOJOSO^i IGOiOCMO
lpOCpt^GOQpOOrHrHf^lCpOp
OOOOCiOSOOOOoOO
COQO^OOHNCOOO^OOH
woHooMooff)00<ooo:
t>I^<qOGpq}CSpprHrHrH<7q
lbibooibibibcbcbcbooo
OiOCOCTOONO^OHOlX)
HTtlNOMiOCOHr)<NOMiO
QOOOOOOffiQOiOOOHHH
CONNHiOOiiaXMOHiOCi
0(NOONC50(M 59 OCN
rHrHrHrHpHrHpHCNfflOlC^C^ff^
uiO 100 ^O o o >oO
m H rt M ro tj- ^ 10 vovo
78 De "
Latitudes, or Horizontal Dis-
tances for Difference of Levels
48
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
GO
H
>
a
@
1
1 1
P
O
5
GO
g
|
H
CO
P
H
C
i
w
of
H
P
B
H
H
h3
* Q _, Latitudes, or Horizontal Dis-
A<w es * tances for Difference of Levels
12 o'
i
2
3
4
5
6
7
8
9
10
ii
12
13
14
15
16
7
18
19
20
ZI
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
50
5i
52
53
54
55
56
57
58
I?
60
Cosines
97815
97809
97803
97797
97790
97784
97778
97772
97766
97760
'97754
97748
97742
97735
97729
97723
97717
977 1 1
97705
97698
97692
97686
97680
97673
97667
97661
97655
'97648
97642
97636
97630
97623
97617
9761 1
97604
97598
97592
97585
'97579
97566
9756o
"97553
97547
97541
97534
97528
97521
97515
975o8
97502
97496
97489
97483
97476
97470
97463
97457
97450
97444
97437
Sines
60'
59
58
%
55
54
53
52
5i
50
49
48
46
45
44
43
42
4i
40
39
38
11
35
34
33
32
31
30
29
28
2
25
24
23
22
21
20
19
18
\l
15
14
13
12
11
10
I
I
5
4
3
2
1
077
O >oO w-io oO >oO 100 oo
11
1!
a3
\
\
CO
p
ft
ft
ft
1
p
go"
p
ft
p
HooiONOoeoo>oc30Nco
cpb^b-b^pppoooo-'*^
b-b-b-b~b-b-b-b~b-b-b-b-b~
OiOiCiaaaGiCiCiCiOiCia
WON0(NC5OC0O00i0iMO
ppqiCic:(X)ooGpoob-.b-b-o
ODODNNNNNNNNNNN
00 00 0000000000000000000000
ON
6
00
(Mt^COOO-^O-^OOCOb-fMOO
0(MOMO(MCh0(NCN"0
(N(N(NhhhhoOOOOQ
obobobobabobabdbocobxb-b-
b- b- b- b- b- b- b~ b- b- b- b- b- b-
00
O
OO00Ot((C0HOOt((hC5O
N^IMOODO^HOMCMO
cfcaoopopobobobobccdoobdbab
0000000000000
vo
GO<M^U3S0COOOHNiM
ti003HOt>OM(NOQ0O
ppppooooooo^-^
obxcbcoababobobobaoobobob
iooooooooooooo
vo
O
N(MNHCO>OffiMNrlUJOO
OONO^OOHOJOOClOOH
popopcpopcpopb-b-b-b-t^b-
obcbabobobobccaodbabobabob
%
(MHO$SOW93'MHO00N
HHHOoopoooooa
csocsoiocicscscscsciooao
cococococococococococococo
CO
TjilCONQOCOCi0500HHH
CO
O
OONHiOCOtMOClWNO^N
OOO"*C0C0<MrHi IOOOOO
lOOOOOOOOOOO^^J
pHrHi Ii Ii ir lr liir- 1 H r- Ii IrH
O
HOOiONOCOMONMONtP
aob-b^b-ooooooo^Tfr
OJOOC10C5GS05GSCSOOSC5
I!
O "10 yn *o "> O *<"> O f>
M HI H tf M tO TJ- TJ- lO U")VO
Departures, or
Difference of Levels
7 K
k _ uepartures, or jjinere
J De8r - Levels
ace c
)I
TABLE II.
49
Departures, or
Difference of Levels
m
>A
K
H
m
g
P
O
Of
w
p
w
ft
iq _ Departures, or Difference of
1<6 "" Levels
12 o'
I
2
3
4
5
6
7
8
9
IO
ii
12
13
14
*5
16
17
18
19
20
21
22
13
24
*5
20
27
28
29
3
31
32
33
34
35
36
37
3
! 39
40
4i
42
43
44
45
46
1 4 l
48
49
50'
5i
52
53
54
55
56
57
58
59
60
Sines
20791
20&20
20848
20876
20905
20933
20962
20990
21019
21047
21076
21 104
21132
21 161
21189
21218
21246
21275
21303
21331
21360
21388
21417
21445
21473
21502
21530
21559
21587
21616
21644
21672
21701
21729
21757
21786
21814
21843
21871
21899
21928
21956
21985
22013
22041
22070
22098
22126
22155
22153
22212
22240
22268
22297
22325
22353
22382
22410
22438
22467
22495
Cosines
6V
59
5
S l
56
55
54
53
52
5i
50
49
48
46
45
44
43
42
41
40
J9
38
is
35
34
33
32.
31
30
29
28
26
2-5
24
23
22
21
20
19
18
3
15
14
13
12
11
10
9
8
I
5
4
3
2
1
o77
*b n O /">o "o >oo oo *->
vo >o >o tJ- ^- M M t) C M M
O
1 t^
If
%3
m
>
B
i
rH
CO
W
O
H
P
r3
<1
H
fe
O
i
3
O
H
CO
W
P
b
H
hH
EH
5
HM'O00O(Mt((Oq0O(MM10
OiMNHOOiiQOtNNHiOCJ
H^OaiMiONOCOCDOHi
t>qpc5p<Ncp^pt>opq5rHCN
obobobdiCiC50ic3ich>620ioo
HHHr- (1 Ii (r- 1 1 IHr- 1 1 1 <M CN
O
00
MNO^OOHiOGiWOOMCO
M^ONQOOHfM'-tiOOOOQ
pt^oppp^cp-'+ippb-qpp
00
^MWCqCTHHOOQOONCD
ipcpi>-qpoprHqqcp^iocoi>.
rHrHi 1 1 1 t 1 1 1 1 IHHHr- Ii IrH
r-.
O
00'OHCHCOHN(flN(MN
l> O "^ CO 1 lOQOMO^IMr- 1 05
^ipCt>CCOOCHCTMTt)TJ<
ic^c^^<>icq<Ncbcbcbcbcocb
pHi It IHr liii it 1 1 Ii IHHH
!ONOOOOH(MtHiOONN
OOKOOOiOlNOiSeJON^
co^ippcpt^cpooqiprHrHqq
OOOOOOOOOrHrHrHrH
O
OWONT}IHQOi<HQOOHCO
cpco^^oppt^t^qocppp
<cbdoaoccc&ob&&aodb
O
CO
noooioo6owxhcoo
OOX(MOOiOQOON(MCOt)l
^c^cpcp^^^xpoppt^t^.
CO
H
Q0J>.i0C0G<lO05l>,C0^rl0qr-IO
lOOOH-^NOlMOQOH^NOJ
rHrH^^t^CpcpcpCp^Tlr^Ttl^rl
O
05C00001CDO^0iC0t>.r- liOO
P.QONCOiOCNOJOfMCO'Jl
COHHHHHHH^IMIMIM
u
*0 *0 O **"> O >oO */"> O >flO o O
m m n p> co co <$ ^- u-> cnvo
Latit
Bonta
Differ
udes, or Hon- j
I Distances for
enoe of Levels '
mm Latitudes, or Horizontal ]
# I es ' tances for Difference of Le 1
)is.
rels
50
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels !
GO
3
>
H
h)
ft
O
F
i
g
a
to
H
go
11
A
s
H
DO*
H
P
B
i
^ q Latitudes, or Horizontal Dis-
XO esr " tances for Difference of Levels
13 o'
2
3
4
5
6
7
8
9
IO
ii
12
13
14
15
16
17
iS
*9
20
21
22
*3
24
25
26
27
28
29
30
3i
32
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
50
5i
52
53
54
55
56
57
58
Cosines
"97437
97430
97424
97417
9741 1
97404
97398
97391
97384
97378
97371
9736"4
97358
97351
'97345
97338
97331
97325
97318
973 1 1
97304
97298
97291
97284
97278
97271
97264
97257
97251
97244
97237
"97230
97223
97217
97210
97203
97196
97189
97182
'97 7S
97169
97162
97155
97148
97 141
"97!34
97127
97120
971 1 3
97106
97099
97092
97086
97079
97072
97065
97058
97051
97044
97037
97030
Sines
60'
59
58
%
55
54
53
52
5i
50
49
48
46
45
44
43
42
4i
40
39
38
11
35
34
33
32
3i
3o
29
28
26
25
24
23
22
21
20
:?
\i
15
H
13
12
11
10
9
8
I
5
4
3
2
I
0*76
*0 "j-iO *o O o O o O l o O *o
P
GO
3
>
a
H
P
P^
ft
Q
O
of
a
p
H
A
CCONONCOOOCCOO(M
^b-b-b-b~b~b~b~b~b~b~b~b--
O
O
ON
0MON^HQ010(MQOO(M
b~b-b~b-b~b-b-b~b-b~b-b-b-
O0O0O0OOO0Q0COGOOOO0QOO00O
O
O
ownomno(mu:nc5(mo5
5(NONTtiHOCOONiO(M
OOCOOOOOOONNNInCOO
b~b~b-bb-b-b~b~b-b-b~b-l>
b-bb~bb-b-b-b~l>t>t>b-b-
O
OO
O
bs
68-206
68-183
68-160
68-137
68-113
68-090
68-066
68-042
68-018
67-994
67-969
67-945
67-920
VO
N(MOOCO(M(M(M(MHOOON
OTf(MQQOCD^(NOOOifflH
abcb<obabc(#cbccbobdbabdo
VO
HOooOONHOOOOiicOH
NNOOOCpcpcpiOpQ IO O
cabcabcaDobcbcbcEaO(Xao
Tjl "^1 "^p TJi ^^ *^T ^T ^^ "^ ^^ "TjH T^ ^^
lOi IQOlOi 1 OO O H 00 r|* O O (N
NO^WCqOOOOCDLO^tMH
csooiOiOiCiopopapopopaOGp
<cbab(obabobobcabaDoDoo
cococowcocococooocoeococo
i
CO
HHHHHHHHHOOOO
WfMHOOOONffiiO-^eOHO
(^(N^^rHrHrHrHrHrHrHrHrH
0Jffio6CJC3OCjC)OQO
CI
NHT)lQOHTjiNHT)(NOCOO
OOOONOCDlO-^rJ(CO<M(MHO
1 (r IHHr Ii (1 Ii 1 H r- IrHrHr 1
iiOSTliONitOSOOOW
b-b-b-l>.b~b-t>.b-b~b-b-b-b.
If
O 00 >oO wi O iflO oO ^ O
H w H tf M Cl -i- ^- >0 OVO
t\ rv.fr
Df
Departures, or
Difference of Levels
7(
J De &- Levels
uue
TABLE II.
51
Departures, or
nee of Levels
ijo'
I
2
3
4
5
6
7
8
9
io
22495
2252}
22552
2258O
226o8
226j7
22665
226Q3
22722
22750
22778
22807
22835
22863
22892
2292O
22948
22977
23OO5
23033
23062
2309O
23H8
23146
23175
23203
23231
23260
23289
23316
23344
23373
23401
23429
23458
23486
23514
23542
23571
23599
23627
23655
23684
23712
23740
23769
23797
23825
23853
23882
23910
23966
23995
24023
24051
24079
24107
24136
24164
24192
Cosines
076
Latitudes, or Hori-
zontal Distances for
Difference of Levels
13 De *
Departures, or Difference of
Levels
?
IS
U5NOOO(M1iONCOH(M
OMNfMOO-t'GONOHiOO
<tCDNOO(Ne:T)iNQOH
G^ 65 ip p" lj 6t>p rH qq cp ip S b-
OOOOOOrHrHr^-lrHrHr^HrH
OOiMCDOfMiOOODOQOHTJf
OH(Nn^pCOI>QOH(MCO
COCOtOTt<M(MHOQQONCO^
t^qpqiOrHcqco-^ipcpi>.ooo
OSQOCDlOCCC^QCSb'CD'^COrH
TliiOONQpCiOOHfNCO^iO
t^oocio.-ir-tcqco^^ioioco
*H00OMON^H00iO(MCi
MCOWTjfiOOCCNQOCOCOO
OOHHfN^WMTttipipOO
00r-ICOCDOirHCOCO00i-IC0lO00
NNOOOOOJOOOOHH^tM
NCOTJiiMHONlOTifCTOOO
TtHOOiOOCOCOONNNOOOO
*onoocto:^nooh
cqcNCTcqcpc^cpcpcpcpcp'^Th
76
Latitudes, or Horizontal Dis-
s * tances for Difference of 1
52
TABLE II.
J Latitudes, or Hori-
zontal Distances for
Difference of Levels
I
fa
H
1
p
fa
QQ
w
H
w
t (
p
O
N
1 i
M
O
W
a?
p
p
H
t 1
H
,
14 Deg- Latitudes, or Horizontal Dis-
x ^ B ' tances for Difference of Levels
i4o'
2
3
4
5
6
7
8
9
IO
ii
12
13
14
15
16
7
18
19
20
21
22
*3
24
25
26
*7
28
29
jo
3i
32
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
50
5i
$
53
54
55
56
57
58
12
Cosines
97030
97022
97015
97008
97001
96994
96987
96980
96973
96966
96959
96952
96944
96937
96930
96923
96916
96909
96902
96894
96887
96880
96873
96866
97858
96851
96844
96837
96829
96822
96815
96807
96800
96793
96786
96778
96771
96764
96756
96749
96741
96734
96727
96719
96712
96705
96697
96690
96682
96667
96660
96645
96638
96630
96623
96615
96608
96600
96593
Sines
60'
59
58
55
54
53
52
5i
50
49
48
46
45
44
43
42
4i
40
39
38
H
35
34
33
3a
3i
30
29
28
26
*5
24
23
22
21
20
I!
\l
15
14
13
12
11
10
9
8
I
S
4
3
2
075
O 100 10O 100 *j">0 >oO *oo
O
S2
S>3
fa
s>
fa
PE|
O
fa
fa
fa
fa
fa
M
P
af
fa
1
Oh
fa
P
CTOiiOfMOOiOHN^OCWffi
OQQQ0i05OC6OOOOCl
O0C0H00CDWON^ONC0
(M0500500MOOCOOCOM
MW^PIHHHHOOOOO
00000000000000000000000000
ON
00
COlOI>-00r-l(N<N<MCO"'*''*Tj<
(MOOCCHOOiO(NC5COCOON
O
00
OOHOHOOiOOCONHTf
(MON^WQN^HQCOiiH
t^- 1>- 1 t^- t^- t>- 1- i>- 1^ t>. t>- 1^ i>-
NCOOTX(MHGiNiO(NQQOO
HONiQWHOOOiflMONiO
(NrHrHr^rHr-ICpOOOOOO
obcbobobobobabobobobaot^b-
HC2NfflrtMOOONiOWiHQ
ccobobobobccobobobobobobob
^P Tji "^1 TJi TJH T71 ^H t^H t^/i T^H t^ '^4 ^^
*
(MN^C3iOOOHO(MN(MN
HOQOCOOrtiClHOiOOCDiOCO
0)Nt>t>NNNNffiOOO
obobaDcboccfeabobobobobaboo
cococococococococococococo
CO
CSOOOOt^COO^COG^rHOG5QO
OQOONOiO^CO<MHO'30N
rHopopoopoppoqs
6666666656660360
CO
c4
COOWONOMOOOHMOOO
OC5O1>NO>0t|1^WCTH
6666666666666
WOCDCTOiOHOO^ONMO
O C3 O O CO X 1 00 N N N O iQ
6666666666666
O
"0 voo >00 uio >o O ^ O viO
hi w H M mm ^tJ-io iovo
Departures, or
Difference of Levels
7
> Deff " Levels
3nce
UJ.
TABLE II.
63
Departures, or
Difference of Levels
m
3
1
O
O
3
&
ft
O
a?
P
H
ft
1 4. Dee Departures, or Difference of ',
" *' Levels
14 o'
i
2
3
4
5
6
7
8
9
IO
II
12
*3
14
15
16
17
18
*9
20
- 21
22
23
24
*5
26
27
28
29
30
3i
?a
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
5o
5i
5* ;
53
54
55
56
57
58
s
Sines
24192
24220
24248
24277
24305
24333
24361
24390
24417
24446
24474
24502
24531
24560
24587
24615
24643
24672
24700
24728
24756
24784
24813
24841
24869
24897
24925
24953
24982
25010
25038
25066
25094
25122
25151
25179
25207
25235
25263
25291
25319
25348
25376
25404
25432
25460
25488
25516
25545
25573
25601
25629
25657
25685
25713
25741
25769
25798
25826
25854
25882
Cosines
60'
59
58
S?
55
54
53
52
5i
5o
49
48
46
45
44
43
42
4i
40
39
38
\l
35
34
33
32
3i
30
29
28
2
25
24
23
22
21
20
19
18
\l
15
14
13
12
11
10
9
8
I
5
4
3
2
075
O to to 00 w->o 00 oo
vo >oo^-^ tort N w i-c
O
o
is
3
1
Q
1
1
1 1
ft
s
<
H
CG
M
ft
O
N
t 1
w
M
O
of
ft
ft
B
H
t 1
H
<1
OCONHiOOWNHOOitQO
rHCO^OI^qOprHCp^Ob-qO
NOOHCNTtfiOONOOH^
rH rH f>1 Oq (jq cq f>} (fl <fq * CO 00 CO
<MCqCM<M<N(MC^0ieq<MCN<M01
00
^NOXMiOOOOWCbOOHeOiO
lOCONOOHDJ^ioO'XOO
Cp^ipcpcpOOHtNcp^ON
cscicscaooooopooo
r-lpHr-lr-lr-lrHCMCMC^^CMC^Sq
00
COCOCOCOG^cqCMCNCN'NCq^Hi-l
OOHtNM^OCpNOOOOH
lOOiOO^OOMNNOOOO
HOXOiOCONOONOitM
ipOCpt^GOqSprHrHCNCp-^lO
1 1 1 1 1 I 1 li li IHHr- li It It- IrH
vo
tO
OONXXQOOOOOOHH
OOWON'lHXJOnON^
OrH!>4CpCpTjlipOCpb-(X)COa)
c<icqeq<?q<jq(q(fq<^c^cqc>q<fqcq
1 li IrHr IrHi It li IrHi IrHi li 1
o
NMOOlMOiOHQOTtiOOCO
NMO^OOr-iN(MOOT|l35iO
cpt^i^opcsppcpr^irHC^cqcp
P- 1 T 1 I-H I 1 T-H T 1 T 1
I
CO
ooiixxMOHioojcoaxNO
(NMWWT|lT|lipippOONN
CO
OONiCWHOOOOTPfMOOpO
CD C3 'M O N O CO O C3 iM H< N
qpqpopCi OOO9O7IHH
O
If
II
CiCONHOO^OOfMCOO^QO
1 iCOTHSOt^GiOr- 1 CO 'H O C^ 00
O
O oO too too too to O too
w 11 cJ d MM + + >o to\o
%
Latitudes, or Hori-
zontal Distances for
Difference of Levels
m pr Latitudes, or Horizontal Dis-
4 O es ' tances for Difference of Levels
84
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
15 o'
i
2
3
4
5
6
7
8
9
io
Cosines
9659?
96585
96577
96570
96562
96555
96547
96540
96532
96524
96517
96509
96502
96494
96486
96479
96471
9646}
96456
96448
96440
'9643 J
96425
96417
96409
96402
9638*
96378
96363
96355
96347
96340
96332
96324
96316
96308
96301
96293
96285
96277
96269
96261
96253
96245
96238
96230
96222
96214
96206
96198
96190
96182
96174
96166
96158
96150
96142
96134
96126
Sines
074
Departures, or
Difference of levels
15 De s-
Latitudes, or Horizontal Dis-
tances for Difference of Levels
O >o O /iO oO "1 O o O ") O
XpOlO^^^COCCCMCMCMr-lrH
0666666666066
OiOHO(MOHOOOOW
WCtOQO(MCiiOCTOC^H
Ciopopopt^t^t^OCpOipipp
6666666666666
00O0GOO0O0O0COO0COO0O0O0GO
NT)tHOOiO(MOO(MCiOnO
(MM<MHHHOOOOOOQ
HQOOCOOOOiOCTON-fHCO
iomhooo^hon^non
oogiopopcpcpt^.i>-i>-t^i^o
10 o 10 10 io o io 10 10 o o 10 o
CNOWfMOOOC^IMOOOO
(NM(M!MCN(NHHHHHOO
^p ^yi ^71 ^"l ^1 ^^ T^l ^1 ^^1 ^1 ^J! T31
N(MN(NOHK5QilaDiMOO
MC^OCNO-ffMHQXOO
obaoobobobooobobobobobaoob
cooococococococccocticococo
N O 10 -f M
OOiCiCiOOOOOGOOOOOQOaO
obobobobobaocofTodoobooobob
CM CM CM CM CM CM CM CM CM CM CM CM CM
oOH05aooiONHM)o
hhOOOOOONOiO^tPM^
CO CC CO CM CM CM CM CM CM CM CM CM CM
iiOCMOO'^O^O'MOO'+i-it^cO
UO>0'*'t"+MWC-l!M(MHH
1OOOOOOOOOOOO
10 I -
>oO *o O **-> O o O oo *o O
M hi M M M CO tj- ^- 10 vrvvo
W /| Departures, or Difference of
^* e8: " Levels
TABLE II.
55
Departures, or
Difference of Levels
1
i
O
1
I
H
P
P4
of
3
B
a
i
P
1 r _ Departures, or Difference of
15 * * Levels
15 o'
i
2
3
4
5
6
7
8
9
IO
ii
12
I?
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
50
5i
52
53
54
55
56
57
58
60
Sines
25882
25910
25966
25994
26022
26050
26078
26107
26l63
2619I
262I9
26247
26275
263O3
26331
26359
26387
264I5
26443
2647I
26499
26528
26556
26584
266l2
2664O
26668
26696
26724
26752
26780
26808
26836
26864
26892
2692O
26948
26976
27OO4
27032
27060
27088
27II6
27144
27I72
27200
27228
27256
27284
27312
27340
27368
27396
27424
27452
27480
27508
27536
27564
Cosines
60'
59
58
56
55
54
53
5*
51
50
49
48
46
45
44
43
42
4i
40
39
38
11
35
34
33
3a
3i
30
29
28
26
25
24
23
22
21
20
I?
3
15
14
13
12
11
10
9
8
I
5
4
3
2
1
074
*b >oo o o 10O >oO >oo
O k-i r}- ^- co co H cJ m ih
11
3s a
w
w
T>
r3
Ph
O
1
rH
M
P
C
r^
CO
O
<
H
CO
P
<1
H
1
3
M
H
of
p
p
H
M
IH
OOfNOO^QO^OO^CONCD
oppr^Cp^lCb-qOprHCN^O
fOOCOQiOHOO^OOfMOO
(M^NO^iONOnOQOO
CT^lOCpt^-pprHCp-^OCpCp
ON
00
lOQOO(N)ONQHWONOH
OHM^lOONOH(MCO0
b-0ppOr7lC^cp^Cpt>-Qpqip
OOOHHHHHHHHHN
O
00
NO^WOQON>OMHONlO
hhhhhOOOOOOOO
rH(>lCp^OCpt>.cpqipprHCN
obcobccao6oobcbdiod)C)
1 IHHr Ir- lr IrHr Ii Ii It iHr 1
vo
CiCOOOC^OO^QOS^CDO^HOO
(MHQOOiOCOHOOON|Oo:
lOCOONqDQOHCTCTW^ip
T Ii Ii Ii ItHt Ii IrHilT-lrHT lr 1
tJ(HOOiO(MCiOMOI>t)*HOO
10
3-
MC5>OHN00OO(M00tJ<OO
lOOONNWOO^OOHNIM
ooH^ipippcpt^cpcpCscsp
OOOOOOOOOOOOH
1 It IHr- Ii IHr IHHr It It IrH
%
CO
^NOJHMiONOiHMiONO
OO^OMNHiOO^OO(MO
NQOQOOOfflOOOHHHCq^
i>^i>t>t>t>cbcbcbcccbdbao
CO
O
il^HCiN'OWHONWJOJ
NOMOOOHHNOfMiOOOH
rH^^C^C^OOCCCO^-H^^O
O
O
OOOHCOHLONODOHOlTJIlO
IOOCOOOOOONNNNN
O
55
*b vr>0 <oO >oO oO >oO *o O
H H rt MMi + >fl o^O
Latitudes, or Hori-
zontal Distances for
Difference of Levels
7-
* Latitudes, or Horizom
X De &' tances for Difference of
alD
Lev
1S-
els
56
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
W
>
w
1
P
g
H
HH
P.
H
B
O
N
3
O
w
m
p
p
H
M
s
h3
|/> _ Latitudes, or Horizontal Dis-
2,0 e8r * tances for Difference of Levels
i6c'
i
2
3
4
5
6
7
8
9
to
ii
12
13
14
15
16
17
18
*9
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
J8
39
40
4*
42
43
44
45
46
47
48
49
50
5i
52
53
54
55
56
57
58
60
Cosines
96126
96118
96110
96102
96094
96086
96078
96070
96062
96054
96046
96037
96029
96021
96013
96005
95997
95989
95980
95972
95964
95956
95948
95940
95931
95923
'959*5
95907
95898
95890
95882
95374
95565
95857
95849
95841
95232
95824
958 1 6
95807
95799
95791
95782
'95774
95765
'95757
95749
95740
95732
95723
95715
95707
95698
95690
95681
95 6 73
95664
95656
95647
95639
95630
Sines
60'
59
58
56
55
54
53
52
5i
50
49
48
46
45
44
43
42
41
40
39
38
36
35
34
33
32
3i
30
29
28
11
25
24
23
22
21
20
19
18
\l
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
073
O o >oO o O >oO o o O
vo V) >o r|- + w to M tf 11 ci
O
to
Ii
3
w
p
A
O
O
3
P
Pn
Ph
h- 1
P
O
w
"P
H
P
M
OCOiOTfWtMOONiOWO
(N X -* O C W * -f Ci iC h N CO
r7ippppcccpi>t^i>-pp
cb cb cb ib 10 10 10 ib ib 1 ib
OOOOOOOOOOOOO
O
ON
CCNO-^GOH^OOHWON
HN^OCOWOOHQO^OO
lO-^^-rtlcpcC^q^CNrHrHT IO
cb 6 6 6 6 c 6 6 6 6 6 6
OOQOOOOOQOOOOOQOOOCOQOQOOO
ON
O
00
HOO^HGOOWOOWOO^
OOKONCCONMONWO
pcccccpt^t-t^pppipipip
cbcbcbcbcbcbcboocbcbcbcb
00
XOHCOiOONCCOJOOHH
ooto?:o^^HooiooN^
CTc^cqq^PTirHrTHppcppcpcp
NNNNNNNNNNNCO
OOOCCCOwOCOOOC
OCMt>.C0a0-**O^O-^O^a0
t^ iC CM Q b- i-O WONiClMON
ppppipipipip-^-rjH-^i^Cp
lOiOiOiOiOiOiOiOiOiOiOiOlO
VO
0"<*(NOOOC^(MC3N10MH
ppppppppopcpcpopqD
00 00 00 CO b- b- b- b- b~ b b> b~ b-
O
OWHOCiOM(MOX'COiO
cbcccccbcbobcccbrocbcfecbcb
cccoct!cocococ?cccosowcoco
O
CO
00MHC5NLOCTON^(MO
CC Ol -h O 00 N C C tJi ^ H O X)
qp CO cp qp b- b- t> b- b b- t> b- p
cbcbcccbcbcccccbcorbcbcbcb
cmcmcn<mcncmcmcmcm<n<ncmcn
to
n
iCNOHOO>OCDGOOH^iOCO
(NhOOOX b- O O 10 Tf CO (N
^1 CT CT W H -H H H H rn H H M
6 ci c 6 6 c d 6 6 6 6 6 6
Pi
MQr}iOCO(MTO^OOHNCO
HOOOOOXCOXNNOO
p p CO ip ip ip ip ip ip ip ip
6000660060006
,1*0 *^0 flO vo O o O o O o O
9
5 :
35 1 H
De
Differ
partures, or
ence of Levels
7r
3 De *' x Levels
nee
TABLE II.
-7
Departures, or
Difference of Levels
GC
fej
1
Ph
hH
P
O
of
H
p
H
<1
Ph
P
1/ _ Departures, or Dillon
16 * P 'Levels
nee of
i6o'
i
2
3
4
5
6
7
8
9
io
ii
12
*3
14
15
16
*7
18
IQ
20
21
22
*3
*4
*5
26
27
28
29
3o
3i
32
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
5o
5i
52
53
54
55
56
57
58
60
Sines
27564
27592
27620
27648
27676
27703
27731
27759
27787
27815
27843
27871
27899
27927
27955
27983
2801 1
28039
28067
28095
28122
28150
28178
28206
28234
28262
28290
28318
28346
28374
28401
28029
28457
28485
28513
28541
28569
28597
28625
28652
28680
28708
28736
28764
28792
28820
28847
28875
28903
28931
28959
28987
29014
29042
29070
29098
29126
29154
291 8 1
29209
29237
Cosines
60'
59
58
3
55
54
53
52
5i
5o
49
48
46
45
44
43
42
4i
40
39
38
36
35
34
33
32
3i
30
29
28
2
25
24
23
22
21
20
19
18
\l
15
14
13
12
11
10
9
8
I
5
4
3
2
1
073
O >flO w-io 10 O 10O ^ O *oo
O
CO
ll
9 S
B o
>
Ph
o
H
Q
fej
H
Ph
&
P
g
c72
o
CY3
i(
P
o
Ph
o
hH
-H
P5
o
w
P
hH
3
H
-+ a nw(M(?iHHOOOXN
OO^CO(MOO^OO(MiOOCO
ipi^X p i^h CM ^ippqopp CM
t^^t^i^cbxxcbxxcbcba>
CMCMCMCMCMCMCMCMCMCMCMCM<M
O
o
O
QOWOIOOOHNINOOWOOM
OWOOOHKOCOHWOOO-t
COOOHO^OOopOOH CO
r t io o b 10 b >b 0666
(M (M <;) N CM w cq q (M (^ CT 01 w
o
ON
O
Hr)iC(X)OHW^ONOOO
3 CO N 00 C O 1 00 Th U3 CD l^ O
OH(NCC^ONajOOH(MO
bq bq cm cm bq bq q b 1 bq 00 cb 00 eb
cm CM CM cm cm CM CM cm CM CM CM 1 CM
o
00
O
10 cq o qo c c: h o o ^ h o o
QCOOCOOOOONNNNCOO
CM p ^ p p t^ X p O rH CM CO ~fH
fflffiOOOOOOOOOOO
Hr-iHHHHrtH(N(N(Mffl(N
o
In
O
VO
OOIMOONHlOCC(NiOO(M
WCTOCNiC-HCTOQ I- iO "*
OCNNCOOOr-KMWCO^iO
cb cb cb cb cb cb t^ b- 1^ i>. r^ b- i^
o
cq - i r-t r- i^H^r-ioooooo
OOiONOCiMON^HN^H
n cc o c 9 h (n n w f t? io o
cbcbcbcb^^4|<^4ti-rj<^4H4]H
o
%
COHNWOLOHO^OOMO>0
NCCKC^OOHNIMOOCCO
OOrHrH CM CO 00 ^^ipippp
o
CO
OHiONOO<Nt|*OCOC3H
O rH O CI CO t^ CM CD '. "' -H X CM b~
CM CO Op CO ~* T* lp p CD CD I- IN
xxxxxxxxxxxxob
o
CCH-S^lMOXO'fCTON
h -t O ". CM lO 00 O CO CD C5 (M -+
US p ip >0 CD O p l_- t;~ W I;- GO X
ib o o o o lo o o o o ib b o
O
COO^OONCOC^OOCMCO't
O fr- X CI rH CM -f CD 00 Ct rH Ol
t> ij* i> b- cp op op co op x x p p
bl CM bl CM 1 CM CM CM CM CM CM CM CM
o
Ii
a*
O >o O w> o ^o O "N O *o O loo
m m n n co co <;* t$- vo u->vo
o
Latitudes, or Hori-
zontal Distances for
Difference of Levels
yo _ Latitudes, or Horizon
O e8 "' tances for Difference oJ
tal Dis-
Levels
oS
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
for
Cosines
95630
95622
95613
95605
95596
'95588
95579
95571
95562
95554
'95545
95536
95528
95519
95510
95502
95493
95485
95476
95467
95459
95450
95441
'95433
95424
95415
95406
95398
95389
95580
95372
95363
95354
'95345
95337
95328
95319
95310
95301
95293
95284
95266
95257
95248
95240
95231
95222
95213
95204
95195
95186
95177
95168
95159
95150
95141
95133
95124
951x5
95106
Sines
4
3
2
1
0-72
Departures, or
Difference of Levels
|W Latitudes, or Horizontal Dis-
JL 4 e6 ' tances for Difference of Levels
O u-io v-io >oO >oO >o O *n O
O
^ fcD
oaoiOfMCuocqoo^oiooo
COOO^OlOHtXMOOCOClOO
b xbicibbibibibicbbioib
O
O
ov
OfMCJiOHNMOOHNMO
90C300QpQpt>NN99p
ocobobooibibib^bibo
OOQOOOQOQOOOGOOOQOOOQOOOOO
O
ON
00
TfOONNWXNNHOOiO
ONwoonaowoio(MQO
66666 6 6666666
b~b-b-b-bi>.b-b-b-b-b-b~i>.
00
O
1^
t 1 <M 1 It Ir-iOOOOb-OO-*
*hqoo(mooj:omon
OOOpcpqONNNOOOOiO
666666 6 66 6 6 66
oooocoooooocooo
OOWNHiOOMNOMNO^
NiCCTONrJ(NCllNT*HOO
moiOTMtNWNHHHHOO
O
HSi0(NOQ0C^HON0
CONNNNNOOOOipOip
b^b^l^b^b^b-b-l>.t-b-b~b-b~
O
E
M
P
O
(NiOQOH-^OOHTfliOQOOCT
OCIHOCOO^WHONCO^
^ffKNCqHHHHHOOOO
cccbc(cb(cbcccb(i)dbcb
cococococococooocococococo
5-
of
B
Ph
co
C0NOO(MHOQ0N10t)(O
cccbcbcbaodbccccb<x}cb
O
CO
O GO'O OtMM^ONOOOOH
(NHOOOOOSOiOiMCOlM
HHHH99OOOOOOO
t It IrHr 1 1 tr 1 r ir lr It It It Ir 1
00>0Or)lTjl85l(M(MHHH
g a
O w->o >oO voO *o O oO u->0
w )-i N e* co co <^- <4- ur> w-,vo
75
^ Departures, or Differe
w e ^' Levels
ace (
)f
TABLE II.
Departures, or
Difference of Levels
17 o'
i
2
3
4
5
6
7
*3
*4
25
26
*7
28
29
JO
3*
32
33
34
35
36
37
|8
39
40
4i
4-
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
5
60
Sines
29237
2926s
29293
29321
29348
29376
29404
29432
29460
29487
295 1 s
29543
29571
29599
29626
29654
29682
29710
29737
29765
29793
29821
29849
29876
29904
29932
29960
29987
30015
30043
30071
30098
30126
30154
30181
30209
30237
30265
30292
30320
30348
30376
30403
30431
30459
30486
30514
30542
30569
30597
30625
30653
30680
30708
30736
30763
30791
30819
30846
30874
30902
Cosines
- 72
Latitudes, or Hori-
zontal Distances for
Difference of Levels
17 Begr.
Departures, or Difference of
Levels
M t-. H O O M N O 't 00 (N O Q
66306a66666666
(MC^OqCMCqCNCOCOCOCOCOCOCO
C0O"^O-*OC000C0a0cMr^.rH
HWOCCr^fJOOOHWOOQH
CO^ipOGOOOrHCOTtllCOOO
OH(M0moON00OOHH
OOh(MWt((ioONODOhN
MiOCDNQOOOHiMCCOON
OWOQOOiMOOfJON-ifH
666660HHHHHHH
<MOO(MOO<M00 01OXr-l
oooooNooioio-^McqtMH
HQOUJCTOOOOON^HOOlO
cpONOOopoOHHqqcpcpri*
j: 10 o 10 h
N(MCOCOO000
Cpt^qOGpOOpprT^rHCviroCp
i^rHp^rHrHrHCqCqCq)OC|Oqe<l
iOOOfMNWOOi<
O O O CO r-H 1
HMiOOCOCiHCO^ONOO
N H lO C M N (M O O i< 00 M N
N(Gpq0O9O9HHHCT(N
aDdooDQodoob6666666
NiOM^OO^WONiOCOO
<* n o o: 13 '/) ^ -t N CI 'M 10 00
opoOOOOOOOOOHHH
i< 00 ono o co n h o d (M o o
Tl CC it StsOQ tN M -tONO
9 9 r. 9090000000
11
IS
V. t<3
II
72
Latitudes, or Horizontal Dis-
Beff ' tances for Difference of Levels
60
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
is^
95106
95097
95088
95079
95070
95061
95052
95042
95033
95024
95015
95006
94997
949S8
'94979
94970
94961
9! .952
9494-1
9493 J
94924
94915
94906
94897
94888
94878
94869
94860
94851
94842
94832
94823
94814
94805
94795
94786
94777
94763
94758
94749
94740
94730
'947"
94712
94702
94693
94684
94674
94665
94656
94646
946 l 7
94627
94618
94599
"99
94580
94571
9,561
94552
Sines
0*71
Departures, or
Diti'. v ;-iee of Levels
10 _ Latitudes, or Horizontal Dis-
AO s ' tances for Difference of Levels
"0 w-10 00 >oO w-10 >0 O oO
vo >o vo^- 'j- to to r) m m
Ij
Sr so
cs a
>
O O --i l^ (N N CO 00 Ti Ci -^ Ci 10
HOOCJOOOaONNOOOip
b * -* rfi -^ -<* tjh ^ <* 4h -^
CiCiCiOiCiCiCiGiCiCiCiCiCi
O
O
ft
Eh
r <
g
K
D
X
H
P
0.
lO I CO CO r lOCiC^COrt<rH05l>.
OkOrHNCOC5"*OOWOOCOC5
O O O f Tj CO CO N CT H H O
kg ib b 10 10 ib ib ib ib ib ib
oowooooooooooooooooooodoo
O
00
iCOCMQCTiOC5<M' ! fNC5Cq
OD ^ 1-1 l^ O O O CM O 10 H N Tji
pooppcscpcpt^r^^pp
cbcooibibiooibibibibibib
w t^ t^ t- t^ t^ t^ b- 1^ t- 1^ t^ t^
00
i*COOOMC(MOQOiO(MOO
N rj* H N * pi O H 00 O H 00
ip lO lO "* ""* T* CO 00 CO CM CM CM rH
'0066660660666
0000000000000
1
ft
O
O
NO
'tNCiiN^NOOl^cDOOOJH
oc3oqoC(mc;n-<*h(X)oco
pppOiCiCiQOcpqoqpt^l^t-
b-t'--t>.0000000000
lOiOiOiOiOiQic^iOiOiOiOOiO
VO
P3
O
KONiotMoonooMoo
iOCOOOOO:OHONi<(MG5N
ipipip^^^^cscpcpcpcMCM
b- l>- t^. t> b~ t^ l> 1>- b- t> l>- 1>- t>
O
P4
1 1
P
O
<1
H
O
N
H
(Nt)*OC0OHC0-)ION00OH
^(MOOOOOCOHCJNiO^N
ppppcicippcccpopooqp
cocococococococQcococococo
O
of
P
H
w
w
***
O
DQ
Q
9
CO
(NCO^HNWOOiMX^OO
COHOQNOiOWMOOOOO
ip ip O -* -* -fT tH "tJH ^ Tf O CO CO
cobobdocb6ocbcbaoa)6o6oob
5 Ol CM CM CM CM (M CM CM CM CM CM CM
O
CO
03
P.
O
ricqco^iOOONOOOO^OO
oi ri 00 n o -t ?: oq oq h
CiGzCiccoooDaooDocccccooao
H
<
h3
HOHN(M00Q0"*O5Oi0
HOOQOQOOOSNOCOiO
ip ip ip tJ< -f -^ << rti tH -^ rti r|H -*
PoPoPPPOJpPPCiCi
O
-3 , v
"i! 1 O lr >O v oO l ^O l oO l oO l ^iO
81*
5 S 00
3^ 1
71
_ Departures, or Differe
L Be ^ Levels
uce <
rf
TABLE II,
51
Departures, or
Difference of Levela
i8o /
i
2
3
4
5
6
7
Latitudes, or Hori-
zontal Distances for
Difference of Levels
1 ft IDe Departures, or Difference of
AO *" Levels
v~> O ^ O o o
o O w-> O o O
O f l^ h iO Oi 00 O O ^ 00 h o
6 rH rH rH rH -^ rH rH CM CM C^ <M <M
cococococococococoo'scocooo
HOOO^MNH'OQCONH
H '.O O 00 O CO O 00 O ^UO N O
&pCiOrHCp^JilOiX>Qp050rHCO
^i^cocbcbobcbobobobocbo
CMCMCMCMCMCMCMCMCMCMCM<MCM
t-H CM CC 0? -H H/i -H JO >C JO lO lO
>o o n oo o h (jq co
cq
un '- .) r uj 'ij r* uu g; u M un pj "t>
NCpOOH^CO'tONCCCJO
-r 1 -h -+ o o ib ib o ib ib >b o so
CM CM CM CM CM C M CM CM CM CM CM CM CM
HOOOHOOOHOOilHNCOO
CO l>. 00 05 O rH CM CO ^Ji lO O CO t^
r^rHrHr^tMCMCMCMCM^CMiOMCM
cmcmcmcmcmcmcmcmcmcmcmcmcm
H^NOC0iO00H^Q(M-il
^fNOONLO^NOOO'COn
OONNOOOOHCMMCOri*iO
cbcobcbobobdociGiCiciicfiOo
HOO00NOO-*f0HO00
O 'O io o o o O O ffl CO
H O H 3 Ol N (M N CT 00 ?: 00 W
O -I t>. CM 'JO CO C5 T O O H CO CM
^ Td O Q CD O N 00 CO a 05 o
CMCMCMC^1(MCMCMCMCMCMCMCMC0
0(M000000(MCOt)(ON
fc>. r I lO C CO t~- rH TO O t^ GO CM CO
CM 00 00 CO -* Tfi <p O Cp 9 CO N N
o66CiOOOOCiQOCJO
OCOOCOHCCO-fHOOiH
OOOCOOQ-i'tNO'NiOOOH
rH CM CM CM CM Op CO CO -H t* -*i -* ip
o Ttno 0>1 iO C :0 N h -ff 00 (M o
O O < SO -j< uj N 00 O H ?i -t O
o h h h -h -1 rn .- (M qq cq a
coobwcbooobcbwcococoboob
vr> o l oO "^ O u-i O ^ O o O
11 1-1 N N c*i co sj- *$- io w-)\o
71
Latitudes, or Horizontal Dis-
es * tances for Difference of Levels
62
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
19 o'
Cosines
'94552
94542
"945 J 3
94523
945H
94504
94495
94485
94476
94466
94457
94447
94438
94428
94418
94409
94399
94390
94380
943JO
94361
94351
9+342
94332
94322
94313
94303
94293
94284
94274
04264
94254
94245
94235
94225
94215
94206
94196
94186
94176
94167
94157
94147
94137
94127
941 18
94108
94098
94088
94078
94068
94058
94049
94039
94029
94019
94009
93999
93989
93979
93969
Sines
9
8
I
5
4
3
2
I
0*70
Departures, or
Difference of Levels
19 es.
Latitudes, or Horizontal Dis-
tances for Difference of Levels
voo ^ O ^ O oO *o O >oO
10 >o ^ ^ tn m r m w
(MrJHt^OrHCO^iOl^aoaO
iOO"OOOHOHCOHOHO
OOC3QCiOQOO05OO
OOOOOOOCONNNOOiO
3
aococoaocoaoaoaoooaoaocoao
ff)CDNQOH(M^-fT)tioiO
^OOCTQO>OHNC?OiOHb.
OnOOC5i3ON00W00
QOOWOOOHCOIOHQO^HN
HH^OOOOOOcpopOON
6 6 6 6 6 6 ib 10 >b >b >b b ib
ooooooooooococo
NNOCpOOipipip^^-iiq:
6 6 6 6 6
iOiOOiOQ
lOiOiOiOOOOiO
<E>qaO"fo<Mt^coo^o-<tf
MOiMOODCMOOOOKO*
CTWCT^HHHHOOOOO
H5<)CO-|<^iOOONNNQOQO
QOOONNNNNCDCOOOOiO
OHNcoa)"fO"t*oooo-i
O W (M O O N O C W (M O C5
CO CO CO CO CO (M CM C-l Ol (N <^1 <M rH
HOOOONCiOi^OlHOQ
OC^'QOqOQpOpCpOOaOQOQOGOt^
6d6oco6occx)6dcc6c:cccoccoo
OOChOhOHN(MN(NN
lO -0 -* -+ CO CO <M <M 11 . O O
^i-f^^^^-^^-^^^^CO
00Ci0
70
Beg.
Departures, or Difference of
Levels
TABLE II.
Departures, or
Difference of Levels
1 9 o'
i
2
3
4
5
6
7
8
9
io
14
IS
16
17
1 8
19
2.0
21
22
25
*4
*5
26
27
28
29
30
3i
32
3 3
34
35
36
37
J 8
39
40
4i
42
43
44
45
47
4^
49
50
5i
52
53
54
55
56
57
5*
s
Sines
3^557
32584
32612
32639
32667
32694
32722
32749
32777
32804
32832
32859
32887
32914
32942
32969
32996
33024
33051
33079
33106
33134
33161
33189
33216
33243
33271
33298
33326
33353
3338I
33408
33435
33463
33490
33518
33545
33573
33600
33627
33655
33682
33709
"33737
33764
3379 2
33819
33846
33874
33901
33928
33956
33983
3401 1
34038
34065
34093
34120
34147
34175
34202
Cosines
4
3
2
I
0*70
Latitudes, or Hori-
zontal Distances for ,
Difference of Levels I
19 e*.
Departures, or Difference of
Levels
10O o O w-10 >oO
u-> u-> -^ <$- to m N N
t^^<MCSOC0i-HG0i0<M00i0 33
lOOMCOOiDHiOOlOO
iOOOOOH^WpONCi9^
in <m c*! cm eo 5 b cb 3 3 V3U 3N
cococococococooocococococo
HiOQO(NOC5COOO(MOaC3
OOmNOHitOQOHCOOOO
66606366666666
lOiOiOiOiOiO-^^-tlWCOiMiM
OH<NWfU5NqDQ9HNM
6 6 6 6 6 6 6 6 6 n n n n
CT (N W a (N (M CT CM (M (M N (N (M
OOfMOO^OCOfNOOTjOOH
OOOQONNNOiOiO3^^
NOOOOHCTOO^OONqDO
c?^rooc^(MHONioo:(M
lpOCNOOOOHHiMWTfip
6666666666666
HHHHHr-((M(M(NN(M(M(N
N -t r- 00 lO (M C O (M C5 O M O
(MM^^iipOONqOCOQOH
OOCCOCOOCCCNN
(MNWQC^SOOOHNCMQO
66666666666600
NQOOHiMCO^OONQOOH
N&OOOOOCOOOOHHWCT
6666666666666
HOO-tHOOHC0OWQ
6666666666660
ol 35 c* * op op op 55 op op op -ft t?
66666666cocooococo
"b *oo o o o o >oo >jo o
70
Latitudes, or Horizontal Dis-
Degr ' tances for Difference of Levels
64
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
CO
P
>
H
tf
H
E
P
8
qq
W
O
H
CO
t 1
ft
i
s
w
co
P
P
H
>i
H
<
rt/\ _ Latitudes, or Horizontal Dis-
U e&< tances for Difference of Levels
20C/
i
2
3
4
5
6
7
8
9
IO
II
12
13
14
15
16
7
18
19
20
21
22
23
24
25
26
27
28
2;
33
3'
3i
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
5
5i
52
53
54
55
56
57
58
59
60
Cosines
93969
'93959
93949
93939
93929
93919
93909
93899
93889
93879
93869
93859
93849
93839
93829
93819
93809
93799
93789
93779
93769
93759
93748
93738
93728
93718
93708
93698
93688
93677
93667
93657
;936+7
93626
93616
93606
93596
93585
"93575
93565
93555
93544
93534
935^4
93513
93503
93493
93483
93472
93462
"9345*
93441
93431
93420
93410
93400
9?389
93379
73368
93358
60'
59
58
%
55
54
S3
52
5i
50
49
48
46
45
44
43
42
4i
40,
39
U
35
34
33
32
3i
30
29
28
11
25
24
23
22
21
20
II
\l
15
14
13
12
11
10
9
8
i
5
4
3
2
0*69
O >j->0 >oO 100 oO oo o O
NO whot)- ^ W M N rJ m w
ON
NO
|1|
if
CO
"H-
Ph
SB
&H
B
p
aT
1
p
OOQOfflQONOWWCTOO)
O r-H O r-i O i-H O 1 1 O rH O rH I
cb cb cb cb 6 cb cb 00 cb cb cb cb cb
C3QC50iC3C5QOC5CiC5O
O
O
ON
ON
NN(MN(MOO"*00(MOC5(M
MM 00 OS T)l O O O O r-H Cp CM
I O -H/i *# CO CO CO (N(MHH09
'^ ^H -^rf -^-H '-+< -^H "V< H --H 1< H --H -^H
XXXXXXXXXXXXX
O
00
IO lO IO IO IO i* -* po (M O O 00 O
n w c; h n r: ci 10 'h n ^i x
H m O O O Ci O GO 00 GO N N O
t>. !>. t^ t>- t>- b- l~- b- I>i b- t>. l>. l>-
O
OO
oocooocooo^ot^ iioownh
t -* b~ CO O CD CO O? tO CM TO O
b- b- t> 5 -+ ^ - co op
b to 1.0 iq o b b b 6 >b b b
ooooooooooo
O
no
HHHHHHCOOOONOlO
00O:iOO CO O N O t h H
CO Cp CO CM S I CM Ol 1 1 t rH O O
6666636660666
O
"* -M -* G5 CO 00 CM 1
00 10 CO * o CO O X O CO O '0
999 00 x x x is t^. t^ i -
6660666666660
O
10
X 00 X X X b- r- O O 10 O -H CO
X O ~t< Ol O X O "* CM O X O -H
b~t^b-b-b-b~b-i^b-b~b~t^t^
cococococococococococococo
5-
O
CO
to
HOHOHIOOLOO^O^N
ot^o^co 10x0 cocqo
rH rH rH rH rH rH rH O
X X X X X X X X X X X X X
CM CM CM CM CM CM CM ON CM CM CM CM CM
^t^-H-H-H^'HCCjCCCOCOCMCMCM
CQ0NOiOi<ni(NHOCiXN
t> t> b- l- t^ b~ b- b- b~ t-
X X X X X X X X X X X X X
N(MNCMN(NN(MOHOHO
O X X l^ l^- O O to -t -* CO
cp co cp cp cp cp cp cc cp cp co ep
66 6 66666666 6 6
O
12 * i <*
8 J o
Sines
1
-^^ "n,.-^.-.*-,-,,., i^tf" ,
,.
Departures, or
Difference of Levels
6S
!><e- ^=F auUl ^ Ui silicic.
' Deff * Levels
TABLE II.
65
Departures, or
Difference of Levels
QQ
!>
W
O
w
1
P
O
w
H
P
OA jj e _ Departures, or Difference of
&" Levels
200'
I
z
3
4
5
6
7
8
9
IO
ii
12
13
14
15
16
17
18
9
20
21
22
*3
24
25
26
27
28
29
30
3*
3*
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
50
5i
52
53
54
55
56
57
5^
g
Sines
34202
34229
34256
34284
343"
34339
34366
'34393
34421
34448
"34475
34502
3453o
34557
34584
34612
34639
34666
34694
34721
34748
'34775
34803
34830
34857
34884
34912
34939
34966
34993
35021
35048
35075
35102
35130
35157
35184
35211
35239
35Z&6
35293
35320
35347
35375
35402
35429
35456
35483
355"
35538
35565
35592
35619
35647
35674
35701
35728
35755
35702
35810
35837
Cosines
6V
59
58
?
55
54
53
52
5i
50
49
48
46
45
44
43
42
4i
40
39
38
11
35
34
33
32
3i
30
29
28
26
25
24
23
22
21
20
19
18
\l
J 5
13
12
11
10
9
8
I
5
4
3
2
1
o*6g
O 00 o O 100 o O >oO 100
no >o>o + ^wwt) M M M
O
ON
NO
u
Is
OQ
P
P
>
Ph
O
A
O
3
P
P
P
1 1
p
P
to
P
O
H
W
3
H
fe
O
3
O
HH
HH
M
of
W
P
E
H
t (
%
P
(N055(NQ0i'HS05OU3HN
CM CO Tj< p b. GO O r^l CM "* lO b- GO
-* -^ ** ** -* -^ b 10 10 ib
cocococooocococooocooooooo
(mio-xiomcoh^oohj:
00o(moncjh-)<oq0o0o
O I> p rH CM CO Ip p b- GO O r^H CM
otcocococococococococoooco
ON
00
ONQOQOdOHWM-tiiOOO
WTt<ippb-pprH(yiCpTt<ipp
b-b-b-b-b~b-cbcbcbcoGbaDao
CMCMCMCMCMCMCMCMCMCMCMCMCM
O
00
HNMOCtQ^OLOOOHO
^MWiMlMHHHOOQCiOO
C5OH(MMtHi0NQ000OO
cb^-^^^^^'^-^-i^'^ib
CMCMCMCMCMCMCMCMCMCMCMCMCM
O
NO
rHOOlOb-COi ICM'+Ob-Ci'-'CM
(moooo-cchcmocoimo
ipcpONOOCOOH^iOp^jp
6 6 6 6 6 P rH rH rH rH rH rH
CMCMCMCMCMCMCMCMCMCMCMCMCM
O
NO
HCJQOOTHiMOOOO'itiNOCO
O O 05 O 1^ *r H N "^ H OO IO rH
J>rH rH CM CO 00 "+ p IO b. b- GO
' b- b- b- b- b- b- b. b- b- b- b- b- b.
O
i
t 1 IO O O O <+ X CO b- CM O IO
CO C2 "H O O i-h b CM GO CO
fp n n co pojoohhwwo:
'cbcbcbcbobcbH^PPP-r*H/iH/i
O
to
H(M(M5;-i(ioONXOOOH
O -+ GO 0-1 OO^M CM COHO
CM CO CO CO -ft -* O iO O O N N
0666666666666
O
CO
OCOiOWOS-flHQO^OS
t C r. 'M O N O O H rti O
aj-iOGO^QooooOHHrt
666666t>bi>bbbb
CM CO ** t> GO O 1 CM ^ IO b- 00
H/i t$ -7^ -t -* -* ip ip ip ip ip ip ip
obcbcbcbcbcbobcbcbcbobcbcb
O
II
"0 o o ^0 w-io <oo -o
_, M cj n m to ^r ^ >o wi\o
O
M
Latit
SEonta
Differ
udes, or Hori-
Distances for
enee of Levels 1
61
J Latitudes, or Horizon
/ e6 '* tances for Difference oj
tall
f Le
)is-
\rels
66
TABLE II.
Latitudes, or Hori-
zontal Distances for j
Difference of Levels
W
>
a
ft
@
E
&
p
ph
m
O
H
m
P
O
S3
1 1
O
w
of
Q
p
H
1 (
H
i-4
01 i> Latitudes, or Horizontal Dis-
tQL e &' tances for Difference of Levels
21 o'
i
2
3
4
5
6
7
8
9
IO
ii
12
J
14
15
16
*7
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
3J5
39
40
41
42
43
44
45
46
47
48
49
So
5i
52
53
54
55
56
57
58
60
Cosines
93358
"93347
93337
93327
93316
93306
93295
93285
93274
93264
93253
93243
93232
93222
9321 1
93201
93190
93180
93169
93158
93148
93137
93127
93 1 16
93106
93095
93084
93074
93063
93052
93042
93031
93020
93010
92999
92988
92978
92967
92956
92945
92935
92924
92913
92902
92892
92881
92870
92859
92849
92838
92827
92816
92805
92794
92784
92773
92762
92751
92740
92729
92718
Sines
60'
59
58
11
55
54
53
52
5i
50
49
48
46
45
44
43
42
4i
40
39
38
36
35
34
33
32
31
3
29
28
11
25
24
23
22
21
20
19
18
\l
15
12
10
9
8
I
5
4
3
2
o-68
O "NO "NO O "NO "NO "NO
VO "OlO^^" MtOH tS M M
O
OO
VO
ii
Eg Eb
a 5
P
O
O
S
A
O
of
a
i
M
OOOWHOOIOIMOOWHNCOCO
lOOiaO^O-^QOCCOOfMNH
WWWCqHOOOQQpcpNN
O
ON
cqioooHejiooooHco^coo
(Mt^<MGOC0G0CO00^HO5^C5^
QOQOOOOOOOOOOOOOGOOOOOOOOO
ON
O
00
coiocqrHooco^oop^ocqoo^
QO^OOHNMO^OOHN
O
00
lOHN'^OOC'OiOHN'iO
^W(^G^q<lrHi7HpcppCiC5Ci
VO
H CO iO (M 00 iO Ol O CT OJ CO M
OOOOGOGpcONNNOOO
crbibobbbibibibb>o>bib
O
"N
OMOO^NH^NOMOOi
COiO(MONT)*(MOO"tHOOiO
ppppopo^^^^opoo
oo66o66cb6666
O
COfMHOOOOMO^NHCJN
T(iiqOOOiOWHC3NLO?3000
W9eOWWN(? ; lHHHHHO
oococococococococooscococo
I
O
CN
O N O -* Ol H O * W H
pcppppppopGpcpcpqpqp
O
I CqHHOOOQOOONOOiO^
NOO^WHOOOONOLOrtl
obobcbcbcbdbcc(cca)cbdb
O
OHOOiOQ^OC5QOWN(M
MW^KMHOOOOOOCONN
O
"8 a
11
1"
"O "NO "NO "NO "NO "NO "NO
IH M M t* M W^'nT <0 "NVO
Tk TVtt 1
Departures, or
Difference of Levels
6
nee
UI
TABLE II.
W
Dfl
partures
or
Difference of Levels
Sines
11 o'
35837
60'
I
3S864
59
%
35891
58
3
35918
S l
4
35945
56
5
35972
55
6
36000
54
7
36027
53
8
36054
52
9
36081
5i
IO
36108
5o
ii
36135
49
12
36162
48
J
36190
4 7
M
36217
46
15
36244
45
16
36271
44
17
36298
43
18
36325
42
19
36352
4i
20
36379
40
21
36406
39
22
36433
38
23
36461
37
24
36488
36
25
36515
35
26
36542
34
27
36569
33
28
36596
32
29
36623
3i
30
36650
30
31
36677
29
32
36704
28
33
36731
27
34
36758
26
35
36785
25
36
36812
24
37
36839
23
38
36866
22
39
36894 .
.21
40
36921
20 '
41
36948
19
42
36975
18
43
37002
l l
44
37029
l6
45
37056
15
46
37083
14
47
37110
1.3
48
37137
12
49
37*64
11
50
37191
10
5i
37218
9
52
37245
8
53
37272
7
54
37299
6
55
37326
5
56
37353
4
57
37380
3
5
37407
2
59
37434
1
60
37461
Cosines
o-68
Latit
udes, or Hori-
zonta
1 Distances for
Diffei
ence of I
revels
ft"! Departures, or Difference of
Zl Be * Levels
3 J
O w-io "lO u->0 oO
ioiotJ-^mwO tf
-o O O
NOlOOIOiOOLOHOHOO
CO t^ O "*l^ r-uo 00 <N 'OOCTffi
(BOHNCOiOONOOHM^
cococococococococococococo
IONCH-JCCOO
^cp-^cpb-qocirTHC^cp-^iot^
(>i cq ch <?q cq oi 6\ cb cb cb cb cb cb
cococococococococococococo
OQOMOMCTOXOiOMOQO
ONCOOOH(M^io:-+ioOO
Cpt^GpOSrHCNCp^lOCDt^OOOS
(X)(i)d)(666666666
OHOHiOOi-OO^OCOQO(M
9hnwtj*9 9N(qoh(n
ib*bob*b>bibxbibbcbcbcb
oooo^ciooNor.HON
ipOCpt^GOOCpprH^cpcp-^l
rHrHrHrHrHrHrH'fl'fq^OqCqcq
QOOT)f(MONiOOOQOOMO
H 00 D (M CI O CM 35 0-1 OS CD CO
OgSOr-lrHGNCOCp^ipipCDt*-
^t^GbaDGbcbobabcbabcbabcb
LOOMNIMOO^X'MOOtP
COOO^ClOOOri-O^NMQO
10 O N H O O M N H U5 o m
NNcpcoaqioooHHHCN
OOOOOOOrHr^rHrHrHrH
NM<CTCiOONtj(HQ0>O(M
t>t-b-l>J>t^t-~b-t^t^l>t>t^
>* b~ 1 1 * 00 1 1
O GO GN CD OS CO CO
COOS' 1 (M OO LO O N O O r- I CO -<tf
1-0 p CD CD CD CD CD CD CD t^ t- t>- t>.
cbcbcbcbcbcbcbcbcbcbcbcbcb
68
Latitudes, or Horizontal Dis-
" tances for Difference of Levels
68
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
22 o'
I
Cosines
92718
92707
92697
92686
' 92 fe 5
92664
92653
92642
92631
92620
92609
92598
92587
92576
92565
9*554
92543
92532
92521
92510
92499
92488
92466
9*455
"9 2 443
92432
92421
92410
9-399
92388
92377
92366
92354
92343
92332
92321
92310
92299
92287
92276
92265
92254
92243
92231
92220
92209
92198
92186
92175
92164
92152
92141
92130
921 18
92107
92096
92085
92073
92062
92050
Sines
0-67
Departures, or
Difference of Levels
22 *.
Latitudes, or Horizontal Dis-
tances for Difference of Levels
I J
O *o O 00 *00 o O >oO vr>o
X^CS^OCOQOiMOO^NO
HOOiOO^XXNIMOOiO
t>9ipT)i^c;c:(N!MHHO
^ ^i ii ^1 (^ <?q cq c?q <jq <?q <?q cq cq
C5 C O Q Q Ci 05 CS C5 O Oi O)
<~20COC:CSOOOSCOaOOOOiO
-^opcC^^rHrrHppcpCiGpqp
oooooooooooooococoooooooo
^HNMO-^OiOHOHOO
N0000'*C5lO-iCC'lNWXT)i
t^t^bb-b~bi>.i>i>.t>.x>.b-i>.
M tO O 00 CJ O WW r *f 10 10 >0
OCO(MQO^HN05iOHSW
O50pqpb-b-t^0^0i0prti"^
COCOOCDOOCOOCDOCOOO
Oip90'r|('^Tl*wepW<N(N!N
10 10 o 10 b ib b b ib o ib ib
lOiOiOOiCiOiOiOiOiOOiOiO
O(N^NCiTttO00O(MWiO
0ON"f(NC5OWH000(N
WMWINfflCTHHriHpOO
<pcboo:b:bcbcbcoo<x>cb
TJi ^^ ^7^ ^1 Tji tji '^i ^p ^^ T^ "^i "^H ^^
N N N N N O C C3 O O CO
cooococococococococococcco
5acOOOMCOOWOO(M5
HNOOOIOTOHOQOO^MH
Gpt>b-b-i>-i^b,t^cppppcp
c^^c^c^c>qcqcrqc<i<?qc^c<icqc<i
^JJ CO CM
'QOOCDOtHWHO
rnv*NCOiO^M(Mn
ipipiOlOip^^tlT^'^^Tt*'*'^
cboocbcocbcbcccbaocaodo
ioo^oooinoH>o
. 10 10 ~t ?? cc 01 oq h h o
67
3>egr.
Departures, or Difference of
Levels
TABLE II.
69
Departures, or
Difference of Levels
Sines
1746i
37488
37SI5
37542
37568
37595
37622
37649
37676
3773
37730
37757
37784
37811
37838
37865
37892
37919
37946
37972
"37999
38026
38053
38080
38107
38134
38161
38188
38215
38241
38268
38295
38322
38349
38376
38403
38429
38456
38483
38510
38537
38564
38591
38617
38644
3867!
38725
38752
38778
38805
38832
38859
38886
38912
38939
38966
38993
39019
39046
39073
Cosines
1
0*67
Latitudes, or Hori-
zontal Distances for
Di (Terence of Levels
3
I
O
o
1
I
c
22
I>eg-.
Departures, or Difference of
Levels
Ci
c c: w w a ?: o o t- o H t-.
fi o n 00 9 H (>) f o o O) s; p
i^ 1^ t> r^- t^ 00 do 00 to 00 to cb ch>
cooocooococooooococoroooco
lOONQOOOHtMM'fOiOO
H M O N ^ 'M -t O TO O O) -t C
N CO G 9 H M tJ ip p X) G O H
M M M ~ "* --t 1 -h "* -f T* "-f >0 Ifi
oooococoaooococococooocooo
OCO'^NOMONON'fHa)
CNQ0OOOHi?1(NMt)i^O
GOHIM^iOONCOOOHCM
(NNHiOO^COIMOO'f NH
(M h h O O O 00 CO N N O IO O
G^OO^iOpcpi^cppprHC-lcp
ONQ0OOOH(M(MC0Mi
NiOMHOOOO^iMOCCO^
^lOCpb-Gpcp05prHG>lC>10t'^
cf i ci cn cf 1 d^ cn dq do do do M do do
<^4<N<^<^ClCNCN<?qCNC^C>1C^CN
USNON
wON
NNCp9 99H(NCNC0'*^ip
^CO<NCOO^b-'-liOCO'7qOOi
CO M G ^ O tO O O h O (M N C- 1
QOOHCT(MCpcpT)<'^iCip9
4h o *q 10 ib ib 10 10 10 ib >b ib ib
OOOOOOOOH^HHC'lN
NHiOO^CO(MOO"*OOCN
CI M 'i' "i* ^ iO ! O O C t>
t>|>t^.l>.l>.l>t>l>t>i>.t>t^t>
555N00OH0HI5OXOO
^j^t^t^oocooocpcpcpcpcpcp
dododododododododododododo
67
Latitudes, or Horizontal Dis-
1>eer * tances for Difference of Levels
70
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
LATITUDES, OR HORIZONTAL DISTANCES FOR DIFFERENCE OF LEVELS
QO Beff Latitudes, or Horizontal Dis-
^O *' tances for Difference of Levels
23 0'
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
*9
20
21
22
2.3
24
25
26
27
28
29
30
3i
32
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
50
5i
52.
53
54
55
56
57
58
s
Cosines
92050
92039
92028
92016
92005
91994
91982
91971
91959
91948
91936
91925
91913
91902
91 891
91879
91868
91856
91845
91833
91822
91810
91799
91787
91775
91764
91752
91 741
91729
91718
91706
91694
91683
9,671
91660
91648
91636
91625
91613
91601
91590
' 915 ll
91566
"9*554
91543
9I53I
91519
91508
91496
91484
91472
91461
91449
9H37
91425
91414
91402
91390
' 9Jl7 I
91366
'9*355
Sines
60'
59
58
u
55
54
53
52
5i
5
49
48
46
45
44
43
42
4i
40
39
38
11
35
34
33
32
3i
30
29
28
26
25
24
23
22
21
20
*9
18
16
15
14
13
12
11
10
9
8
i
S
4
3
2
1
o-66
O oo 00 >oo >oO ^o voO
vo vo 10 ^- ^ co co N tf M M
O
VO
VO
11
GO
e
h?
O
1
1 1
O
tzT
3
p
g
W
P
OCOOOtN^OOOOHfN^^
O CJ Of l>- (71 OO^CiCONHO
OOOOOCCNNOipOf fM
(^rHrHr^r^rHrHrHrHrHrHrHrH
OOOOOOOOOOOOO
OS
Wi*(MHOQOOHCOLOCOO
c<i cq 6 1 bq <N bq bi cfq bq bq cq bq bq
OOOOQOGOOOGOGOGOQOOOOOOOOO
00
o-^OMooHioannioooHM
pipipip^-^cpc^cqqqrHrHp
i>i>-t^i>.i>-t^t^i>t^i>.i>.i>.t^
00
000006060000
vo
CO O O (M 35 O (M GO O H 00 r)( H
(^1^^11000000000000
ib b 10 ib 10 10 rt< rj< -* -* ^ -^
lOiOiOiOiOiOOiOlOiOiOlOiO
VO
(MOOMhqoiONOOWON
OCiOOOCpCOCpNNNNCp
cbibibibibibibibibibibibib
5-
ON^NQCD(MC5O(N05CD(M
(NOMONOOOOCOHQOOt)!
ODNNNNNCpipOcpipipip
006666066666
cococococococococococococo
3.
CO
O00Ht)<NO(Mt)(NC5(M^O
piOOipipipiOTtl^^"^-^'*
cqcqc<i<7q(?qoqoqcq(M(M<?q(M<?q
CO
OC1NOtHC5HOQ0CD'^00H
HOOONOiO^COHOOCOS
t(obccbcbob<c<aooooo
M
lOO^OOWCOHUJQWNHlO
OOOOOOONNOiOiO^-^M
C^rHrHr^HrHrHrHrHrHr^HrHrHrH
O
If
HI 11 C< H CO CO ^ *$- W"> ovo
CO
6<
r> ^ Departures, or Differe
B Be *' Levels
Departures, or
Difference of Levels
nee
ji
TABLE II.
71
l teparl ores, or
Difference of Levels
1
1
O
g
O
n
1
r
t 1
P
O
w
M
P
H
Q
OQ Dee. departures, or Difference of
^^ ' Levels
23 o'
I
2
3
4
5
6
7
8
9
10
ii
12
13
14
5
16
17
18
*9
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
i 40
4i
42
43
44
45
46
47
48
49
50
5i
52
53
54
55
56
57
58
60
Sines
39073
39100
39127
39153
39180
39207
39234
39260
39287
393H
39341
39367
39394
39421
39448
39474
39501
39528
39555
39581
39608
39635
39661
39688
39715
'3974 1
39768
39795
39821
39848
39875
39902
39928
39955
39982
40008
40035
40062
40088
401 15
40141
40168
40195
40221
40248
40275
40301
40328
40354
40381
40408
40434
40461
40488
40514
40541
40567
40594
40620
40647
40674
Cosines
6d
59
58
U
55
54
53
52
5i
50
49
48
46
45
44
43
42
4i
40
39
38
36
35
34
33
32
3i
30
29
28
26
25
24
23
22
21
20
:?
15
13
12
11
10
9
8
I
5
4
3
2
o-66
'o o O >00 v/-, 10O *00 100
vo oo + ^- MMM c M 11
vo
vo
GO
ft
O
W
Ph
g
O
Ph
<tt
H
O
<
(72
s
fc
O
2
1 1
O
w
H
P
E
H
HH
H
39-073
39-207
39-341
39-474
39-608
39-741
39-875
40-008
40-141
40-275
40-408
40-541
40-674
ON
OOOOtN^OQOOiM^OOOO
rHCN^Opt^GOprHtMOO^O
cocococococococococooococo
00
O O b- 1>- 00 O O Q r-i <M <M 53 55
1 Ii Ii lrHrHrHr^-IGN(fqcq(l<^<jq
cooocococococococococococo
OO
rHiSGOCqOCDCqCOOCMlOOOrH
Cp^ippt>GpCipprH^CO^
vo
^(NOOOOi((MOOOO^(MO
cocbcbcbcbcbcb^H/iHH^HH^
(N(N(M!M(MN^iMN(M(M(Mjq
O
VO
NWON^HNTflHNrfON
MONCOONCOONMONCO
ippcpt^cpcpppOrHcqcqcp
6666066666666
1 ir-Hr-li lr Ii Ii ICq<?q(M<yqC^C<l
O
S-
OWOOWNOMNOOOO
(MOOWOO^CJiOOiOHOHO
Cpcpt^b-OOGpqipprHrHlMCN
ioibibibibib>o66cb666
O
to
(M cq cm cq cq c?q cq co cq cq cq cq cq
(MOO^CCMOO^OONOO
NNcpqDOpQOOOOHHN
rHrHrHrHrHrHrHCqC?q(fqcq(fqC<|
1 Ii Ip- IrHi Ii 1 r- Ii 1 H H 1- irHi 1
O
c">
O
10 1 1 00 10 cq go *o ci oo *o cq oo o
HTficouHiNOfMiOdOOW
QpcpoDcpOCJOOOOOHH
t>i>t>t^t>t>t>cbobcbobobcb
O
t^i 1 "f l>- 1 1 * !>. 1 lT)INr ! "^ b-
O (N M "^ O N 00 O H !M -t ).? C
OiOOOOOOOOOOOO
% 22
a s
a
EH
"0 "lO *oo *> o ^o >oO o O
m M ti N ci f<l ^ ^J- n-> ir>vo
CO
Latitudes, or Hori-
zontal Distances for
Difference of Levels |
/ /> Latitudes, or Horizontal Dis-
00 eff * tances for Difference of Levels
72
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
24^0'
1
2
I
4
5
6
7
Cosines
o^SS
91343
91331
9T319
91307
91295
91283
91271
91260
91248
91236
91224
91212
91200
91 1 88
91 1 76
91 164
91 1 52
91 140
91 128
91 1 16
91 104
91092
91080
91068
91056
91044
91032
91020
91008
90996
90984
90972
90960
90948
90936
90924
90911
90899
90887
90875
90863
90851
90839
90826
90814
90802
90790
90778
90765
90753
90741
90729
90717
90704
90692
90680
90668
90655
90643
90631
Sines
0*65
Departures, or
Difference of Levels
24
Latitudes, or Horizontal Dis-
s ' tances for Difference of Levels
O v o O *o O
C Q N H O C5 W N H C C CO
c: Oi CT H H O O G OO CO N O CD
c: c oi 00 *i< o o cq n c: co w 00
i-H O rH o O IO O + GO cc 1-- cm o
(Ol ^-1 rH p O 05 CO CC b- t> CD CO IO
CCCOGOCCaOCOCCCCCCaOCOCOCO
KOCHWONOOHJI^KJ
OOcjQO^G^O-tO^OiOO
c c c: G Cp CC N N n o 9 LC p
cb cc <fi sq cq cq cq cm cm cq cm cm cm
b- b- b- b~ b~ b- b- b- b~ b, t> b- t^
CO O if! W h C N iO N C N "^ Ol
3 <M 00-55 Oi o n 51 qo i<
p p cp cp b- b- p p p p 10 ^ rtt
CO CO CO CO CO CO CO ^ CO CO CO CO CO
cocccooocccoo
NN(NOO"^C0 01OCC(N>CQ0
b-b-C0COC0a0a0CCI^b~CDCD>O
N^HOOIOOIQOMON^H
CO ". pipipiO"^^-^H<cpcpcp
ib b us i!c >"c b >b ib ic 10 10 b
(MQO^OOfMOO^OOHNIM
id O "+ "+ -* -* CO CO CO CO cp m CM
cbcbcbcbcbcbcbcbcbcbocbcb
cococococooocococococococo
OOOHMIONOHCTtIIOOOO
OCCNCMHGCOO^ Oi'O CO
Tf op cp cp cp cp cm (Oi cq cm cm cm rH
b-b-b-b-b-b-b^b^b-b^b-b-b-
gmcmcmcmcmcmgmcncmgmcmgmgm
HOMOCOHONIOMHQOO
b-c-HcocMi<oioob-oiococq
(T^CMCMCMCMCMrHrHrHrHr^rHrH
cccccbcbcbcbcbcbcbcccbcbob
iOO-fOOCTCO^NHlOO
CQINNHHOOOOOKNOCD
, 7 H 'T l 'T lrHrHr r ( 'T lc ? <: ? < ? >< ? >< ? < ?
G5C5C5C5C5G5G5C505G5C505C5
65
_ Departures, or Difference of
Beff - Levels
TABLE II.
73
Departures, or
Difference of Levels
Sines
40674
40700
40727
4075?
40780
40806
408 j j
40860
40886
40913
40939
40966
40992
41019
41045
41072
41098
41125
41151
4 n 7 8
41204
41 2 j 1
41257
41284
41 3 10
41 J 37
41363
41390
41416
41443
41469
41496
41522
41549
41575
41602
41628
41654
41 68 1
41707
41734
41760
41787
4ii3
41840
41866
41892
41919
41945
41971
41998
42024
42051
42077
42104
42130
42156
42183
42209
42235
41262
Cosines
0-651
Latitudes, or Hori-
zontal Distances for
Difference of Levels
P
C%A t Departures, or Difference of
i uegr. Levels
oo >o O oO <oO k~>0 *oO
"O^^- + MMN H II l-l
O
CT "* CD op
. 05 CO CO
b 00 05 1 I 0\
OQOHHHHHHHHfflN
COCDiOiO^WiNHOOOOSO
cpt^qpcppcNcp^ipcp^C5cp
cbcbcbcbt^t^i^t^b-t^t^b-cb
O3COCOC0COCOCOC0C0C0COC0CO
C5ir-U^COC5iOi ll^COOO^O
^0QOI>00Q0OOOO
ipcpt^cpC5cprHCNcp^pt-ao
oi(^cqc^(f<icbcocbcbcbcbcbcb
cococococococococococococo
^ipcpb-qoC5prH(?qcpcp^p
<CCCcb<d0C565O5(05C5C5C5
T*Tj<C000C0Cq^rHOO05C0t>
OQOO^iMOOOO'^NCiNiO
^^lOCONOOOOOOHHfMc:
NWOO<MOOOHt>COO)lOH
WONMOOWOCOWQOCO
CO^t*"rtllOCOCDI>-000005050rH
66666666660HH
8coco05C^ooOi 1 eo co 05 <M 10
(Mcpcc^^iopcpcpb-t>qpq5
^o^ocbcbcbcbcbcbcbcbcb
rHr-tr IrHi IrHrHi li IrHr (r IrH
10rH00^r-lt^^t<O>C0OCD<M
C0CO00rH^CDC5<N-^l>.Q<^iC
rHi-Hi-l(M(M<M(NCpcpcp^Tt<^
cbcbcocdbobooccdbobaDaDdo
NHrftNO^NOMNOWO
OOOOOCTM^ONCOOHJI
OOOHHHHHHHWCTW
"o *00 *o O oO >oO ^ o o o
M M t) WM + + ^ <0O
5 ti
B B
/j e Latitudes, or Horizontal Dis-
OO X>e& ' tances for Difference of Levels
74
TABLE II.
Latitudes, or Hori-
zontal Distances for
Q K jjg- Latitudes, or Horizontal Dis-
*w tances for Difference of Levels
Difference of Levels
Cosines
O 10O *oo *-> *oo >oo oO
S m
25 o'
90631
60'
"O ^-> vr> ri- ^- co co H w m
If
I
90618
59
%
z
3
90606
90594
58
s 7
VO
4
S
90581
56
GQ
HONIOMHQOCDMOOCO
90569
55
>
MCO^QONiOOSMNO^N
Oiptp-^cpepfMHHOOffiOO
6
7
8
'9557
90544
90522
54
53
5*
OO06666666606
OOOOOOOOOOOOOOO
(_1
.
9
90520
5i
00(^OOiOCi(MCOOiOH
ipip^-^cpqqoqHHOOOqo
1
IO
90507
5
fe
ii
90495
49
O
ON
1 IrHrHpHrHrHpHrHrHrHpHOO
ON
12
90483
48
oooooOQOoooooooooooooooooo
I?
14
*5
90470
90458
90445
46
45
O
CO
1-5
0>OOiOO>00>OOiOOiOO
ip^rti039(N(NHHOOQC
16
17
18
'9433
90421
90408
44
43
42
Ph
O
00
00 '
>
m
l>.l>.i>.i>t>t^t>t>.t>.t^t^t^t^
*9
90396
4i
1
1 1
ft
^
20
90383
40
(MOOiOHCOiOHNCOOJ^OiO
fCpCpcpc^NHHOOOCO
Ph
21
90371
39
O
22
90358
38
t^
WWM03MWM(NCi|
OOOsDOOOOCDOOOO
r^
*3
90346
*7
O
24
90333
90321
36
35
5
Q0HTtlNOC0U5Q0ONr)iCN
NiiOOWCJiOHOO-ttQOtN
00 CO 00 C^ <?q rH-rH rH O O O O O
26
90309
90296
90284
34
QQ
O
27
28
33
w
VO
^^^^^^^^"^^-rtHOOOO
v
32
lOiOiOiOiOiOiOOKJiOiOiOiO
29
90271
3i
Ph
30
90258
30
"
Ph
90246
i0^03(MHOO00COTOHO
H00i0(MG5O(MOC0C0ONC0
OINNCTHHHpOOOOQ
1 1
31
29
H
p
3*
90233
28
zn
O
"
33
34
90221
90208
%
ii
P
o
ibibibibioibibibibibib^-^
o
Ph-
35
90196
15
H
^
36
90183
24
cqoooDoooooooooooooo<Mb-c<j
5(NOMO(MONiOWQfl50
NINiMHHHHOOOOOffi
CO
37
90171
23
H
3.
O
38
90158
22
fe
00000000000000000000000000
^-
39
90145
21
O
5
40
41
90133
90120
20
19
OH(MMUJONffiOH(NCOTJ(
42
90108
90095
90082
18
K
OONiOWHOiNOiKMOQOO
r r , T lr 7 Hr r ,r r l '?"? > PPP < ?oo
NNNNNNNNNNNCOO
**J
43
44
3
O
CO
O
CO
Ph
Ph 1
G<lG^CMCq<M<M(MCqG^CM<?qcM<N
P
45
46
90070
90057
15
14
(NHOOONCOOMNHOOON
47
90044
13
^
48
90032
12
m
49
90019
11
W
cJ
oboDobdbobobobobdbobdbb-t^
M
50
'90006
10
P
H
5i
89994
9
52
'89981
8
otib-r-i^oocqcooooi^'-i^oo
53
54
89968
89956
89943
I
O
CiOiO-tCOWtMi^mOOQQO
oppppppppopoo
O
55
5
666606666660000
56
57
'89930
89918
4
3
it
*b "^ * *o *r> O ^O *o O
58
89905
2
w h d d wm^^- v iovo
E3
89892
89879
gines
0*64
1
-p. tyo-
inrtA /^-r
De
Diffe
partures, or
renoe of Levels
6
4 - vvmum, ^sr
311C0
TABLE II.
75
Departures, or
Difference of Levels
25 o'
I
2
3
4
5
6
7
8
9
io
ii
12
IJ
14
15
16
7
18
*9
20
Sines
'42262
42288
42314
42341
42367
42394
42420
42446
42473
42499
42525
42552
42578
42604
42631
42657
42683
42709
42736
42762
42788
42815
42841
42867
42893
42920
42946
42972
42999
43025
43051
43077
43104
43130
43156
43182
43209
43235
43261
43287
43313
4334o
43366
43392
43418
43444
43471
"43497
43523
43549
"43575
43602
43628
43654
43680
43706
'43732
"43759
43785
4381 1
43837
Cosines
6&
59
58
11
55
54
53
52
5'
5
49
48
46
45
44
43
4Z
4i
40
39
38
11
35
34
33
32
3i
3
1
0-64
Latitudes, or Hori-
zontal Distances for
Difference of Levels
O f\ Deg . Departures, or Difference of
^^ d Levels
lOOOIMOOOH^NOW
CD ~ "I
cn 55 us
^ ^1 ^ rjl
"^r *^^ ^T ^P ^^ "^P ^^ ^T ^^
' 00 co co
COOtsOO(N-^COQOC)HWiO
cprHqqcpipcpt^opq5rHc^cp^
cbdodbcbcbcbcbc6666
cocootcocococotocococococo
OiOOOHCDHOHOO
COOGOOCq^OGOCii-ieO^O
XNCOffiiO^MtMHHOOQO
ipspt^qpCiprHCqcp^ipipO
6666666666666
Gs|<?q(M(M(?qcOCOCOCOCOCOCOCO
b- 10 ** Ol
rH ^ 55
10000010x010106666
c<ioqoqcqoi<MOicqoioio)Ojoi
HNMQO'fOCOHNWOOOOOO
WOO(M05ffi(MC:5(Na)iOH
i I il i IHHr- IrHrHrHrHrHrHrH
ot^ocooooocooooooqo
OlOHCOHOlMNCTNeOQOW
csgiOOHHcqcqww^-^io
66t^t^t^t^t>t^b-b-t>-t^t^
OOOOQONOOlOiO^cOMfMH
NHlOOKNHlOOJnNHO
ONNNcpopOOOJOOHr- 1
oq^<^(^<N<^c<joqoqoocbcbcb
(MC53HQOt)(05DC0010HN
Ot^OCOOOOr- ICOCDOOr IrJHCO
6o6oaDao6o6occccao6oao6o6o
05(NOQ(M500H^NHt((
(NCOiONOOHC5 , <tONOO
cqcqcqoqcqcqcococooooScoco
151 y
O ^ O o o
64
Begr.
Latitudes, or Horizontal Dis-
tances for Difference of Levels
d 2
76
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
m
ft
O
M
I
w
fi
g
a?
O
%
H
CO
M
R
p
p
H
t 1
H
3
C\n Be Latitudes, or Horizontal Dis-
wU "' tances for Difference of Levels
26o'
i
z
3
4
5
6
7
8
9
to
11
12
J 3
H
5
16
7
18
'9
20
21
22
23
24
*5
26
27
28
29
30
3i
32
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
5o
5i
52
53
54
55
56
57
58
g
Cosines
89879
89866
89854
89841
89828
89815
89803
89790
89777
89764
89751
89739
89726
89713
89700
89687
89674
89661
89649
89636
89623
89610
89597
89584
89571
89558
89545
89532
89519
89506
89493
89480
89467
89454
89441
89428
89415
89402
89389
89376
89363
89350
89337
89324
893 1 1
89298
89285
89272
89259
89245
89232
89219
89206
89193
89180
89167
89153
89140
89127
891 14
89101
Sines
60'
59
58
%
55
54
53
52
5i
50
49
48
46
45
44
43
42
4i
40
39
38
11
35
34
33
32
3i
30
29
28
26
25
24
23
22
21
20
19
18
\l
15
14
13
12
11
10
9
8
I
5
4
3
2
1
9 "63
O <flO vo O vo 10O o >o O
vo 10 ur, -^J- ^- m m M tf m m '
co
it
1-3
CO
>
k5
Pn
O
Q
3
a?
&
H
(^
W
ft
G5O^Hb~C000C000C000<MOrH
NHU5QO(N>CiO(NOQCOOO
OOCO^OOO^TtlCpC^C^rHrH
0666666666666
ooooaooOGOGOaoaoaoooaoaoao
O
O
HMCDQ0HNt)<K5N00OOH
O00t>HOOi*00(MOO^O
opqpt^t^cocoio^^cococqi 1
0066666666666
00000000000000000000000000
O
O
(MHOOOOiliMO)iOWH
oooioo^o^caeooowoo
Oopopt^OOipip"^-^ooo'D(?q
rHrHrHrHrHi-HrHrHrHrHr^-lrHrH
O
00
O
3OOHOh>0Otj(QiMOh
HNtNQOOOM'OiOOCOHN
O
VO
N03H(MiioSQOOaOH
oopqpopt>b-cpooioioo^
vo
VO
mon^hnt)<hoo^hooo
050opopopb-b-b-ocpcpipp
^^ ^j ^tj "^ "^ "^ "^ ]jt1 , ^ "^ "^ "^ "^
^T ^X ^^ "^^ ^^T "^T ^^ ^3* ^n^ "^^ ^T "^^ "'vT
VO
OCMOt^^(MOt^-*^HO 0^t<
OQOOpODCpNt>l>NCpoO
cococococococooocococococo
3-
O
CO
rfl t^ 10 O N N 00 00 05'05 05 O O
C0iKNOC0ffl^(MOQ0i0 5:
C5C5C5q5opopopqpopt^t^t>b-
6666666666666
CO
OMONIOCTOOMOOWO
NOiOCOtMr- 1 05 00 b- CO <* CN
05050505050500000000000000
i irHi 1 1 IrHi 1 1 lr Ir-lr 1 r 1 1 1 r- 1
00>-lvOC5(nCDO5COCOCOb
XOONCCOiO^^COMNHH
0500505050505050505050505
obcbobobobooobobobobobobob
II
v O vo O vo *o vr O >oO oo
t-i m rJ H co co ^- tJ- vo vnvo
vo
/>o ,* Departures, or Difference of
DO De& ' Levels
De
Differ
oartures,
ence of I
or
evels
TABLE II.
77
Departures, or
Difference of Levels
GO
I
ft
O
ft
ft
S
ft
M
P
O
of
ft
ft
p
H
ft
si
ft
A
0/ Departures, or Difference of
26 * Levels
26 o'
i
2
3
4
5
6
7
8
9
io
ii
12
13
4
15
16
17
18
9
20
21
22
23
24
25
26
2 7
28
29
30
31
32
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
50
5*
52
53
54
55
56
57
58
60
Sines
43837
43863
43889
*439 T 5
43942
43968
43994
44020
44046
44072
44098
44124
441 5 1
'44 T 77
44203
44229
44255
44281
44307
44333
"44359
44385
44411
'44437
44463
44490
44516
44542
44568
"44594
44620
44646
44672
44698
44724
44750
44776
44802
44828
44854
44880
44906
44932
44958
44984
45010
45036
45062
45088
451 14
45140
45166
45192
45217
45243
45269
45295
45321
45347
45373
45399
Cosines
60'
59
58
?
55
54
53
52
5i
50
49
48
46
45
44
43
42
41
40
39
38
11
35
34
33
32
31
30
29
28
26
25
24
23
22
21
20
19
18
\i
15
14
13
12
11
10
9
8
I
5
4
3
2
1
0-63
O w-iO o O o O mo *o O 00
SO W"> H") *$- r}- CO CO Cl tf M M
CO
vo
I!
CO
3
1
ft
ft
Q
ft
ft
ft
F
s
ft
c
ft
ft
g
H
CO
M
Pi
a
ft
hH
ft
cz?
ft
p
p
H
NCOOOOOOOOOOOQO
OJOQiMOQlMiOOOH^OO
cccspc^opTjtvpt^qpptHG^cp
ON
MHQ0OWHQ0>0(MaONO
T)*ip9)aiOH(MnpONqO
6666666666666
O
00
O-^CSC0I^(^OO^00CqK5C5
NNNQOOOOOOOOHHH
OH(NmTt*kpcpqpOHqq9
ibxboibibibK5ibib6666
COCQCOCOCOCOCOCOCOCOOOCOCO
00
CDNOOHW^iOOSOOOO
OONOOiO^COtNHOOQON
pt^rcpOrHCqCO^ipippt^
OOOOHHHHHHHHH
cococococococococococococo
OOOIOCOHGNICIMOQCOCO
COCp^ipppt^CpppprHCq
666666660NNNN
CMcMCM<M<Mt>l<MCqcq<M<M<MCq
vo
O
ooiio^oiaoiooioovooj
HQO^HOO^HN^ONMO
ppOrHrHCNCpcp^ipippp
rH rH cq tfi (fq cq (fq cq c-i cfq ct i^q cfi
Cq<?qCqcq!M<MCqcq<MCM<MCqCM
%
lONOH^OOOON^OaOO
wcocco^o^oiooooo
lpip'OONNCOOClOOHH
1lrHrHi Ii It IrHrti 1 1- 1 r ( 1 ti 1
5-
C">
HOC5ffiQONCOLO-i(W(^HO
rHrHqqCqOOCpCp-rJH-^lxpiOlOp
cbocbcbcbcbcbcbeticbcbdo6
1 IHr- It Ii- 1 1 Ii Ii 1 t 1 r- 4 t ( 1 Ii i
CO
O
NMOONQOiiOCWOO^O
NNO)cpqpqpCiffiOOOO
cdocccooQbdodb6666
O
^NOWOOCTIOOOHtJINO
Q0OH(MWt)ionQ0OH(M'^
T^H ^^ ^^1 ^^ ^5^ ^41 ^ji ^p *^i ^1 ^1 ^31 ^^1
Eg ^
3
"o "^ O "i O *o O vo O *o O "o O
hi 11 t< H co co <$- -<j- 10 u->\o
Latit
zonta
Diffei
udes, or Hori-
1 Distances for
ence of Levels
/> q Latitudes, or Horizontal Dis-
O O 1>es ' tances for Difference of Levels
78
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
27" o'
1
2
3
4
5
6
7
8
9
10
Cosines
89 1 01
89087
89074
89061
89048
89034
89021
89008
88995
" 81
88955
88942
88915
88902
88875
88862
88835
88822
88795
88781
88768
88755
88741
88728
88714
88701
88674
88661
88647
88634
88620
88607
88593
88580
88566
88553
88539
88526
88512
88499
88485
88471
88444
88431
88417
88404
88390
88377
88363
88336
88322
88295
Sines
o'6z
Departures, or
Difference of Levels
27
De Latitudes, or Horizontal Dis-
tances for Difference of Levels
O ^->0 >00 o O 00 WO ""> O
a 05 oo 00 00 ao
00 00 00 00 00 00
00 00 00 00 ao
00 00 00 00 00
HHH(MHHHHO05Q0NU5
C5 CO t^ 1 iiOOMNr- I ^ 00 <M CO
rHrHpOpCOOpt^r^piOlO^
0000050505050505050505
oooooooot^t^t-t^t^b-t^t-t^
HN^WQO^HNMffiiOOO
NCTHHOOOCiODNNOO
rHrHrHrHrHrHOOOOOOO
H-^QOr- I -* GO i I CO CO 05 <M "* CO
NfMNWOOMO-^o^OiOO
WMCTNHHOOQffiOOOQO
cocococooocococococococo
HOHHHHHOOOOQON
CfNOOr^OCxMOO^QiOHN
^^Cpcpcp<^CqrHrHpO>p05
cbcbcbcbcbcbcbcbcbcbcbcbo^
iOiOiOOiOiOiOiOiOiQiOiOiO
ON^HN^ONnOlOHN
>OHQ0>CH00iOHQ0^r-lXlT}(
iO*0-**"*^COCOCO<M<MeNjr- I pH
O^NH^NOTtfNO^lOOO
O lO O O 10 C 3 IO 10 O lO >0 O
CO CO CO CO 07 CO CO CO CO 07) CO CO CO
0000000000050500
:0 H C5 N O CO H Ci N O N O CO
NNOOCDOOiOiOiOiOO'*
cbcbcbcbcbcbcbcbcbcbcbcbcb
It
CpCONNNNNNNNOOCO
OCONOMNOCONOCOffiOi
HOO00NNOOO^W(N
ppopopopopopopopopopopop
obobobdoobcbobobcbobobobob
62
Degr.
Departures, or Difference of
Levels
TABLE II.
79
Departures, or
Difference of Levels
27" o'
i
2
3
4
5
6
7
s
9
10
ii
12
13
14
!5
1 6
17
IS
19
Sines
'45399
'4542S
4S4SI
'45477
45 So J
4SS28
45554
45So
45606
45632
45658
45684
45710
4S736"
45761
45787
45813
45839
45865
45891
45917
45942
45968
45994
46020
46046
46072
46097
46123
46149
46175
46201
46226
46252
46278
46304
46330
46355
463 8 1
46407
40433
46458
46484
46510
46536
46561
46587
466 3
46639
46664
46690
46716
46742
46767
46793
46819
46844
46870
46896
46921
46947
Cosines
0*62
Latitudes, or Hori-
zontal Distances for
Difference of Levels
27 ***
Departures, or Difference of
Levels
mo <oO J">0 mo mo mo
0>0^ + tflW tf HI H
o
O^OQOH^NOWCO
cpipcpt>oprHcp-^pcpqoOi
lqiq^ibibcbocpocpcbcbo
9
OOHHHHHHHHfflNM
co a <m 10 00
CO^iOCONQOOOHCNW-^O
cooocococococococococoooco
OOHHN^cqWMWCOOOm
NNOOt(iW(NHOOQONO
rHrHrHG<i(7qcq(^i(7q(fq(fq<^(^(?q
cococococococococococococo
ffiNOiMONiOCTON^HOO
WHONiOOlOOOOMHOiO
(MCOCO^OCONNQOOOOH
OOC^GHO(NOO>OHQO^ON
ONQOQOCOOHiMNCOil^
rH(^C<|C0C0T^-^ipipCOCpt^l>.
cbaDccbccbcccb(aoc3bcbdb
QOSOO^fMHOOON 1
cotfococococococococo-^^Tti
Cp rH r^H rH rH C<J (?q ' _
o03oc5(mjnowo05(mo
^ooncjohmthocoooo
lpipipoocpcpcpcpcpcpcpcp
^^ ^sH ^^ "^^ ^J^ "^^ "^J^ ^^ ^r* ^^ ^^ ^^ ""m*
o m O m o
10O m O m O mo
e* d -<i- <4- m m\o
62
Latitudes, or Horizontal Dis-
ff " tances for Difference of Levels
80
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
m
P
>
O
P
i
H-l
P
M
w
w
H
m
H
P
<!
H
g
O
i
ro
Q
&
H
W
I
^q Latitudes, or Horizontal Dis-
AtO Be8r " tances for Difference of Levels
28 o'
2
3
4
5
6
7
8
9
IO
ii
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
5o
5i
52
53
54
55
56
57
58
60
Cosines
88295
88281
88267
88254
88240
88226
88213
88199
88185
88171
88158
'88144
88130
88117
88103
88089
88075
88061
88048
88034
88020
88006
87992
87979
87965
87951
87937
87923
87909
87896
87882
87868
87854
87840
87826
87812
87798
87784
87770
S7756
87742
87729
87715
87701
87687
87673
87659
87645
87631
87617
87603
87589
87575
87560
87546
87532
87518
87504
87490
87476
87462
Sines
60'
59
58
56
55
54
53
52
51
50
49
48
46
45
44
43
42
4i
40
39
38
11
35
34
33
32
31
30
29
28
26
25
24
23
22
21
20
19
18
\l
15
14
13
12
11
10
9
8
I
5
4
3
2
1
o*6i
"ovoOvoOvoOvoOVfcOvoO
Ifl <0 + + M M S H H
It
m
P
>
g
o
H
o
1
H
P
tf
o
w
s
p
3
w
p
M
1OCDQOOO1 I <N (?3 G<1 CO CO <M <M
ftCTiCOOfNiOgOH^NOWCD
(MNH990<(X)NcppT)(
GO0000O0O00OO00OQ0OO0000OO
o
o
O
XOCCfMOOOO^r-HOOCOCOOiCD
COO-^QOHiOCiWOO-^NH
^^cpqq<?qfHppo505Qpi>^
66666666cdbdbdb<x>
o
OS
00
O-HHOHCDO^00CqO0i
MOOfMNHOOiOOCOOOtMO
COOiO^T)(COCO(MHHOOO
66666666606605
iS.I>l>t^t>Ist^l>t-t^Jst^O
o
00
IS
QiOHOHOHOHN(MN(N
CptT-I^pCpipip^rjiOOCpCNiqq
rHrHrHi^rHrHrHrHrHrHrHrHrH
o
VO
NMOiOHNCTGO^OOHN
CiOqcqpqpb-l>C)poipiOTH
iOiOOiOiOiOiOiOK5iOOiOtO
o
VO
O
44-147
44-113
44-079
44-044
44-010
43-975
43-941
43-906
43-871
43 836
43-801
43-766
43-731
o
O
QOOCOOQOOMlONCiHCOiO
HQOKOOOiOCTCJOilHQO
m^wqq^MHHoppOQ
10 10 ib 10 b ib 10 *h b b ib -*
cococococococococococococo
O
to
Q0Q0NNO0^i*WCqHOO
QOO-tlMOCOO^lMOOOOCJ
^^"^^^cpcpcpcpcpc<ic<ic<i
6666666666666
o
CO
O
O
If
H
OiO(NOOTjiOO(Mop5HCOiN
lO-^WHOONO-tCC^OO
ocpcpcppipipipipipipipTi<
rlHr 1 i 1 i Ii Ii IrHrHrHrHrHi 1
O
M
(M(MhOOOQOQONOCOOtP
dbcob<#cdocb<ccbcbdbdb
O
"o oO >oO w->o o O o o o O
M M c* H CO CO <$ t$- U-> OVO
oo
,, T\'fF
>nce
of
Departures, or
Difference of Levels
6:
L esr ' Levels
TABLE II.
81
Departures, or
Difference of Levels
ft
>
ft
ft
w
p
of
ft
p
ft
p
rtO Departures, or Difference of
28 ** P ; Levels
28 d
i
2
3
4
S
6
7
8
9
IO
ii
12
H
s
16
7
18
19
20
21
22
23
24
25
26
27
28
29
30
3i
32
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
5
Si
52
53
54
55
56
57
58
s
Sines
46947
46973
46998
47024
47050
4775
47101
47127
47152
47178
47204
47229
'47255
47281
47306
47332
47358
47383
47409
'47434
47460
47486
"475"
'47537
47562
47588
47614
47639
47665
47690
47716
47741
47767
47792
47818
47844
47869
47895
47920
47946
47971
'47997
48022
48048
48073
48099
48124
48150
48175
48201
48226
48251
48277
48303
48328
48354
4?379
48405
48430
48455
48481
Cosines
6V
59
58
57
56
55
54
53
52
Si
50
49
48
46
45
44
43
42
4i
40
39
38
11
35
34
33
32
31
3
29
28
26
25
24
23
22
21
20
19
18
3
15
14
13
12
11
10
9
8
I
5
4
3
z
1
o*6i
O o O >j~>0 vo O o O vo O vo O
VO IO "1 + + M M tl H M 11
ll
11
ft
s
a
O
pq
O
ft
ft
fa
fa
h- 1
P
m
fa
H
m
M
P
O
3
W
ft
P
I
1 1
H
^ t> O 0: O 00 H -H^ O <M O CO
Q O (N CO * io t> op O 71 w ?: ^
t |> b, |> t"- t>- t> fr* GO 00 cb 0?
^^ ^^ ^^ ^r ^^ ^nP " t: t "*^ *^r "*^ ^p *^ ^j^
cqoocoo-Ho^o^ci^coco
iOOOOOH(MT((iONOOCHCO
^CO^ipNCpOOH^^CO
g^ g gn (N ch gm 0? cb cb cb 00 2 2
T^ T^i ^1 T^l T^l "^Jl ^^ "^ "^ "^ "^ *^T* "nP
00
OOOCOOOOO^'ONOKMLO
lOOOOONNWNNXODOO
iOb-00OrHGN0pTi<avpl>~
b-t^b-b-b-obdcGbdoobcbobcb
00 co co co 00 co co co co co 00 cc co
00
concciMfM^HOOOooooN
CO IO * CO (M H O C5 00 >o ^ CO
GOC50r7HCNCp'^^pcpi'-opC5
g^ c^ cb cb cb cb cb cb cb cb cb cb cb
co co co co co co co co co co co co co
vo
ODiO(MOOCOOOC005 0(MO
O ^ (N O N IO (M O O CO rH CO
H CM CO OI t^ 10 O N N GO 9 O O
obob&obobobcbobabdbdb66
GN GN GN GN CN CM GN CN GN GN GN CN GN
COOOtMOO^COfMOOCONO
Ncoooc:oiocico-t<Hi>rti
^lOOCNNOOOOOHHIN
cb cb 00 cb cb co cb cb cb -^ ^ ^ ^
GNCNGNGNGNCNGNGNGNGNGNGNGN
vo
OOHCOt)(iO'ONCOOOH(M
t^C000C000CCXC0CC'--t<O-t i Ci
J>.C000OOOOrHrHGNGNCpC0
000000006066666600
1 (i li li li li 1 1 It IHr- It 1 r 1 i 1
iMHOCOOOC5HOOOO^
oo (M co n 1-1 lo c: *
OHH(MCTNcpcOMT)l'iiLp O
1 It It It It It It ItIt It It It It 1
O
OH'OOIOOCOO^OtOHO
QOH^OOHTfOO CM 7* t- O
CO il TJI rP t(* 10 9 ip 9 9
6666666666000
O
ICOOOCOOOCT^NOCCjiOOO
O O O) W -* LO N 00 O H 01 cc ^
O b- t-- b- l^ t^ t> t- > GO Op CO CO
if
v o oO vo O vo O "~> o vo o vo o
00
Latitudes, or Hori-
zontal. Distances for
Difference of Levels
Latitudes, or Honzoi
1 *>eS"' tances for Difference (
ital j
)fLe
Uis-
vels
D 3
82
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
00
>
c
H
Q
s
S
H
R
tf
O
W
H
0Q
1 1
R
3
w
P3
of
w
R
5
H
M
H
h3
qq Latitudes, or Horizontal Dis-
v eff * tances for Difference of Levels
29 O'
i
2
3
4
5
6
7
8
9
IO
li
12
13
14
15
16
17
18
19
20
21
22
23
24
15
26
27
28
29
30
3i
32
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
50
5i
52
53
54
55
56
57
58
e
Cosines
87462
87448
87434
87420
8740s
87391
87377
87363
87349
87335
87321
87306
87292
87278
87264
87250
87235
87221
87207
87193
87178
87164
87150
87136
87121
87107
87093
87078
87064
87050
87036
87021
87007
86993
86978
86964
86949
86935
86921
86906
86892
86877
86863
86849
86834
86820
86805
86 79 x
86777
86762
86748
86733
86719
86704
86690
86675
86661
86646
86632
86677
86602
Sines
60'
59
58
5<5
55
54
53
51
5i
50
49
48
46
45
44
43
42
4i
40
39
38
36
35
34
33
32
3i
3
29
28
S
25
14
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
I
S
4
3
2
1
o"6o
O oo oO *oO oo oO <00
VO "Oio^^-MMN cl it w
O
O
VO
2*
If
P
H
O
5
of
ft
(MHOOQ0N5M(MO000(N
OOOHONOMOON^NO
^cowcMrHrHpocc<pb~cpcp
GOQOOOOOUOOOOOQOOOOOOOQOOO
O
ON
OfNOOiOOfflHNCOOOOONCq
HOQ0<MOOOOWNO^
NOipiprr<MMCl(^H0005
cbcbcbcbcbcbcbcbcfecbcbcbb-
O
ON
O
00
OrHlOO^OO^NHOQ^OO
OOcocpt^ocpipip-^coeocM
O
00
CO^^lOlOlO-H^^TjH^CMr-l
cm t> cm i>. cm t^ 01 1^ cm t^ cm ^ cm
rHrHrHrHrHOOOOOOOO
ocoooocoooooooo
O
VO
N rf( (M O N Tf( h CO IO Ol Q O H
ffMNWPlCqHHOOOO
CM CM CM CM CM CM CM CM C^i^i CM CM rH
O
VO
HlflOdOWNHOO^NH
t^cp ( pOipuoo^^'*cpcpcp
O
lOOQOOHCO^iONCOOOH
COU5<MONT)(r-icOiO(MQNTrl
Ocpoocpcpqpb-i--t>cpocp
C0COCOO2CO00OTC0CC)C0C0COC0
%
CO
ONOiOCCMOOOOO^CTH
CTWHHHHHOOOOOQ
ocbocbocbocbcbcbcbcbib
CMCMCMCMCMCMCMCMCMCMCMCMCM
CO
(MTOrtlOO^NOOQO^OiOO
CO Ci <M lO 00 - IWCOQfMONO
t^t>b-t^t^t^b-cpcpcpoocp
abcboboboboocbcbcbdbcbccob
O
11
O oO "lO 10O >^"> O vr> O >0 O
M 11 tS N CO CO -^- tJ- *0 IOVO
O
on
-p. iv/r
De
Diffei
partnres, or
once of Levels
6r
J Deff " * 'Levels
TABLE II.
83
Departures, or
Difference of Levels
XII
O
N
r
P
P*
O
w
M
P
H
ft
W
P
aa _ Departures, or Difference of
4i V De *" Levels
19 o'
i
2
3
4
5
6
7
8
9
IO
ii
12
1?
14
15
16
17
18
19
20
21
22
a?
H
*5
26
2 7
28
29
30
3i
3i
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
5
5i
5*
53
54
55
56
57
58
60
Sines
48481
48506
48532
48557
48583
48608
48633
48659
48684
48710
48735
48761
48786
488 1 1
48837
48862
48887
48913
48938
48964
48989
49014
49040
49065
49090
491 16
49141
491-66
49192
49217
49242
49268
49293
49318
49344
49369
49394
49419
'49445
49470
"49495
49521
49546
49571
49596
49622
49647
49672
49697
"497 2 '3
49748
49773
49798
49823
49849
49874
49899
49924
49950
'49975
50000
Cosines
60'
59
58
56
55
54
53
5*
5i
5
49
48
46
45
44
43
42
4i
40
39
38
11
35
34
33
32
3i
30
29
28
11
15
24
*3
22
21
20
'9
18
3
J 5
H
13
12
11
10
9
8
I
5
4
3
2
I
o"6o
O w->o oO oo v^o **"> O 00
VO >o o + rj- m rt c< ih m
O
O
VO
la
It
w
3
P
>
H
P
tf
O
ft
Q
1
oq
3
3
EH
s
g
P5
of
W
P
O
H
H
M
H 00 (5 (N a O (N c: w 00 ^ Q
^HCpb^GOCirH^Cp^Cpt^opp
^1 T51 "^^ t^ ^4 ^H ^J1 ^1 *^H t^ "T^ ^H lO
O
ON
OONHOO^OO^^OWNQ
K"fCNOOHK-)(iOSOOO
ONOOGiCMW+iOONOOO
^T" ^T 1 ^T 1 ^T* ^P ^T 1 ^vT 1 ^^ ^sT 1 ^T 1 ^T ^^ ^T 1
ON
O
OO
OOOOO-iMidoONOOOQ
0000C3QOQC3OOOO
NOOCiOHCNOO^iOCONOOO
0)0)0)6666660666
cococccccococooococococo^
O
00
O
N O O ^ (M H O 00 S IO CO (M O
2i]Hor^xNoi*(MHO
COH(M(NM^iOONOOCiO
cococococococococococococo
O
O
VO
OiOHNWOiCiHNWO'HO
OOCiiHOC'^NON'tfNO
p m q-i cc cp -+ t>- op p p
6000060666666
CM<M<M(MC^GN<MC<ICqC<lG<l<MCO
O
VO
O
O-^COt I^OOt I-tHOOt l"^t^O
^OCOMOiOfMOO^HNMO
(NOCOTJtfiOOONOOCOOO
-*
cqco-^ioooi^oooooooo
O"^0~+0-+O^0^t<0
6666066666666
1 IHr- It Ii 1 H H r- IplHHr 1 CM
%
CO
iKMOCMOWHOOTiKMO
^00(MOOCONH-<#00(NOO
lOiOCiOONNGOGOGOOOO
CO
Cl
C0(MNCT00CC00^OtHO>SO
O'M^NQ'MiiNGfMONO
(^r^t^t^i^opopqpqppppp
6660666660666
OOH'tOQ(M'tNO(MONO
-fONOOOHWMKJONOOO
Goooxoooooooppppp
la
0* -r.
S
2^
It 11 fj H CO CO ^ -<4- W> OVO
O
On
Latitudes, or Hori-
zontal Distances for
Difference of Levels
/j|> Latitudes, or Horizor
%}\) !> tances for Difference c
ital Dis-
>f Levels
81
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
Cosines
30"* 0'
86602
60'
1
86588
59
2
86573
58
3
86559
57
4
86544
56
5
86530
55
6
86515
54
7
86501
53
8
86486
52
9
86471
51
10
86457
50
11
86442
49
12
86+27
48
13
86413
47
H
86398
46
IS
86384
45
16
86369
44
'7
86354
43
18
8634
42
'9
86325
4i
20
86310
40
21
86295
39
22
86281
38
23
86266
37
24
86251
36
25
86237
35
26
86222
34
27
86207
33
28
86192
32
29
86178
3i
30
86163
30
3i
86148
29
31
86133
28
33
861 19
27
34
86104
26
35
86089
25
36
86074
24
37
86059
23
3
86045
22
39
86030
21
40
86015
20
4i
86000
19
42
85985
18
43
85970
T 7
44
85955
16
45
85941
15
46
859=6
14
47
8591 1
13
48
85896
12
49
85881
11
50
85866
10
5i
85851
9
52
85836
8
53
85821
7
54
8,-806
6
55
85791
5
56
257-7
4
57
85762
3
58
85747
2
59
85732
*
60
85717
Sines
0-59
Departures, or
Difference of Levels
30
Latitudes, or Horizontal Dis-
*' tances for Difference of Levels
io >o i <J- w to rt c* m m
o
CNONMONMOiO-HCDHN
O^iOOOHCCOOOH-^OOH
OiO-^(WW(NHOOQ0Nl>
c 6 6 6 6 6 6 6 o ib 10 10
00000000000000000000000000
(MNHOC5WN005NO(NiO
Oocqpt^ocpip-^-^ic^crqcNrH
ppopopt^-ppip
oocsodsobobooobobobabob
0000000000000
WHOOONOiMOOO^lN
(MNOIO-O-iOhioOiOQ
OOO
OOOOOOOOOO
OOOOOOOOOO
HO)iOO(M'XOJi50>00
OHNc:X"tOiOOO(MNCO
CiOGOOONNOOOipip^'i*
r^r^HrHi^HrHrHr^H-Hr^-lrHrHrHi^H
I00i0i0>000i00i0i0uoi0
HLOTOHUJXH-fKOWOQO
OONOiiOHOC-tiONWCSio
(^^C^rHr^r-lOppOOOpcp
2222222222222222?l253?3?3^
*^r ^j^ "^^ ^^ ^^ *^T ^T ^^ ^^ ^^ ^^ "^J^ "^f
HfMCOWTtioiCOOOOON
CpO>iOipiO'*ri(Tt('^MCOCO(N
cocccococococococococccoco
HOMOCCHONiKMONiO
OOOrnONiKMOXOCOH
ppppqpopopopqpwb^i^b-
ib 10 10 o ib ib ib ib >b ib ib >b ib
cm cm cm cm cm cm cm cm cm cm cm cm cm
OO^2(MNWCC50Q0
NOaN^HOX)NiOT)(
WWCNCN(N5i|NCNHHHH
OMOOOH^OCJHilK^
oc-fc:r'M-'oooxNN
OOOOOOOOOiOOOiO
oocbcbaDcbobdoaDobcbobaDob
59 De &-
Departures, or Difference of
Levels
TABLE II.
86
Departures, or
Difference of Levels
Sines
50000
50025
50050
50076
50100
50126
501 51
50176
50201
50226
50252
50277
50302
50327
50352
50377
50402
50428
50453
50478
50503
50528
50553
50578
50603
50628
50653
50679
50704
50729
50754
50779
50804
50829
50854
50879
50904
50929
50954
50979
51004
51029
51054
51079
51 104
51 129
51154
51179
51204
51229
51254
51279
51304
51329
51354
51379
51404
51429
5H54
51479
51504
Cosines
0-59
Latitudes, or Hori-
zontal Distances for
Difference of Levels
QA _ A Departures, or Difference of
OO * F 'Lev,!,
1 gf
OOOOOOOOrHAlrHf-^
QMCOWiOQQH'tOQHM
QH(MT(i>OCNC50H(Ni'iO
9 7 1 ^ 9 7 'P 9 ^ ? 9 r 1 ^ w
ibibibibibibibibib6666
, ^p ^p m^ ^^p ^^p ^^ ^t^ ^p ^p ^^ ^^ ^^ *^
81 1 1 icqcqcocococococococo
000000000000
ohimm^loonoooohim
6o66666666hhh
^^ ^^P ^^' ^^ ^^ ^^ ^^ "'^ ^^ ^^ ^^ ^^ ^^
000^<M000 10WOOO>0 05
00NSOi((NHO05NO0
OHUJCOMHOONNOOOiO
O 1 1 ICOWN(MN^QC(MK(M
OMO(MOMO(MONiO(MO
OOHiMOOOjTfioOONOOO
6666666666066
cococococooorococococococo
O93OOH^C0O(MONO(M
OO(MQ00HN05OO(Ma)0
OOHHNopcCrHipoOON
1 10 ib o 10 i ib ib ib 10 ib ib
00-<HHHH(M(M(N(MNH
OOOlOWHGC'O'f^OO^H
O W N H LO 00 (M O O W N H O
OOOHHrHqqq'icpMW^f
ib ib ib ib ib ib ib ib ib ib ib ib o
OlOOlOHOHCHOHCDH
O (N lO N O ^ C N O CI lO N O
OOOOri 1 H H (N (M (M <N M
6666666666666
OCOiDCOOWiOOCOWiSCOO
OHOK? i O 1 - X OH(NM5
OOOCOOOOHHHHH
ibibibibibibibibibiooioio
r Q Latitudes, or Horizontal Dis-
0\) Desr ' tances for Difference of Levels
86
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
CO
9
i 1
P
tf
O
Pn
CO
W
H
CO
t I
p
3
H
O
l-H
3
O
w
co"
P
s
H
M
H
<!
Q1 n Latitudes, or Horizontal Dis-
OJL es "' tances for Difference of Levels
jio'
i
2
3
4
5
6
7
8
9
IO
ii
12
J
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
3T
32
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
50
5i
52
53
54
55
56
57
58
60
Cosines
85717
85702
85687
85672
85657
85642
85627
85612
85597
85582
85567
85551
85536
85521
85506
85491
85476
85461
85446
85431
85416
85400
85385
85370
85355
85340
85325
85310
85294
85279
85264
85249
85234
85218
85203
85188
85173
85157
85142
85127
85112
85096
85081
85066
85050
85035
85020
85005
84989
84974
84959
84943
84928
84912
84897
84882
84866
84851
84836
84820
84805
Sines
60'
59
58
?
55
54
53
52
5i
5o
49
48
46
45
44
43
42
4i
40
39
38
11
35
34
33
32
3i
30
29
28
26
25
24
23
22
21
20
19
18
3
15
14
13
12
11
10
9
8
I
5
4
3
2
0-58
O oO vi too too too too
vo vi >o ^- ^- w to tf m M
00
to
p
It
IS
CO
h3
>
O
H
O
5^
P
O
co~
P3
D
H
05
p
P
HrfCOH^COOHOOlClOOO
10 1 10 10 10 ib 10 1 ib -rt< -^ -^
GOOOQOOOOOGOQOOOOOOOOOOOGO
ON
^NO^NOMOOWOOIM
ON
O
00
^TjIMWCqiMHOQOONC^
NHlCOCTNHtOOOICO'i
ipip^e5M(N(MrHOO05O00
O
00
(MOO^OOOIONQO^HNW
O *+ O * C; CO 00 0: N (M N H
p^qoqpb>t>-Ocpipip^T}Hco
6666666660666
OiOOiOiOiCiOiOiOiOiOiOiO
0>00OO^XWNH100CO
WQ0-*O-tO0HO(MNlM00
^MCOfiilOlWHrlOOClOOp
HHr 1 i lr- IHHHHHOOO
lOiOiOiOiOiOiOiQiOiOiOiOiO
xO
to
00HMi0NO(M-f<CNaiHOl
lO CM 00 * O 1^ CO CI lO i 1 t^ ^ O
qpqpb-t^t^opipioip-^^^
bq bi bi bi bi cm bi bi cm eg bi bi cm
O
to
<*
snooocdo>oio^^c:ct
QOOWGCMON'tHCCiOCM
CqN(NrtHHHOO9O039
cootoootiwcocococococococo
%
CO
ioeooN^CToe^ooo>OH
1 Gi b COIONOKHX'O'*
b-cpoocopipipipip-^-^^
ib ib ib ib 10 ib ib b 10 ib ib ib ib
CM CM CM CM CM CM CM CM CM CM CM CM CM
CO
CO00CO00Ct'O0C?CX)fMb-<M?Di 1
^ PI H O CC O LO r (M O O N CD
^^^ooooooocsocro
(M^SOHifOQHOOCCO
NOC-i'^COCMHHOOCOQO
ipipipipipipipiOipiO-^'*^
caDooooobaDcccoocdoob
g^ "b to to to u-) t^o 100
5 s I
ghj| CO
Departures, or
Difference of Levels
5r
S^- ' Levels
TABLE II.
*7
Departures, or
Difference of Levels
GO
>
9
O
O
P
B
p
m
n
3
p
H
*
p
Q1 #* Departures, or DifTerence of
OL e S . Levels
31 o
2
3
4
5
6
7
8
9
IO
ii
12
'3
4
5
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
3i
32
33
34
35
36
37
33
39
40
41
42
43
44
45
46
47
48
49
50
5i
52
53
54
55
56
57
58
I 9
60
Sines
51504
51529
51554
51579
51603
51628
51653
51678
51703
51728
51753
51778
51803
51828
51852
51877
51902
51927
51952
51977
52002
52026
52051
52076
52101
52126
52151
52175
52200
52225
52250
52275
52299
52324
52349
52374
52399
52423
52448
52473
52498
52522
52547
52572
52597
52621
52646
52671
52696
52720
52745
52770
52794
52819
52844
52868
52893
52918
52943
52967
52992
Cosines
60'
59
58
11
55
54
53
52
5 1
50
49
48
46
45
44
43
42
41
40
39
38
11
35
34
33
32
3i
30
29
28
2
25
24
23
22
21
20
19
18
\l
15
13
12
11
10
9
8
I
5
4
3
2
1
0-58
O oO ^ O o O oO vno vr0
O
OO
H
M
Q00C0l^(MOO**00 < 10 00 <M
O^iONOlM 85 N- O <M -*
DC
-
1
ON
WOOOOrHCOlOOOOOO<MCO
'OONCJOHfMCO'^iONOOQ
-
O
00
25S22353'rj'r , ooooi^coioco
OOOOQOOOCJOOOO
1 1 1 1 1 IrHHtHHHHfflfjlKlW
00
COOb-^rHOOlOCqOOlOrHQO'*
JOTjKMHOOONO^KCqOO
OrHf>lcp^1^ipcpt^Q0OOO
cococococococococococococo
H
(1
-
c
(MN(MOH100^0CONH0
ONiO(NON5(NQN"i(Cq05
OqiprHG^CqcprJH-^ipcpl^tv.
OOrHi Ii IrHrHrHrHrHrHrHr-f
cocococococccococococccoco
6
(M^OC>HMU5NffiH(MT)(0
b-OpqpCipprHrHfMOOCO^T^
5
an
9
HHHHHOOOQOXNN
OLCOiOOOOOCiitO^O
OONNOOXOOOOOhh
OOOOOOOOOrHr^rHr^
C
HQ0OO000(MOOC0H00
10 00 (M :: n h ^ qo cq a
^TMOppCppt^t>t>Qpopop
ib ib ib >b ib >b ib >b ib b ib ib
iir- li 1 1 IHHHr- IrHi It-Hi It 1
fO
s
c
O
HOOiOOiOOiOO^OrffOO
O (N O N O (M C N O (M * N C5
co w 00 w f f f Tt< 10 10 c
0000000060600
O
u
off
-
I
O
OMOOOOWONOIMTilNO
L0ON00OH(MW0ONQ0Cl
r^ H H H (^ (N W C>1 (N ^ (>1 <N (Tl
ibibiboioibibibibibibibib
n
"q "> o >oO >nO o O 10O >oO
CO
Latit
zonta
Differ
ides, or J-
Distance
sncc of I
ori-
B for
evels
51
s Latitudes, or Horizont
* * tancefl for Difference of
ftlD
Lev
s-
1>
88
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
3
1
rJ
tf
f^
1 1
P
8
ft
O
1 (
P
1
N
3
O
H
of
P
B
H
t 1
H
3
OA _ Latitudes, or Horizontal Dis-
04i eB ' tan ces for Difference of Levels
32 o'
i
2
3
4
5
6
7
8
9
IO
ii
12
3
H
15
16
7
18
19
20
21
22
*!
24
25
26
27
26
29
30
3?
32
33
34
35
.36
37
38
39
40
4i
42
43
44
45
46
47
48
49
50
5i
52
53
54
55
56
57
58
&
Cosines
84805
84789
84774
84758
84743
84728
84712
84697
84681
84666
84650
84635
84619
84604
84588
84573
84557
84542
84526
845 1 1
84495
84479
84^64
84448
84433
84417
84402
84386
84370
84355"
84339
343'3
84.308
8.;i92
34-77
84261
84245
84230
84214
34198
84182
84167
84151
84135
84119
84104
84088
84072
84057
840 j.i
34025
84009
83994
83978
8396^
83946
83930
83915
83898
83882
83867
Sines
6V
59
58
%
55
54
53
52
5i
50
49
48
46
45
44
43
42
4i
40
39
38
37
36
35
34
33
32
3i
30
29
28
26
25
24
23
22
21
20
19
18
M
r 5
14
13
12
11
10
9
8
I
5
4
3
'
0-57
O o O o O oO oO mo oO
CO
1
is
PR
O
w
&
P
O
of
W
p
1
P
M
OOS03HOQ0O(Nri(C0
qpt^OiO^-^f. 00CM--H^O0iQ0
00000000000000000000000000
O
O
O
o\
TJH 10 tQ CD 1 iO iO VO -^ ""* cq -h
iMOQOH-t*NOCO*OOCTiOOO
cpq^rHr-ipciOopt^cpoic^
oooooibibibibibibibib
O
On
O
00
O
OO
^ 00 ^ O O ?: N O * 00 (N O
O
CO O IO 1 IO(NNMNN<MN
Or-JiOO^OrDOOtTq^rHOO
CpCpCN^rTHOpCiOSOpopt^l^
CiCiociCiociobobobobobob
O
^:Q-<oocot^oc<iioooo
oomo^oooioooHOffi
opopt>-t>pppppTii'^coco
0000000000000
QOWQO-iOOSJOOHNM
^NNN(MHHOOOOiO
23 3 ^3 23 23 ^ 3 1 * Cq >1 rH rH
O
%
S'zlQS^^^s^^^ooot^
NOOtMOOCCOt HHISTjl
popqpopt^b-b~t^pppii
o?cb<rocbcbcb<wcbcbcbcbcbeb
cococococococococococococo
%
CO
Hooio^ooiooioo^HNrjo
t^i 1 05 N -t (M O N LO ?5 O 00 O
ib ib ib ib ib 1 ib ib ib ib ib ib ib
-^ O O IO O W 00 ?1 O H 10 3i CO
o^^HdoootocooioMN
poiCipopopopcooooooot^t>.
0000000000000
rHr Ir 1 r It- IrHrHr Ir-Hr (r 1 1 Ii 1
M
OMON<M^OOOO(MION
obobobobobobobobobobobobob
O
| 2
7 bo
O o O voo voo o O *o O >oO
w m c4 N m w + ^- >o v>vo
erw ^ Departures, or Difference of
Ol * Levels
Do]
Differ
lartnres,
ence of L
or
evels
TABLE II.
80
Departures, or
Difference of Levels
go
p
>
h
O
O
m
gj
P
Ph
O
0?
p
S
p
00 _. Departures, or Difference of
OZ Be *' Levels
32 o'
I
2
3
.4
5
6
7
8
9
10
ii
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
5i
52
53
54
55
56
57
58
6o
Sines
52992
53017
53066
53091
53"5
53i4o
53164
53189
53214
53238
3263
53288
53312
53337
53361
53386
534"
53435
53460
53484
53509
53533
53558
53583
53607
53632
53656
53681
53705
5373o
'53754
"53779
53803
53828
53853
53877
53902
53926
53951
'53975
'53999
5 402 j.
54048
54073
54097
54122
54146
54171
54195
54220
54244
54269
54293
54317
54342
54366
5439i
54415
'54439
54464
Cosines
6^
59
58
g
55
54
53
52
5i
50
49
48
46
45
44
43
42
4i
40
39
38
36
35
34
33
32
31
30
29
28
26
25
24
23
22
21
20
19
18
\l
15
14
13
12
11
10
9
8
I
5
4
3
2
1
0-57
"0 u-io *" O "lO wi O oO oO
vo 'i >o ^r + w w h n m
If
GO
I
H
1
3
g
3
GO
O
H
GO
3
O
O
GO
I
(-3
(MiOQOH'fNQCOiONOlM'f
Oi iClOO'^pI^opOOCNCt'T'
IO IO LO IO IO O IO lO IO O O IO
ON
o:^ic>ooonnoooooooon
OOH^WtlOCNQOOlOH
occciOr^cMco^ippr^pp
t^i^i^ccc<docbccdocbd>
ON
00
COtMHOSC-fMOOOCOfiOH
OC5C00T0Q0*C0Q0NNNN
OO^ippb-oppcprHCqcprHip
22222222222^222222222222
O
00
0,
qo w cq h X 1 >o M <M
9HWM^lpCpONCpOOH
b- t^- t>- t^ b- t> t"^ t*. r^ t^ r^- co 00
cocococococcc^cocccocococo
th h a c h 00 co n
NO)CiOOHNMcp-T*ipOO
r 1 -! rH rH 6 ~\ CM CM <Tl CM ffl CM CM CM CM
cccocccocococooocococococo
O
vo
10
G;iOr-HQO-l*COfM'X^HNCO
^ipOpi^cocepOOrHr-HCM
c6 666c66onnnn
CM CM CM CI CM CM CM CM CM CM CM CM CI
O
3-
S O LC O -1^ ?M H C O CC N CO
O ~* c. -r a ^r -. -+ 25 > 55 00 00 oo
r^ cm cm si S3 rr -7 ip p p t- b-
rHi Hi- < -H r It '1 1 i-H r If 1 r 1 1 1
CM CM CM CM CM CM CM CM CM CM CM CM CM
%
ro
CO^HOOiOiNQOfNOOMO
QWNO-fMHOOlNOOO
OOOOOOOHHHMNMSQ
lbooooooooocboo
O
CO
comcoctnhoooo^cco:
O fM i* N O CM f N O h 1* O 3
iO C5 O CO CD N N N N CO CO CO Cp
0000000000000
rH r IHr It 1 i 1 i I 1 1 r- It lr Ir IH
OH-fOCOH>OX'OCM^O
C H (M 10 -fi O N X 3 H CM CO i
cm S3 S3 cc w K K ^* sp 7 + ? y
^ CO
1
5 fee
eo
Latit
zonta
Differ
iides, or Hori-
Distances for
ence of Levels
5'
m Latitudes, or Tlorizor
1 3>egr. tances for Difference o
tal Dis-
f Levels
90
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
>
w
HJ
pq
P3
PR
1 1
p
e
s
H
GO
1 (
P
H
C
s
3
w
PS
r/f
P
D
1 t
h3
qq j% Latitudes, or Horizontal Dis-
OO ee * tances for Difference of Levels
3J d
i
z
3
4
5
6
7
8
9
IO
ii
12
13
14
15
16
7
18
19
20
21
22
*3
24
^5
26
27
28
29
30
3'
32
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
50
5i
52
53
54
55
56
57
58
60
Cosines
83867
83851
83835
83819
83804
83788
83772
83756
83740
83724
83708
83692
83676
83660
83645
83629
83613
83597
83581
83565
83549
83533
83517
83501
83485
83469
83453
83437
83421
83405
83389
83372
83356
83340
83324
83308
83292
83276
83260
83244
83228
83211
83195
83179
83163
83147
83131
83114
83098
83082
83066
83050
83034
83017
83001
82985
82969
82952
82936
82920
82904
Sines
60'
59
58
?
55
54
53
52
5i
50
49
48
46
45
44
43
42
4i
40
39
38
11
35
34
33
3*
3i
3
29
28
26
25
24
23
22
21
20
19
18
3
*5
14
13
12
11
10
9
8
I
5
4
3
2
0*56
O o O oO -> O 10 O *oO >oO
SO iO<0 + + MN H ih M
O
I|
If
DO
E2
W
O
i 1
P
af
S
D
H
1
w
p
t^OOOOiCiOiQOOOOOt^OiO^
OOOlM^OQOOtM^OOOO
Qpi^i^pipTt<cpcpcqrHpoiCi
OOQOOOQOOOGOQOOOOOOOOOGOOO
ON
OOi iCOCDCifM^t^QCO^OOO'l
^^COqqrHrHppOTGpt^Cpp
O
OO
T*GqCDCOOSlOCDC<J0003aOCO
OJCOCOOMNH-^oOHiboOCT
pppcpt^t>-pip*p^cpcp
ocooooooocoo
00
58-707
58-654
58-596
58-540
58-484
58-428
58-372
58-316
58-260
58-203
58-146
58-089
58-033
SO
OiOW5l>.C2i (COiOt^OOCii 1 <M
M(M(MHH0000500QONt>
66666666i6Qffio6
SO
COOiKVHOCCOiOHNCOOJO
pqpqpqpt^t-. pcpipipf *
r^rHr^rHrHrHrHrHr^-lrHrHrHrH
NNWCTOOOOMHOCDt)*(M
Tf H OO O ^1 OO 'O (M O O 'M C3 O
xpip^^"^W0p0pCqC<J<NrHrH
cocqcocooococococococococo
I
oooNaiOHO(Moo^o>oH
OWH00CD^HC5O-i<(MC:N
HHHOOOOQGiQffiOOOO
O
CO
O
cooono-^oo<mcooonh
NiO^(MHQNO^(NHaoO
1 IrHr- Ii IHr IHHHr- 1 1 1 1 1 1 1
O
M
l^OirHCOCt^05^HCOlOt^OOO
OONNOiO^MMWHOOO
<<dD<oocbcb(cb(oodocb
11
|3
*b "OO o O <flO >oO w-10 >oO
hi m c* c4 co co rj- 3- u-> u->vo
O
CO
Departures, or
Difference of Levels
5
b De ^ ' Levels
TABLE II.
91
Departures, or
Difference of Levels
CO
P
>
h-i
Q
O
I
P
H
1
P
OO Be _ Departures, or Difference of
Ajeveis
33 o'
2
3
4
S
6
7
8
9
IO
ii
12
13
14
15
16
7
18
9
SO
21
22
*3
M
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
4 2
43
44
45
46
47
48
49
50
5i
52
53
54
55
56
57
58
g
Sines
54464
54488
54513
54537
54561
54586
54610
54635
54659
54683
54708
54732
54756
54781
54805
54829
54854
54878
54902
54927
54951
54975
54999
55024
55048
55072
55097
55121
55145
55169
55194
55218
55242
55266
55291
55315
55339
55363
55388
55412
55436
5546o
55484
55509
55533
'55557
55581
55605
55630
55654
55678
55702
55726
55750
55774
"55799
55823
55847
55871
55895
55919
Cosines
6c/
59
58
%
55
54
53
52
5i
50
49
48
46
45
44
43
42
4i
40
39
38
11
35
34
33
32
3i
30
29
28
26
25
24
23
22
21
20
19
18
\l
'5
13
12
11
10
9
8
I
5
4
3
z
1
0*56
O >^0 >oO ^0 wio oo *> O
O
VO
i
|3
co
1
ft
O
H
O
a
i
CO
O
H
CO
M
P
1
1
a
w
a
of
W
I
|
^CDGOOr-HCq^iQCOt^OOCia
QOOtMiONOHCCiONOH
th^m'^m^h 7* ta g >b b >b ib 10 b
ujooiooioioiooiaoioio
w
NNNOiQ^05(NHOOS
HfMWtiOONOO^QHHiM
PrHC-lCpThipOt^OOOrHC^CO
66qc5 666q6666
ON
00
HOOCOHOOiOfMOONOO
ipcpb-CpCiOrHCqCp^ipOt^
^ji ^^ ^1 ^1 '^1 ^1 Tji ^4 ~^i ^i ^1 ^j< "^t
O
00
iOO>OOCOHOOOOt|(ON
(M h Ci * O O 0: (M O 05 N 5 il
H^CNM^lpCNQOGOqiOH
cococococococccocococococo
vo
HiOXOMOO(MiiNO(M
NiO(MGNi*H]OOnONiO
CNxxooHH^oo-^Ttfio
oococococococococococococo
VO
COOiOHNKCliOHNoOOO
3-
O^MfMOONOTJi^HOX
X W X ^ 'X CM l^ (M b- <>} 1^ . 1 CO
t>xxoaooHrt(Noqwc:
rH 1^ rH rH rH (f 1 jq 'M (f 1 ff 1 (jq (fl (jq
<MCq<MCM<?q<M<M<M<MCNCNCM<M
O
CO
OOtMOiONX^HNMOO
MNH'tXIMOCi^OO-^N
cpcc^^^ ipipippcpb-b-b-
0066666666660
to
WNHOO^OCOSHOOtH
OH^OOH^OMmKOX
OOOOiCCpOOOOHHHH
M
OOHWiONCiHTfOQOOW
^W5NXGJQhi^OOXC5
ibobibibibbibibbbibib
O
^ fcJ3
ee g
"O *o O oO voO >oO oO oO
w m c* rt co co <j- <$- o wr^so
O
CO
CO
51
r* Latitudes, or Horizoi
3 ^ tances for Difference
Latil
zonta
Diffe
udes, or Hori-
1 Distances for
'ence of Levels
ltaJ ]
f Le
Dis-
vels
92
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
LATITUDES, OR HORIZONTAL DISTANCES FOR DIFFERENCE OF LEVELS
<\A Latitudes, or Horizontal Dis-
Otc es * tances for Difference of Levels
34 o'
I
z
3
4
5
6
7
8
9
10
II
12
13
14
IS
16
17
IS
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
39
40
4i
42
43
44
45
46
47
48
49
50
5i
5*
53
54
55
56
57
5*
6o
Cosines
82904
82887
82871
82855
82839
82822
82806
8279c
82773
82757
82741
82724
82708
82692
82675
82659
82643
82626
82610
82593
82577
82561
82544
82528
82511
82495
82478
82462
82446
82429
82413
82396
82380
82363
82347
82330
82? 14
,82297
82281
82264
82247
82231
82214
82198
82181
82165
82148
82131
S2115
82098
82082
82065
82048
82032
82015
81998
81982
81965
81948
81932
S1915
Sines
60'
59
58
1?
55
54
53
5*
5i
50
49
48
46
45
44
43
42
4i
40
39
3
36
35
34
33
32
3i
30
29
28
26
25
24
23
22
21
20
19
18
3
15
14
13
12
11
10
9
8
I
5
4
3
2
1
o-55
O "1 O J-iO >^">0 "lO *oO *oO
vo "0>0 TJ- ^- m to M tf w w
O
If
li
p
>
O
fe
P
w
PI
B
H
Pw
P
*(MHN0WONi0M000
OCT^ONOHM^OQOOH
CO N O ip -^ f M CT H O C5 O
CM<MCM<MrM<^CMCMCMCMCM^-lrH
QOOOOOOOGOOOQOOOOOOOOOOOOO
M
ON
^Ot^COCSiOCMI-^CMapTjHOOCO
H^OOH^Na(M^N05(M
OiO^MMCTHOOOQONN
O
o\
O
00
WCOWNINOO^OOCqOQOW
9CNHTHOCOt>NCpOip
oooooibicb*bbibbb
000000000000
O
00
COlOH"^0HWON0
WNHOO'+OOWt^HiO'^
pGiOQ0Qpt^OO>0p^CCCp
(MM^iOONOOCOCOO
^^Tt(-t^-t^
^OOOO^^CpO^CMCMrHrH
SO
O
10
(NHO00NC00;(NHt>
iOHN(NGO^OOCTQO^5
*f9NCNrtHOOC5
rHrHr^rHrHrHrHr^r^-lrHrHOO
^J1 ^1 ^1 ^H ^i TJi ^J1 ^Ji ^H ^H ^H ^Ji ^^
I
(MOT)fHCOiO(M0050
OW05OMCOe:OOKOO
HHpOOOOOqOOOQONN
cbrewccroeMCMCMeMrMCMCMrM
cococococococooocococococo
%
O
CO
HNCTNCOOO^O^lO^
N^(MNT)iNNi((MN
QOCOCONNSNOOOOipip
^J1 *^4 T71 *t-jH ^p T-p "*-^ -^H t^H T"f^ "^4 ^r^ "v^
CMCMCMCMCMCMCMCMCMCMCMCMCM
CO
HT)(QOiniOOCOOO00)Q
OOO^COHQQOO^COHOOO
0000000000000
0(M-*OCOOHW100000H
OCONOiO-t^r^HOOO
cm cm cm cm cm cm cm cm cm cm cm cm i-h
cbcococbcccbcbcbcbcocbcfec
O
H
li
i!
go
^O >o O >^o w-io u-> O u-> ""> O
w 1-1 rt H M w ^ <^ io iovo
CO
Departures, or
Difference of Levels
5.
D Deer - 'Level's
TABLE II.
Departures, or
Difference of Levels
>
ft
H
5
W
i
P
O
of
p
H
W
ft
Oyi D Departures, or I ;i 1
O^E *' Levels
34 o'
2
3
4
5
6
7
8
9
io
ii
12
13
14
15
16
7
18
19
20
21
22
23
24
s
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
50
5i
52
53
54
55
56
57
58
60
Sines
'559*9
'55943
559 6 7
56016
56040
56064
56088
56112
56136
56160
56184
56208
56232
56256
56280
56304
56329
56353
56377
56401
56425
56449
'56473
56497
56521
56569
56593
56617
56641
56665
56689
56712
56760
56784
56808
56832
56856
56880
56904
56928
56952
56976
57000
57024
57047
57071
57095
571 19
57143
57167
57191
57215
57238
57262
57286
57310
57334
57358
Cosines
60'
59
58
11
55
54
53
5*
5i
50
49
48
46
45
44
43
42
4i
40
39
38
36
35
34
33
3*
31
iL
29
28
26
*5
24
23
22
21
20
19
18
\l
15
14
13
12
II
IO
9
8
1
5
4
3
2
0-55
*o O *> O o O *AO ^o w>
NO IO ^- ^- W M N 11 M
H
w
ft
Ph
O
O
3
i
ft
O
m
ft
<
1 1
ft
ft
<1
H
fe
O
N
H
g
O
O
GQ
ft
ft
B
H
H
ft
OOOOHHHQOOOOOOO
r-H + O X O (M 'f O X' Q i-h CC O
COH(NtJ(iOCONOh Ox CO
1
On
:
NO'fdOOO^tMONiON
(MM^iOOCNOOOOOHiM
* 9 O N 00 O O H cp ^t p 9
OOOOOOOrHrHrHr^Hf^r^
lOiOiOWiOiOiOiOiOiOiOiOO
ON
00
>0(M00iOO(M00'*O'0HO
C0M(N(M(NHHOOOOO'X
t^xqsprHCvicp^iccpot^cp
3 3 3 l ^ ^ iS ^ L ' IS iS l ^ IS
O
00
O
W00(MOO^0Cl(MOQ0O
TtHMHOOOO-tCOHOGCSO
Hcqmoj^ipoNcpoooH
66605666666666
oococococococococococo^"*
NO
CT^OQOONiiOOOQHCClO
lONOO^HOtHOOOt r- -1
00l>OOaOHi?l(M05^
ocoocococccocococcoococoto
O
NO
O
0000000000000
OG^X-*OOC^X~*OOr-U^
OOOHWWCpWfipipOO
t^xxxxxxxxxxdbx
O
*
Oi-nOrHOOi-OOiOO-^O-H
co^^iOiOCOOt^t^qcqpcpO
(^ ^ (N cq ^ -fq <jq di (fq 61 <^i (fi <>i
(N<M(N(MCTN^(M<M(M(N(NCq
*
OiMQO^OCOlMQO'lOOHN
NHijiooiMiOOINCJOMNO
NQOOOaDCQQOOHHHIN
rHi 1 1 Ii ! 1 1 1 lr- It IHHHr- It 1
O
<*#00<NOOtHX<NOO"*Xt-h
OOOKOOOOIMONO'M'i'N
O
O
cq-^oxoffq^oxQ^i-^o
lOOOOOfflOSt>NNN
lbibibiboooiboibooo
O
B OD
s-3
"o >oO >oO >flO >flO >o O *oO
Latitudes, or
zontal Distanc
Difference of '.
Bori-
esfor
^evels
e c Latitudes, or Horizon
00 Deff * tances for Difference of
tal Dis-
94
T
ABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
O
W
O
w
i
i
H
m
1 i
P
i
w
off
w
p
p
H
t i
H
<1
h3
qk Latitudes, or Horizontal Dis-
OO ^ tances for Difference of Levels
35 o'
i
2
3
4
5
6
7
8
9
10
12
n
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
3
31
32
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
5
51
52
53
54
55
56
57
58
60
Cosines
81915
81898
81882
81865
81848
81832
81815
81798
81781
81765
81748
81731
81714
81698
81681
81664
81647
81631
81614
81597
81580
81563
81546
81S30
81513
'81496
81479
81462
81445
81428
81412
81395
81378
81361
81344
81327
81310
81293
81276
81259
81242
81225
81208
81 191
81 1 74
81157
81 140
81123
81106
81089
81072
81055
81038
81021
81004
80987
80970
80953
80936
80918
80902
Sines
60'
59
58
11
55
54
53
52
5i
50
49
48
46
45
44
43
42
41
40
39
38
36
35
34
33
32
31
3
29
28
11
25
24
23
22
21
20
19
18
3
15
14
13
12
11
10
9
8
i
5
4
3
2
1
o # 54
"0 *o O *o O *A O w-> "O O *oo
vo >o >o <i- ^ w m H M m m
O
II
if
QQ
a
H
2
F
Ph
i i
P
&
O
w
m
B
P
iO<NQP^OCDHN(MN(nN(M
HM^OMOH^^ionqoo
AlrH^-lrHrHrH^H-Hr^r^-lAlOO
GOOOGOGOOOQOOOOOQOOOOOOOOO
M
ON
00
ip-tCdfMqHHOOOOONN
b >~ >~ ibibio-*i(^i(^
00
O
O(N^5ONC0C5QOOHH
'*Q0(MC0O'tQ0NOHi0C5W
wcqq^rHrHcppciQpqpb-cpp
10 o 10 o >o o o
O
vO
05OC5000000OO0ii(MH
^OOOOXX'NNOOLOIO
2322222222222
VO
O
NOTti(MOQOOCOHQOOnH
iOHNWC5^00(MNC0055
6606666666666
%
OOOOCDCqoOrtiHNCOOlOH
COMOOWOOWaOtMOO
cococococococococococococo
%
CO
*<*CS^CS^CDCOCOCOt^<M<Pi-i
TJ1 *^4 "^71 Tp """T TJ1 *^p TJ1 TJ* T^ ^^1 ^ji Tji
CO
WOOnOOiMiOQOH^SO
00 O IO CO r- ICiOOCO^COr- 1 OS 00
6666666666666
HWlOOOOOHCO^CONffiO
C300NOOOt)(00(NHCOO
r 7 Hr T Hr r lr r lr 7 lr r ,r r lr r lr r ,, ' > '
obobccbcobcbcobaocdoob
M
11
if
V <D oO >oO u-io >flO w->o *o O
m m H M wm + + vi o>o
O
CO
Departures, or
Difference of Levels
5
* 8 "' Levels
iiice
ox
TABLE II.
90
Departures, or
Difference of Levels
35 o'
z
3
4
5
6
7
8
9
io
Sines
573S8
57381
S74S
574*9
57453
'57477
575oo
57524
57548
57572
"5759
57619
57667
57691
577H
57738
57762
57786
57809
57833
57857
57881
57904
57928
57952
57975
57999
58023
58047
58070
58094
58118
58141
58165
58189
58212
58236
58260
58283
58307
58330
58354
58378
58401
58425
58449
58472
58496
58519
58543
58566
58590
58614
58637
58661
58684
58708
58731
58755
58778
Cosines
Latitudes, or Hori-
zontal Distances for
Difference of Levels
35 Be *-
Departures, or Difference of
Levels
v> O v-iO ^ O w-io ^n O ^0
VI l^l ^ ^- W M fl fj M II
o ,
>o N O H ?: io N QO o on o i>.
(M w co ^ o o co 1^ t* -/j 35 35 o
rHT^rHrHCh01Cq(^Cq(?qC<JCq(n
OOiOOiOOOiOiO0OiO0
3
O^NOCOOOOliONONO
IO CO H O 30 O -^ JO H Ci X tD -fi
1 KNCOTJHOCOt^OOaOO! 1
66666666666hh
H 00 O W O N "* H X O Ol T- O
Tt^ioOONOOOOOHHiM
^^^^^^^TtHoooo
eococococococococococococo
0000Q000X00OOOC1CJO35
^(NNN^(^(MGNiN<N(NiM!Cq
COHCOOCOHOOOCOON^H
^ 05 00 00 CO GO Ol t^ Ol t* r-H CO 11
OQOOHr- 1 <c^ <C^ CO CO TiH O
<fq<^cbcbcbcbcbcbcbcbcbcbcb
NMO^OO^NlMNCOQOil
o * n h 10 oo ^ 10 a o) c r. co
w w n cp cp cp -^ -*h o lo o ep
r-tocicot^OTjiaoi-iogogjco
NOHTdOOr- 1 CO O O JO O
ijTtHOlOOOOOOONNN
OOOOHJOiONOHCHOX)
W^ONOOQOHCOiiCON
NNNNNNCCCpqpOCXX V
11
J z
o w-io "> o oo vq oo v-,o
c * Latitudes, or Horizontal Dis-
04 De8r# tances for Difference of Levels
96
T
ABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
m
>
Pi
W
&
H
A
M
Ph
CO
W
O
H
W
ti
fi
1
W
Pi
w
P
p
H
h- 1
\
n/j _ Latitudes, or Horizontal Dis-
OO es ' tances for Difference of Levels
36o'
2
3
4
5
6
7
8
9
IO
ii
12
13
14
IS
16
17
18
19
20
21
22
23
24
as
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
5o
Si
5*
53
54
55
56
57
58
60
Cosines
80902
80885
80867
80850
80833
80816
80799
80782
80765
80747
80730
80713
80696
80679
80662
80644
80627
80610
80593
80576
80558
80541
80524
80507
80489
8047a
80455
80438
80420
80403
80386
80368
80351
80334
80316
80299
80282
80264
80247
80230
80212
80195
80178
80160
80143
80125
80108
80091
80073
80056
80038
80021
80003
79986
79968
79951
79933
79916
79898
79881
79864
Sines
6^
59
58
5 l
56
55
54
53
52
5i
5o
49
48
4 l
46
45
44
43
42
4i
40
39
38
36
35
34
33
32
31
30
29
28
26
25
24
23
22
21
20
19
18
3
15
14
13
12
11
10
9
8
I
5
4
3
2
1
o'53
O 100 o O >oO 10O 00 >00
vo loio^-^mnn c hi hi
CO
10
11
GO
w
p>
m
a
Pi
1
s
of
p
p-1
iMOO-^oOiMOQNiOQOHM
O H CO Tt< IO t> OOO H (^ O IO O
C5iX)NiCfMCTCqHOC5QO
ooooooooooood)
OOOOOOQOQOCOQOOOQOQOOOt^t^
ON
CM-fNOCqiONOH(MTHN
HCOCOOOW^OOHMiON
t>oipip-^ep(>iMHoaicp
cq "h <fi cq oq oq cfq ch cq cq cfq i-h rH
l>i>t^i>t>.t^i>.t^i>.l>.t^fc^i>.
ON
00
(MW^ioOOOQOOOOHO
(MOQOH-tNOnNOWCO
NffiipiprJiMcO^HHOffiQO
^^^^-^-ii^-iw^-^cbcb
00
HHHHHOOOflOSSOil
M N -J 10 rr N O tJ 00 (M O O
00>O^CO01(NHOOOQ
HOOOCOICMNONIOCOHOO
TtfOWOOOOOOWNINIXMNH
lp-^-^MMWNHHOOqJO
ccobobrcb&aDc&dbb~t^
VO
O
10
HOOLO(MOOW050(MOiOH
^<tMNCTHHHOOO01
OOOOOOOQOOOOOi
"^ "^ '^ ^H tJH "^H '^ *^ '^ *^ Tt* CO CO
O
h(mqowt)(ooou;oo
w m .'1 w h h h o o o c5 o
(?q^(JqCq<fq^(NCq(NCN(?qrHrM
cococococococococococococo
HLOOMN(M0-^NH00
NT)iHOOTt(H050e50QOiO
CT^^rHrHrHrHOpppCiO
-*H "^ ""+ 1 "^f "^ "^f "^ "^ "^ tJ^ tJ< CO CO
CNOq(MG^(MCq(MCMOq(M(N(MCq
c*
ococooi(?q^t>0<?qioouoco
rHrTirHrHrHOpPPPPPP
H
OOONOiO-HWCCfMHOQQO
ccdbcbdbcdbccbdbdbt>i>
HI
li
"o ^ O ^ O mo oO 100 w-o
HI HI N M fOCO^T^-Wl IOVO
T~i TV-ff
Departures, or I
Difference of Levels 1
sr
5 es: " Levels
TABLE II.
97
Departures, or
Difference of Levels
>A
g
h
1
3
1 1
P
M
m
s
1
w
p
q/j _ Departures, or Difference of
OO De * Levels
j6o'
i
2
3
4
5
6
7
8
9
IO
ii
12
*3
14
15
16
17
18
*9
20
21
22
23
24
25
26
27
28
29
30
3*
J2
33
34
35
36
37
38
39
40
4 1
42
43
44
45
46
47
48
49
5o
5i
52
53
54
55
56
57
58
60
Sines
58778
58802
58826
'58849
58873
58896
'58920
58943
58967
58990
59014
59037
59061
59084
59107
59131
59154
59178
59201
59225
59248
59272
59295
593i8
59342
59365
59389
59412
"59435
'59459
59482
59So6
59529
59552
59576
59599
59622
59646
59669
59692
597i6
59739
59762
59786
59809
59832
59856
59879
59902
59926
59949
59972
59995
60019
60042
60065
60088
601 1 2
60135
60158
601 8 1
Cosines
60'
59
58
11
55
54
53
52
5i
50
49
48
46
45
44
43
42
4i
40
39
38
S
35
34
33
32
3i
30
29
28
26
25
24
23
22
21
20
19
18
\l
15
4
13
12
11
to
9
8
I
5
4
3
2
1
0-53
O ^ O *o O 00 ^>0 oO 10O
VO V)lOi + MMtl M M m
if
IS
m
A
H
>
a
O
3
%
P
g
W
O
K
1 1
P
O
N
1 i
a
a
es
of
H
P
P
s-<
1 1
H
3
000-^HQOiO(Mfl50(MC5iOH
N C H CO rfl O "JO O H ^ -t 3 00
*>- X O -71 ?1 w Hh ip t^ qp p r^
30O)6Qa6666di665
KJiOiOiOOCiOiOiOiOiOSO
on
O O ri H C^l ?M W TO "f -^ IO IO
ooHwcoi(iooNa)CiOH
lOiOiOiOiOiOOifliOOiOOiO
00
WNHW5C5(MOOWOO<M0
(MHHQOiaONNOOOTt*
prHCqcpcp-^ippt^QOPPrH
NNNNNNNNNNNQQob
00
ionht)(oooohco^os
^(MOONiOCOHCOOOiliM
rH(NW<TOTtlipipi>.CpqpC5prH
vo
NQOOOOOOOiOGOOOO
ib 10 10 10 ib ib 10 ib ib ib
cocococococooocococococooo
vo
O
CiQOOiQ't*CO'-lQGOO'+COr-l
QOtOOfMOO^OiOHNMO
cp-^ipipcONopaDQr. OO
6po6c5oooc3Qo66
<M<MC^CMd<M<?qcq:>jcqcqcoJ5
%
Hooio^oofMOoroooe:
H IO O C3 ^ O ^ * W X' W N
ip 5j 9 9 9 t> n op 00 9 9
WMWMMcbo:?OM-+^
%
^O^O^OiOOiOOiOOrd
99NNi>opopop9a!00
t l 1 1 il 1 IHr- 1 i 1 iH i 1 i Ii 1 i- i 1
C<">
O
COOCOOOOOCOOMO
NN0000000000OO05OOO
rH^HrHrHrHrHrHrHr^lrHrHCJq^
O
OOOHOJIONOOO(MM>ONOO
NOOHPlM-tiONQOQOH
QOQO99O9OOO9999
ibibibibibibibibibibiboo
il
|3
^O "o O O *o O *o O v->0 ""> O
ih w c* c* co ^ <^- wn "TO
Latitudes, or ]
zontal Distanc
Difference of I
lori-
es for
revels
eq Latitudes, or Horizon
OO Deg >* tances for Difference
tal Dis-
f Levels
98
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
37 o'
i
2
3
4
5
6
7
Cosines
79864
79846
79828
7981 1
79793
79776
797S8
79741
79723
79706
79688
79670
79653
79635
79618
79600
79583
79565
79547
79530
795 1 2
79494
79477
79459
79441
79424
79406
79388
7937 1
79353
79335
79318
79300
79282
79264
79247
79229
7921 1
79193
79176
79157
79140
79122
791 05
79087
79069
79051
79033
79015
78998
78980
78962
78944
78926
78908
78890
78873
78855
78837
78819
78801
Sines
4
3
2
1
0-52
Departures, or
Difference of Levels
I
C
n:
9
o
W
c
CO
P
P
H
H
3
37
Degr.
Latitudes, or Horizontal Dis-
tances for Difference of Levels
TO <j-iO oO *o O >oo *o o
wi<o ^ ^ to w rt N w m
o
COOOOOfM-^ONQOOOOH
ONOOOHOqco^COOQOOO
OOl^OCpipTjHCpCNrHpCSGpa)
N0005OH(MH(M(NCTNHH
NQH^OOOOIM^OOOO^
C0t^l>-CCiO^Tt<0tiC<li 1000
OHOOOaoDOiO^!MH
ONkoooowoaooooHTii
Qpqpt^O'PO-^OpcpS^rHrHp
^mcqoooNTiicoHoooMH
O^OOC^OCiOOt-O^OOCNiX)
Oiqpt^t^cppip^opcpqqq<jrH
QOXJWON^HOOlOHQO^H
HOHOO"CO-*NitQ0WQ0
HOO^O(MNCOC5^0>00
COOO^OWSHCOtMNKO^O
CiOiqpqpcpt^b-cpcppippo
rHrHrHpHrHrHrHrHrHrHrHrHrH
oococooococooococococococo
CiMOO^NO^NH-^NO
OCOOOOiONON^OqQOT)(
OffiOOOOOOOOONNNCOCOO
COICOOO(MONC5(M^OCOO
NtOMCTOQOOilMHQNO
ppCDqigiopqpGpqpopt^t^t^
OOOOOHCTMiOCONQOOiO
oot>oco"C^n(NHOoooo
II
52 Deff -
Departures, or Difference of
Levels.
TABLE II.
90
Departures, or
Difference of Levels
37 o'
z
3
4
5
6
7
8
9
10
Sines
60181
60205
60228
60251
60274
60298
60321
6o344
60367
60390
60414
60437
60460
60483
60506
60529
60552
60576
60599
60622
60645
60668
60691
60714
60738
60761
60784
60807
60830
60853
60876
60899
60922
60945
60968
60991
61014
61038
61061
61084
61107
61 1 30
61153
61 176
61199
61222
61245
61268
61291
61 3 14
61337
61360
61383
61406
61428
61451
61474
61497
61520
61543
61566
Cosines
Latitudes, or Hori-
zontal Distances for
Difference of Levels
37
Departures, or Difference of
Levels
o
k->0 >o O ^ O "> O *oO **"> O
HOO^ffilOHOHNflNH
OOOOOOOOi IrHt I 1 I r- 1
0000000000000
5c
i I CM
**'* ii i< t)( tji t)( -+ 10 10 o
iOU5OOiOW5iOiO>OiO0OiO
U5Q0HWOOHWONOHC0
^CO(NHOOC500N&OiO
H(NW*OONNQ0ffiOH(N
N00C5H(M!MC5^i05OO
O00NOMHOt>10C5rH
rH^^co^ipoot^cpop
cq c-i <?q cq <ri cq cq <?q cq o-i <fi 00
C5QQOONOOIOt)((MHO
ONirtOOiatMOOWONI*
rHrHCq0pcpTtiOpipt>QpCpCi
cocococococococococccococo
HONi0NO00O05HOiOC0
O-^OO(M00C5Q0HO^C0
0000000000000
cococococococooocococococo
05OiOCTQ0^ONWOOHO
OHH(M(MC5C005-^'^0>OC'
<MCqCM<M<MCqoqG>lGN<M<N<MCM
"^O-^O
,oo<MOO(MOQe:ogeoN
OOfHrlH^(Nqqe5 05^f f
(cbcbcb(cccccb((aDdDa)
OOWCDO(M5(X)H^ISOW
MOOOOfNWNOtM^OffiH
OOOHHtrlHH(>l(N(N!NC5
00 O H 05 -^ O CO
HCS^IOONCO 1 -
OOOOOOOOHHHHH
?3
"o viO > o **> o oO <j-iO "> o
52
Latitudes, or Horizontal Dis-
De8r " tances for Difference of Levels
100
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
38 o'
z
3
4
5
6
Cosines
78801
78783
78765
78747
78729
7871 1
78693
78676
78658
78640
78622
78604
78586
78568
78550
78531
78514
78496
78478
78460
78442
78423
78405
78387
78369
78351
78333
78315
78297
78279
78261
78243
78225
78206
78188
78170
78152
78134
781 16
78098
78079
78061
78043
78025
78007
77988
77970
77952
77934
77916
77897
77879
77861
77843
77824
77806
77788
77769
77751
77733
"777 1 5
Sines
0-51
Departures, or
Difference of Levels
38
Latitudes, or Horizontal Dis-
ff " tances for Difference of Levels
HH(MSqHHHOC5QQNffllO
OHNMTJ*Ot>N0005OH
t^t^t-t>.t>.t>-i>.t^ t>. > i>- t~- i>-
6666666666660
HONOMH
^ O Ci !M iO 00 -
OQqDQONffiOLO^MOONH
co 6* 6* <fi & i 6* <h 1 <^ 1 cn <ri ^
't^qohio05<NCOO
<-* t lO <M
f7-ipoc:ciopb~b-cpioip^"^
HOCOOlOHNNNMOO-t<0
00(MNHOHiCO-^OW00(M
(^(TqrHrHppciCiqpt^t^cpcp
NNNNNN6066666
OiOHOQiOOiOO-^oocON
0OHCO?iNMCOWO'fQ0
^wspffq^HHOOooQcp
666666666obobobcb
cooococococooocococococooo
ip^^^CpOOCO(^J<?<lrHrHrHp
1 lr IHr- IrHrHrHrHrHrHrHrHrH
cococococococococococococo
^HCOOWONOiM03-<#H
<M<Mq<N<nq<M<M3q<Mq(M
OfN^COCCON^OOOOlHCO
^(^OOONkOWHOiNCOTH
OHCqW^lOCDNXOOHH
' iJ(M(NHO05 0100N
coooqpqpopt^t^t^t^
o <flO >oo ^o *n o <> o >oo
IH w N r) t*"> to t^- rj- U-> i^\o
o
00
51 De -
Departures, or Difference of
Levels
TABLE II.
101
Departures, or
Difference of Levels
m
>
ft
O
g
O
9
p
t *
p
M
1
H
p
OO _ Departures, or Diftere
OS De &' * Levels
nee of
j8o'
2
3
4
5
6
7
8
9
IO
ii
12
14
*5
16
17
18
19
20
21
22
*3
24
*s
26
27
28
29
30
31
3*
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
50
5 1
52
53
54
55
56
57
58
60
Sines
61566
61589
61612
6163s
61658
61 68 1
61704
61726
61749
61772
6179s
61818
61841
61864
61887
61909
61932
61955
61978
62001
62024
62046
62069
"62092
621 1 5
62138
62160
62183
62206
62229
62251
62274
62297
62320
62342
62365
62388
6241 1
62433
62456
62479
62502
62524
62547
62570
62592
'62615
62638
62660
62683
62706
62728
62751
62774
'62796
62819
62842
62864
62887
62909
62932
Cosines
60'
59
58
U
55
54
53
52
5i
50
49
48
46
45
44
43
42
41
40
39
38
36
35
34
33
32
31
30
29
28
11
25
24
23
22
21
20
19
18
\i
15
14
13
12
11
10
9
8
I
5
4
3
2
1
0-51
O flO ^ o o O o O O
VO "o>o^.^mm el HI M
H
li
If
|3
Q0C5O(^C0k0ONOOHC0
lOONOOHWM^ipNQOO
i
OS
cwoooH'fooHcooNai
O H H H (M W "M 5* CO OJ 5 CO 5
^hipOt^qocsprH^O^OO
ibibibibiboooooooo
00
iO^M(NHHOOODNOO't
CNOtTfipOb-CpcpOOr^lCNOO
05666666666666
00
9
P4
H
p
OOSNOOOO0i0^e0M
CONiOMHCONiOWHCiNLO
OHNM-^^ipcpNOOGpCJO
cbcbcbcocbcocbcocbcbcoco'i*
VO
OOOtsO-^CTHONiOMHO
^ N * H QO >o H 00 O (M r. 1.0
9 h ct ct m f f lo 9 N
ONNNNNNNNNNNN
cocococococococococccococo
O
w
H
M
P
O
S3
C0O00>0(MOOMOOe5OO
QOitQlOrHOtNOC^COOO
NqpqpOOOHHfNfNM'^'il
OOOOHHHHHHHHH
cococococococococococococo
O
5-
O(Nfl0^05U5HOHN!MQ0W
(NNHOOOOi*C5X(NN
OONNCCCOOOQOOHH
<*1
O~*00C0t>.r-li0O^a0O}C0O
Tt<ipiptpooot>t>b>-qpqpQp
aocbdbcbdbdbcoro&dbcbccdo
CO
3
O
of
W
P
p
H
H
<
Hi
MOO(NiONOWOQCH-)(0
HMOCOO(MONCJH^OaO
O
N00ffiH(M^ifflO0DOH'M
6666666666666
M
11
II
*b ^0 "> wio <^>o ^o
00
CO
Latitudes, or Hori-
zontal Distances for
Difference of Levels
51
1 Latitudes, or Horizon
L De v tances for Difference
tal I
fLei
)is-
els
102
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
m
P
>
3
3
F
&
p
a
%
H
m
> t
P
J
H
O
S3
O
w
PS
of
p
p
H
H
<
qq Latitudes, or Horizontal Dis-
Ov *' tances for Difference of Levels
39 o'
i
2
3
4
5
6
7
8
9
IO
II
12
13
14
15
16
17
18
J 9
20
21
22
23
24
25
26
27
28
29
30
3i
32
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
50
5i
52
53
54
55
56
57
58-
60
Cosines
77696
77660
77641
77623
77605
77586
77568
7755
77531
77513
77494
77476
77458
77439
77421
77402
3S
77347
77329
77310
77292
77273
77255
77236
77218
77199
77181
77162
77144
77125
77107
77088
77070
77051
77033
76996
76977
76958
76940
76921
76903
76884
76866
76847
76828
76810
76791
76772
76754
76716
76698
* 7 fe
76660
76642
76623
76604
Sines
60'
59
58
3
55
54
53
52
5i
50
49
48
46
45
44
43
42
41
40
39
38
\i
35
34
33
32
31
30
29
28
3
25
24
23
22
21
20
19
18
3
15
14
13
12
11
10
9
8
I
5
4
3
2
0-50
vo >o o ^- ^(- to to c< N M M
O
O
w
3
>
J
PR
w
M
p
of
p
3
p
O00H05NiOCqON-*HQ0-<*
H^WW'fiOCNNOOOOO
t>.b-t-b-b-i>-t^t^66666
ON
C0rH00<MC}CDC0CSO<MC0C0
T|iCONOH(M^CDNQr- I(Mt|(
OCONOOiO^M^HHOQ
ON
O
00
CqQOiOT-(CO'*OCD(? ; H^'MOOCO
NONONOWiOOOOWiOQO
OOCOCDOOOOOOOOO
00
OO<MI^CC00000i^05Tt<0iC0
OMNO^NHTi<OOHlOQO(M
^cpcq<^HOOoqpcpNOO
VO
OTPOMOOWNfMCOOiOOfM
CTNHOOOffiiiOOWNHO
(pip^^^COCTCNrHrT-ippOi
0006666666660
^^ ^^ ^^ ^^ ^^ ^^ "^^ ^^ ^^ "*^ ^^ ,,! ^ "*^
NH100WNH0((N>00^
l0HOHt>(MXM00-^QT((O
OOOONNOOiOW^7Cpcp9
<^<cbcc<db<cbcb<x><x>c
C0C0C0C0C0C0C0C0CQC0C0C0C0
*0
<*-
OO^HNCOOCtMQlOHN^
OOOOOOqpqpNNNOO
HHH0666666666
eocococococococococooococo
5-
to
HOOiOCOON^NaOMOOO
ooN^fNqqHHHOOopo
MMMcb6wWMMWM(^
to
O
W-^OCOOHW^iONOOOH
^CNOOOOiOCOHONlO^fM
ibibibiboobbibbibibo
HHr- 1 1 li Ir-Hi IHHr- It IHH
O
HNCO^OVOONQOQOOlOO
I^OiO^COCM hOOOONNO
b-t^b-t^l^b-b-b-ppppp
1-c
g-ISb
w MM^NcotOrhTl-ir) u-)VO
On
CO
Diffe
partures
rence of
or
levels
5
*. ""*" C 'Levels
TABLE II.
Departures, or
Difference of Levels
39 o'
i
2
3
4
5
6
7
8
9
io
Sines
62932
62955
62977
63000
63022
63045
63068
63090
63113
63135
63158
63180
63203
63225
63248
63270
63293
63316
63338
63361
63383
63406
63428
63451
6347J
63495
63518
63540
63563
63585
63608
63630
63653
63675
63698
63720
36
63787
63809
63832
63854
63877
63899
63921
63944
63966
63989
6401 1
64033
64056
64078
64100
64123
64145
64167
64190
64212
64234
64256
64279
Cosines
4
3
2
0*50
Latitudes, or Hori-
zontal Distances for
Difference of Levels
Of| ^ Departures, or Difference of
39 De *- Levels
O 'flO oO >oO v>o "> o
>0 -t + <*i to N M
o
(MiOOOOCOOOOON^ONO
eo -* 10 n oo o o -M ^ -)< o *o qo
OOHNM-^ONCpOOHJI
OOO660OOOOOOO
OONCO>OOSOOOOOHN
cpt^qpcsprHqqcp-^ipob-op
TtiWfNHOOCONOO'tMq
00Ti<ipOt>b-QpCiprH<NCpTr
OOOOOOOOrHr^-lrHrHrH
(MHOC500NiO^(MHONO
lOOJHOOO'tlMOOQ'OWHO
9HNN9
^H ^^ *^H ^JH '^4 "^4 ^7^ ^4 ^^ ^^ ^^ "^^ "*^
ON0(NONIO(MG10MOOO
to <m q o ?: o o c : CJ o cj o o
t>.cpqpCipprH<>iCNcp^ipip
r^t^t^i^cfcdooboboO'Xobooob
cococococococococococococo
O(MCii0rH00"*OC0(MC0Tt<O
0(Mt>O^OOHN(M(X)^
rHrHrHrHrHrHrHrHrHrH<f*<^<fj
cocococococococooococococo
cooocooocooocooo
NHCOOiOOl^OO
COOOCOOOCOOOC^t^OJ
10 io < o t^
dooboOOOOC5C50C20105005
HtOQHMO
^ O 00 H CO o
CD OS <M ^ t> '
00OM0NO(N ,
ipCDOOCpcp^t^t>b-qpqpop
CO^ONOOOHCTM^ONOO
O0666666660OO
50
Latitudes, or Horizontal Dis-
" Deff " tances for Difference of Levels
104
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
4oo'
Cosines
76604
76586
76567
76548
76530
7651 1
7649Z
76473
7643-6
76417
76398
76380
76361
76342
76323
76304
76286
76267
76248
76229
762IO
7619I
76173
76154
76135
761 16
76097
76078
76059
7604I
76022
76003
75984
75965
7594 6
75927
75908
75889
758 7
7585I
75832
75813
75794
75775
75756
75737
75718
75699
75680
7566l
75642
75623
75604
75585
75566
'75547
75518
75509
75490
75471
Sines
60'
59
58
%
55
54
53
52
5i
50
49
48
46
45
44
43
42
4i
40
39
38
11
35
34
33
3^
3i
30
29
28
26
I
5
4
3
2
1
0-49
Departures, or
Difference of Levels
d.fl Dee Latitudes, or Horizontal Dis-
T=v * tances for Difference of Levels
u
O mo *^> O 00 100 o O *r>n
r)(HNCOC53HCOHOHC&H
OOfMtNHOOOONCiOf
cbcbcb<bcbcbcbibibbbibib
CO O O r-l
<* CO b- 05
05 00 t^ CO
cb go 00 00 '
CD CD CD CD
p^COC<JrHCppC5
b-
o
00 00 00 co 00
CD CO CD CD CD
'f GO CO GO CO b- 1 I lO C5 CO b-
OOOMiOOOOMiOQOONkON
* CD lO <# CO
GNGNrHOOOCOb-
1 I r-i H t I O '
CD COCO O CD
> O O O O O O
> CO CD CD CO CO CO
GN1 C5 <M CD 05 <N CD O <M O O CO
cpip^^cocqcNrHcppocccp
cocbcbcbcbcbcbcbcbcbc^cqc^
(MNO"*SHIOOOH^NOW
C0Oi0 05C000(MC0r- iiO05-fCO
ppcOb-t^ppipip^cpcpC^
o ib b ib b ib b ib >b ib ib b 1
TT Tr "^ T^ t}< ^1 T^ *^ t^ "^ t^ "^ t^
CT0!HT)iNOWiOXOMiO
OiOOOHO(NN(NNMQOeO
CpCNGNrHrHCppcppcpcpt^b-.
cbcocbcbcocbooi>-b~b-b-b~b-
cococococococococococococo
g^NOCTT)<OaOO<M^O)QO
"*COGN!05iOiib-'*OCD<MGO
cpcpipip^^^cpcocpc^GNi-H
0000000000000
cococococococococococococo
H?JiONfflOiM-*iONXOH
05C5g5Cpqpcpcpt^t^t^Opp
HfiqejioosaoQOHffjM"^
(NOOOO^NOOONiOCOHOJ
TOMNINfNWNHHHHHO
ibibibibbibbibibibibibib
OrHC<l<MCOCO'-HlO-OCDCDt>.b.
OiO"tW!MHOOOONOiOT|(
CD CD CD CD CD CO O O ip ip ip O lO
b^b^b^b^b~b-bt>.b-b-b-b~b~
o v no *o O ^0 *^-> o oo ^o
AQ _ Departures, or Difference of
*v s ' Levels
TABLE II.
105
Departures, or
Difference of Levels
4C0'
1
2
3
4
5
6
7
8
9
10
11
12
J
14
15
16
7
18
9
20
21
22
*}
24
25
26
27
28
29
JO
31
32
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
5o
5i
52
53
54
55
56
57
58
60
Sines
64279
64301
64323
64346
64368
64390
64412
64435
64457
64479
64501
64524
64546
64568
64590
64612
64635
64657
64679
64701
64723
64745
64768
64790
64812
64834
64856
64878
64901
64923
64945
64967
64989
"65011
65033
65055
65077
65099
'65122
65144
65166
65188
65210
65232
65254
65276
65298
65320
65342
65364
65386
65408
65430
65452
65496
65518
65540
65562
65583
65606
Cosines
60'
59
%
55
54
5?
52
5i
50
49
48
46
45
44
4?
42
4i
40
?9
38
36
35
34
13
V-
3i
30
29
28
II
25
24
23
22
21
0-49
Latitudes, or Hori-
zontal Distances for
Difference of Levels
4-0 eff. J,, 'i M1 ' llllv s wp Difference of
^* v Levels
o 100 viq oo oo ^o "">o
OOHjqcO-tiOiOOOOOO
QOClOHtNMidOONQOCiO
t>l>-OOCX)QOQ0QO0OQ00OQO
OiOiOiOUJiOLOiOOiOiO
(MHOC5NOi.o-t::c (
t(<OCON00OOh(M
5> r^io
o n 10 01 o 00 o 00 h r. n t ^
OOH(Ne5M'<tO'OCNQpO
QOtHhNtH^
C?MOOMOO00
> i>. co ci
<N 30 CO
w 00 o so
10 O Nt> cp o o o O h ?r;i ^
xxxxxxxooocscbes
cococococococococococococo
OiOHCfMSCMOOCOQOWQOM
TtfOiOOCOHNCqQOOOCi^O
pH rH <OJ CO M^^ipiOOONCC
(fi bi 0-1 en bi bj b i bi 01 oq oq oi oq
cooocococococococococococo
r-H o <* x co 1^ oi h o 05 -r
NNCOCpcpCiOOOr-iMHCM
10 b 10 ub ib b o 6 6 6 i i i
o^oqoioqoioioioioioioioioq
MHOOOHlOOOHeOOH^X
oqcpcpcp^'^-*ipipppcpo
OOOO^'OOCJHWIONOH
W5 N O <M "t O X H K C 1^ Ol
QOCpCiCiCiCJOppcppp-H
(Oj oq 01 oq oq bi bi cb co 00 co 00 co
is
i -
2^
OOOOHISM^CNXOOh
(M c: ic o t^ x 1 ' 01 co >o
Tt* * ^t -t -* -t 1 ~i< 'p o 10 it 10 10
49
Latitudes, or Horizontal Dis-
^ tances for Difference of 1 .
106
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
41 d
i
2
3
4
5
6
7
8
9
10
Cosines
75471
'7545*
75433
754H
75395
75375
75356
75337
75318
75199
75280
75261
75241
75222
75203
75184
75165
75146
75126
75107
75088
75069
75050
75030
7501 1
74992
74973
74953
74934
749*5
74896
74876
74857
74838
74818
74799
7478o
7476o
74741
74722
74702
74683
74664
74644
74625
74606
74586
74567
74548
74528
7+509
74489
74470
74451
74431
74412
7439^
74373
74353
74334
743H
Sines
0-48
Departures, or
Difference of Levels
41
Latitudes, or Horizontal Dis-
^ tances for Difference of Levels
O >oO vr>0 v-iO *"> O O >oO
VO >o >0 ^ + M Cl O M M
O
NN00Q000C5C1OOOOHH
^rocMrHppXJ^t^pip-^cp
ncooosqohi:tJlonco
pxt^pip^^cpCMi-HOOX
t 1^- b- 1-- b- t-- r^- b- r^-. t^- b- O O
SOiNOiCO(M>ONOH
No^wNOHt:ooooc:io
^ :: 01 h o c 9 cp n o o 10 ^
666666666666q
OOOOOiOiOiOiOOiOiOiO
O Cv (M C C ?>\ iC Ci (M lO CO CM
Op t^- p p p Tfl Tf cp CM CM i-H p O
CM CM CM CM CM CM CM ^M CM CM CM CM CM
COkOOOOKiONO^-fiONOO
r-H ic a CO I- -M
00 CM
CM CM r-t r-H O O
O "* X
X X t^ t- cp o
ONON^ONOHCC^ON
ccoo^o^cmr.cousoio
t^ppipip^-^opcpCOCMCMrH
cooccooococccccccocococcco
COOfNiHONCOOHCmnOL'S
00 o h n w :: 10 'N 00 -+ o ^) cm
OOCOCOOOOCMCMCMCMCMCMCMCM
HCM^tOOOOOOOHIMCO^'f
rj< 11 X IO CM O O -f 1 I x 10 CM a
Ppipip^^^^^cpcOCOCM
CM CM CM CM CM CM CM CM CM CM CM CM cm
CM CM CM CM CM CM CM CM CM CM CM CM CM
T)HOONOOQOQOOH(N(aM
ONiOWHClNOilMOOOO
OOOOO9 9QQQCiC00p
t^ t^ X X
TtH CC CM i
1000 o o ^
OCiOOHHHH
cixx
"^1 "^i ""^ *^H T"p "^H
48 De s-
Departures, or Difference of
Levels
TABLE II.
107
Departures, or
Difference of Levels
m
3
3
>
hi
3
3
3
p^
1 1
p
of
3
P
H
1
p
4.1 De* Departures, or Difference of
** Levels
41 d
i
2
I
4
5
6
7
8
9
lo
ii
12
13
4
15
16
17
18
*9
20
21
22
23
24
25
26
27
28
29
30
3i
32
33
34
35
36
37
33
39
40
4i
42
43
44
45
46
47
48
49
50
5i
52
53
54
55
56
57
58
&
Sines
65606
65628
65650
65672
65694
65716
65737
65759
65781
65803
65825
65847
65869
65891
65913
65935
65956
65978
66000
66022
66044
66066
66087
66109
661 3 1
66153
66175
66196
66218
66240
66262
66284
66306
66349
66371
66393
66414
66436
66458
66480
66501
*S 523
66545
66566
66588
66610
66632
66653
66675
66697
66718
66740
66762
66783
66805
66836
66848
66870
66891
66913
Cosines
6c/
59
58
3
55
54
53
52
51
50
49
48
46
45
44
43
42
4i
40
39
38
3
35
34
33
32
3i
30
29
28
26
25
24
23
22
21
20
19
18
3
15
14
13
12
11
10
9
8
I
5
4
3
2
0-48
^o 100 oo "-o >00 oo
voiOiOTJ-^totortNwM
O
00
u
GO
S
w
3
1
&
P
M
P^
W
I
t 1
P
H
fc
O
1
O
O
af
5
H
H
<!
O O iO iC -f W (M h O 00 N C 9!
O ^H N M -+ >0 53 t- OB X ^OH
CNlOCSOHWOOiiirjOQOO
ON
IO -* CO rH Ci 00 CO T* 11 O J > -t Ol
3 -* -r -* M eo r: co cc S sq -m -m
OrH^cpTtiipOb-qpciO-T-oj
6ooooo66ji6666
OOOiOiOiOOiOiOiOOwC
ON
00
>000)iO(MONiONiO
00 t> c -t t: c-i h qo n -t ::
^ipONODOOOHMrjiiip
<n <* cfi <?q oi ;>i 05 02 6 02 09 02 03
00
^HoO'tHNWOcwxnc:
(MONLCMOOOCKhX'- 03
ClOOHfNWep^ipOONOO
t^ ^1 *^i tji ^4 "^i ^^ "^^ t^ ^1 Tip ^^ -^H
O
VO
noicHOCTScqooMQo^oo
O (N 35 w c: o 1 GO O H X )*
Wit^OOONOOCOOOOH
66666666356666
csoococococococococo-^-^'*
XMN(?qOHiCO-f<X(MO
OOHOiNNCJoOiiO'fOiO
CCOpS^CiOOHHOlCqW^Tti
NcqiyicqcococoeacQeboscbw
cococococococococococococo
O
U1
NCO^NHLOOO<MiOOO(MiO
* 00 co n h -fO :: n i
cqcqcpco-^"-t<ip*oioc30b~b-
666666 6 666666
*
to
HiONOCOOOH-JfOOHil
XHTfXH'+NH'tNO^N
pt^^i^XXXppppp
635.66006606666
Hr- 1 1 1 1 i 1 1 1 Ir-Hi IHH(MM
to
cm ^ op x 0? - f-i 05 x
66666 6 eo 666666
HIMNMiiOONXaOOH
CN00CO- l '5l??-*ON X O
10 w' w op p p p p
6 6 6 6 6 cDocecDcocob
Is
if
h
"b "flO oO >oO ^ O *<> ^o
II M N N MM ^ + >0 wivo
Si-
Latitudes, or Hori-
zontal Distances for
Difference of Levels
4
ft Latitudes, or Horizon
5 ff * taucefl for Difference c
tall
fLe
vels
108
TABLE II.
Latitudes, or Hori- I
zontal Distances for '
Difference of Levels
Cosines
74295
74*75
74256
74*37
74217
74198
74178
74159
74139
74100
74080
74061
74041
74022
74002
73983
73963
73943
739*4
73904
73885
73865
73845
73826
73806
73787
73767
73747
737*8
737o8
73688
73669
73649
73629
73610
73590
73570
73551
73531
735"
7349 1
7347*
7345*
7343*
7341a
73393
73373
73353
73333
733H
73*94
73274
73*54
73*34
73215
73195
7375
73155
73135
Sines
741 19 50
0-47
Departures, or
Difference of Levels
42
Degf.
Latitudes, or Horizontal Dis-
tances for Difference of Levels
E;;
I =
If
* 1 r-i r 1 oi oi o-i q SR w co so So
CO (N iH p C5 op t>- p O tjh CO Ol 1 I
^^^^cbcbcbcbcbcbcbcbco
>ONOff)WiOOOOOOHH
Q0C3OMi(oOSXOH(M
xt^^cpip^cpqqr-ipocsoo
6 6 6 6 6 6 6 6 6 6 o o
0000000000000
H ^ 10 00 h (M w >o 3 o K on
lo n o h co o 00 o irn o 'X o
r^cpoqqqrHpGiClCpb-OiOiO
GZGiCids&GiVDOOOOOOCDOCCC
o c io 10 o 10 io >o o c 10 LO o
ppqpopt>.ppO'*^cpc<ir-i
(OTrHrHrHrHrH^-lrH-l-li^-I^HrH-H
Q0OH5i(ONNOOOOH
"^T "^ "^ '^ "^ "^ "^ "^T "^ *^ T^ "^ Tt^
NCOOH(MCOi<T)(OOONN
lOOlOHOHOHfflHffiHO
HHOOOOaoqDNNOOip
t^r^^b-oo 0000000
cococococococococococococo
losoooooHincqwco^^
(N ^ O N W O O h N Q O
NOOOiCi0^^i<COcO(MiM
o o
J^ -tl
(NNCqWHHHOOOOOO
53 01 6q oi -ii cq tfi oq eq cq n ,-h .h
G^c^cM(M<?qo^(^oq(MOqc^oqG^
WCOTH-fHOiQ'OCOOONNN
O ^ (M O X O t)( (M O 00 O * 'M
COGpOOCONNNNlNOOipo
Tp ^1 "*^ Tp T^ "*^T ^T ^T "^T *^ "^H ""^ "^"p"
HHHH
r-< Cq Oq (M Ol CO CO CO CO CO CO CO CO
co 01 h o a co s o 10 't ^ 'M h
^^^^cpcpcocpcococococo
M M H PJ M WtJ- + >0 VOVO
47
Deg.
Departures, or Difference of
Levels
TABLE II.
Departures, or
Difference of Lrvcls
GO
p
>
a
1
P
O
rsT
3
p
H
w
p
i
a g\ _ Departures, or Difference of
42 * * 1
42 o
2
3
4
5
6
7
8
9
io
ii
12
13
14
15
16
7
18
*9
20
21
22
*3
*4
2-5
26
*7
28
29
30
31
32
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
50
5i
52
53
54
55
56
57
53
g
Sines
66913
66935
66956
66978
66999
67021
67064
67086
67107
67129
67150
67172
67194
67215
67237
67258
67278
67301
67323
67344
67366
67387
67409
67430
67452
67473
67516
67538
67559
67580
67602
67623
3&
67688
67709
67730
67752
67773
67795
67816
67837
67859
67880
67901
67923
67944
67965
67987
68008
68029
68051
68072
68093
681 1 5
68136
68157
68179
68200
Cosines
60'
59
58
%
55
54
53
52
5i
50
49
48
46
45
44
43
42
4i
40
39
38
36
35
34
33
32
31
30
29
28
11
25
24
23
22
21
20
19
18
\l
15
14
13
12
11
10
9
8
I
5
4
3
2
1
0-47
O i^iO >oO v-iO ^0 mo vr>o
NO 0<0^<j-MM H w
O
8*
On
CO
>
O
O
2
i
P
O
00
1 1
p
<
g
O
O
( 1
of
p
D
H
a
3
1-1 CM CM CC -* U? 1- *0 t^ CO X O O
P O rH CM CO rt< ip O t- X O O CM
m (> l'^ I^NNNNNNNaD*
55^ecooNtoceNtoflDcoNS 9
ON
<MO3M0003 i MX'fO
(NHHHHOOOO5XX30
71 M -+ p O b- cp p Ci O rH CM qp
0000000000000
O
00
Ot>WC5iOHNO^OJOO
MHOXN'OiMHOXNO
ip O N N 00 3 O H <M CO W + ip
I0i0i00>00i0i00l0 000
O
OO
QOOOHOHCOhOhioO
COHOO^H^O-fHCJO-f
cp p p p rH cm cm cp -* ip ip p 1 .-
OOOb-i^b-r^i^i^b-t^r^t^
O
00Nff)NHiOO-i<X)'M0
6666666066000
O
NO
OO^X00NO?5NO
iO H C h N 'M N ?: X -t C5 ^
^ LO ip O O N N X X O CO O H
cocbcbcbcocbcbcoc'ococb'*'^
cococococococococococococo
O
WO
lOXM'SX^iOCSMiSNO
O O O O CC CO CM O O O O 00 CO
n cp x cp cp cp 9 h h h w qq
CM CM CM CM CM CM CM CM CM CM CM CM CM
O
CO
CO
"<* -h 00 IO CO O CM -* X p
NON6--30oojg
6^H^i!-H^C>ICMppCpp^'*
6666666666000
CM CM CM CM CM CM CM CM CM CM CM CM CM
13-383
13404
1,3-426
13-447
13-469
13490
13-612
13-533
13-555
13-576
13-597
13-619
13-640
H
0i O -H CM CO j* O O - CO O p S ' 1
t~- t^. r^ i> b~ t> t> *> > ^ f- x
6666666666000
O
11
M H H MW + ^'fl ^ONO
<4-
Latitudes, or Hori-
zontal Distances for
Difference of Levels
m & Latitudes, or Iloiizor
*i De8r " tances for Difference c
tal Dis-
f Levels
110
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
go
J
S
ft
O
tf
W
ft
a
go
W
SB
H
GO
B
H
O
C
af
E
H
3
a<\ _ Latitudes, or Horizontal Dis-
*0 e &* tances for Difference of Levels
43 o'
z
3
4
5
6
7
8
9
10
ii
12
13
4
15
16
17
18
9
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
50
5i
52
53
54
55
56
57
58
I 9
60
Cosines
73135
73096
73076
73056
73036
73016
72996
72976
72957
'72937
72917
72897
72877
72857
72837
72817
72797
72777
72757
72737
72717
72697
72677
72657
72637
72617
72597
72577
72557
72537
72517
72497
72477
72457
'72437
72417
'72397
72377
72357
72337
72317
72297
72277
72256
72236
72216
72196
72176
72156
72136
72116
72095
72075
72055
72035
72015
71995
71974
71954
71934
Sines
6c/
59
58
55
54
53
52
5i
50
49
48
46
45
44
43
42
41
40
39
38
36
35
34
33
32
31
30
29
28
27
20
25
24
23
22
21
20
19
18
l6
15
13
12
II
IO
9
8
I
5
4
3
2
1
C46
O u-io *"> O oO *oO >oO >oO
V3 10 10 ^ ^ M M H c m w
O
VO
^ 03
It
Is
S3
GO
1-3
ft
ft
ft
&
p
go"
ft
p
a
ft
P
HOQCCNCpip-^MNHOO
cwwcMCMCMCMCMCMCMCMCMCMrH
i>i>i>.t>.t>i>.t^i>.i>t>i>.i>i>.
ON
-^(NWCOOWOOOOWfNfMHr- 1
cpb-cpip-^cpq^rHr-ipciqpt^
OS
00
00QOOOOOOOC5O00N
O(Ni0NCiHM0SQ0O(N'*
lp^CpC^rHrHCpCiCOb-b-Olp
cbcboocbcJDcbobb^b-t^b'i^b-
O
00
fTHiTiCpcpOCCl^t-Cpip^^OO
rHrHrHOOOOOOCOOO
VO
1 1 CM CM CM CM CM <M CM CM NIMHO
COIMOO'taXNOC'tX'MC
GOCOI^t^Cp OIC^^^CM CM rH
cococococococochcochcococo
Tj4 "^4 ^^1 ^^ ^^ "^i ^^1 *^qi TJi ^p ^P ^1 ^31
VO
t^aoooao-Doooooooocooot^t^
OhOhOHOhOhOhC
ioo^"*cococq(Ni7-t' 1 p
6o66ecc6cb6cco
coc^ctcccccocococococococo
lOHNCOOiOHNKOlOHN
(MGMt-HrHCpOCpOOqpopopt^
Cioscsch>cbccccccab
CMCMCMCMCMCMCMCMCMCMCMCMCM
3-
0r _| T _| P _|,_| t _, r _lT-lrHT-lT-H
rfiHQOlO'MOOCOON'tHOO
c;oqpcpcpb~b~b-t^o<po*p
rHr^r^-lrHrH^-!rHrHrHrHAlrHr^-t
cmcmcmgmcmcmcmcmcmcmcmcmcm
CO
(NOCOO't(MOX3'+(MOCO
cpcp*pppipo^h^'*^-^cp
1 Ii lr 1 1 It Ir It < i It It IHHr- 1
HOOXNOiO^MNHOa
CO CO CM CM CM CM 'M CM CM CM CM CM nH
O
if
a*
"o >oO vo O 00 oo w-io ^10
M M t* H fM + + >0 Vr>VO
rr
Departures, or
Difference of Levels
4
6Deg ^^.
TABLE II.
ill
Departures, or
Difference of Levels
3
>
P^
O
3
F
1 1
p
3
&
H
P3
P
40 De( _ Departures, or Difference of
*^ Levels
43 o'
i
2
3
4
5
6
7
8
9
10
ii
12
13
14
*5
16
7
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
50
5i
52
53
54
55
56
57
58
g
Sines
68200
68221
68242
68263
68285
68306
68327
68349
68370
68391
68412
68433
68455
68476
68497
68518
68539
68561
68582
68603
68624
68645
68666
68688
68709
68730
68751
68772
68793
68814
68835
68856
68878
68899
68920
68941
68962
68983
69004
69025
69046
69067
69088
69109
69130
691 5 1
69172
69193
69214
69256
69277
69298
69319
69340
69361
69382
69403
69424
'%%
Cosines
60'
59
58
3
55
54
53
52
5i
5
49
48
46
45
44
43
42
41
40
39
38
?
35
34
33
32
3i
30
29
28
26
25
24
23
22
21
20
19
18
11
15
14
13
12
10
9
8
I
5
4
3
2
1
0*46
O ^O u-,o *o O 00 100 vo
O
VO
*
I!
it
J
hh
to
1
1 i
P
O
SJ
Q
1 1
1 1
lO
1 1
O
m
"A
P
P
H
1 1
H
3
OOlMQ0i<O>0^C?HOHC
h h 01 :: :: -f -f 1.: 1: c *c
01 w -^ 10 9 n a; Ci 7 01 :: -t
0000000660000
ON
OOHO(NNMNHO-OC5
co n n c !: i* -t ?: 03 oi <-*
ep Tt* ic 9 n op c: h N er -t i^
OS
O
OO
OOOiOO^QOCONHOOM
0'tWHoa;co?:5'ioa)t>
ipONCOOpOprHCqwilf ip
^ -* "^ t* -^ -^ ib 10 ib ib ib
lOiOiOiOOiOiOiOiOiOiOOiO
O
00
O
Q'*ONHOO'?'lOOC0O
NCOQOOOHHNri't'tiOO
O
SO
O "* b- i 1 -^ 00 1 < "^ GO 1 1 * b O
<?qx^HNJ:oc<M^iOHoo
OQOHH(NMW^T)<ipCO
OOrHrHrHr^rHrHr^-lr^rHrHrH
^^ TJ1 Tp ^1 ^T T^ "^^ ^^H TjH TJ1 "^1 ^1 ^1
VO
vo
OWOOCTiOCOOM^OOHW
OiOOiOHC-NfMNOVO)^
H H M S>1 9 CO f + 9 ip 9 O N
^^1 ^TJI "^71 ^PJl "^1 "*4l T^l ^1 T^ ""-^l Tfl T"P ""T^
woticticococooocococccococo
O
vo
00<MOOiO^::N-30-t<00
(Mcoco^^^ioipoob-r^b-
b, b- b- b- b. b- b- b. b. l^ b- b. b-
<M CM Ol CM CM Ol CM CM CM CM CM CM CM
O
co
CM^LONC5H(MtJ(ioNOOO
OC^OCOHOCOH^NO'f
^^OiOipOOOb^b-b-cpap
6000600006000
CM CM CM CM CM CM CM cm cm cm cm cq cm
O
to
O
OH^T((i0ON0CCOHiN!0
** 00 <m -* x w q b-
CCOt^NNNNCpCpODOpcp
TOrocbwrec^6cbcbcbcba3o3
O
OHH(N(SMWT(*iOiCOOS
CM 00 -t C O N X ^ O ^ C>l 5
ooooooooooxxxc:ooOwj
6666666660000
a
S SB
II
*x mo o O vo O *o o vo vno
O
ro
4
U Latitudes, or Horizon
b Deff " tances for Difference
Latitudes, or Hori-
zontal Distances for
Difference of Levels
tall
f Le
)is-
yelfi
112
TABLE II.
Latitudes, or Hori-
zontal Distances for
Difference of Levels
i
3
ft
A
&
w
H
O
H
w
A
1
PS
of
R
p
H
1 (
H
3
^A Latitudes, or Horizontal Dis-
*^* eB ' tances for Difference of Levels
44 cf
2
3
4
5
6
7
8
9
10
ii
12
13
H
15
16
17
18
9
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
4i
42
43
44
45
46
47
48
49
50
5i
52
53
54
55
56
57
58
I 9
60
Cosines
71934
719H
71894
71873
71853
71833
71813
71792
71772
71752
71732
717"
71691
71671
71650
71630
71610
71590
71569
71549
71529
71508
71488
71468
71447
71427
71407
71366
71345
71325
71305
71284
71264
71243
71223
71203
71182
71 162
71141
71121
71 100
71080
71059
71039
71018
70998
70978
70957
70937
70916
70896
70875
70854
70834
70813
70793
70772
70752
70731
7071 1
Sines
6cf
59
58
%
55
54
53
52
5i
50
49
48
46
45
44
43
42
4i
40
39
38
11
35
34
33
32
3i
30
29
28
11
25
24
23
22
21
20
19
18
\l
15
14
13
12
11
10
9
8
I
S
4
3
2
1
0-45
. iV ID
V ioio^+MWH H H w
a
>
pa
PB|
O
K
O
Is
ft
A
P3
of
H
Ph
3
A
M
^MNOCNiSWOOOOMH
W?:iM(N(M(M!MHHHH
pxt^pip^cpcMrHppxt^
HHHrlHHHHHHOOO
O
OS
^lOiOONTDOOO-i CM W ^H
"^ -t* ^ ^ -i* + -i* -i< tj< w c'r c'^
O
00
-* C QO O M -t O N i: h 0: c 6
W^cpMCTHOOOpqpNCO
00
CflOHTJiNOOUOOOH^OO
cpcMCMrHppcsxb~b~pip^
666666666^666
OOOOONOiO'f^^OIBN
OOf?NHi5CNHi?0C(M
HHOOOOONNOOiO^^
CO CO CO (f 1 CM bq (?q <jq <fq bq (f-| oi <f 1
SO
O CO 00 N N O O C lp -f -f cc
10 ib ib ib ib b b ib >b b b ife >b
cococococococococococococo
%
^COCOCN(Mt-lOC500^.COiO^
n 00 10 h n r: X -i" O X C>1 TO
xxxxxxxxxxxx x
CMCMCMCMCMCMCMCMCMCMCMCMCM
%
CO
ip ip ip -^ "*""? cp co co 05 cm cq oi
CM CM CM CM CM CM CM CM CM <M CM CM CM
m
t^OCDCOCOiOiOiO'^'fCOCO^T
XO-f^)OX'C-|"MOX'CT|i
COCpCOCOCOCMCMCMCMCM^rHr-i
*^i ^^1 Tp ^^ ^fi ^i ^-p T71 t^H ^r^ r^ "*-ji ~^i
O
M
11
iff
COCOCOOOCOCpCMCMCMCMCM t^H
CONOiOTftMINHOCOON
r r lr r ,, T l 'T ,r r ,r 7 Hr 7 Hr r ,, T lr 7 HC ? < ? :>c>
O
O "OO ij-iO >oo k->o **-> ^0
m hi rj e coco^-^10 iovo
41
T T . _
Departures, or
Difference of Levels
r Departures, or Diliere]
J e8r * Levels
jce c
1
TABLE II.
113
Departures,
or 1
Difference of Levels '
Sines
44 of
69466
60'
i
69487
59
i
69508
58
3
69529
H
4
69550
56
5
69570
55
6
69591
54
7
69612
53
8
69633
51
9
69654
51
lo
69675
5
ii
'69696
49
12
69716
4 8
3
69737
4 7
H
69758
46
15
69779
45
16
"69800
44
"7
69821
43
18
69841
'69862
42
9
41
20
69883
40
21
'69904
39
22
69925
38
13
24
W
S
15
69987
35
26
70008
34
27
'70029
33
28
70049
31
19
70070
3i
30
70090
30
3i
701 1 1
2 2
31
70132
28
33
70153
% l
34
70174
26
35
'70195
15
36
70215
24
37
70236
13
3
70257
22
39
70277
21
40
'70298
20
4i
70319
19
42
70339
18
43
'70360
l l
44
703 81
16
45
'70401
15
46
'70422
14
47
70443
13
48
70463
12
49
70484
11
5o
70505
10
Si
70525
9
5i
70546
8
53
70567
7
54
70587
6
55
70608
5
56
70628
4
57
58
70649
70669
3
2
59
70690
1
60
7071 1
Cosines
0-45
Latitudes, or Hori-
zontal Distances for
Difference of Levels
a a Departures, or Difference of
*XTc ee ' Levels
100 ^iO oO *^>o >oO inO
10 >0^ ^r w w H N w w
o
OOU5ONHxt00Hi3 00H
ONSNOO'XCiCOOOOH
^iipONCpOOrH^-ldpON
60566606666666
OOOCOtON^NM>Nt>-
HHOOOOOIiNOOO^^
loONoooOwiOH^cpTtoao
ctcmcmcmcmcmototototwotot
COCDCOCDCDCDOCOCDsDCDCDCD
WOOMCDOWIOQQH-^OOO
I00i0000i000000
HMOS
M O 00 LO iM Q
cpONQpQOOHWWOJ-^f
obobobobobc6666666
^ t^H rjl r^i -^ ^1 ^ t^I ^ "^ ^ ^r ^T
OfNiONOtMiOOOHWiOffl
ooTtoowocHN-toog
Or^.OOOOCSCiO'-'i-lCNOTW^
^^Alr^rHr^CMCMCMCMCMCNCM
C000C000"^O-^O^O
NI>00 00OOO
_ iq O *
^ * 05 09
COCCCOCCCOCCC0CT>C3C0C0C0C0
CDCOOCTMOCOOOOQ^W^
10 r. jo n h o o -)< oo
^r^i^r^t^i^obobobobdbQbob
CMCMCMCMCMCMCMCMCMCMCMCM<M
OH(MT)HOONOOOOH(Mn
^NO^^OiMOXJHOOOH
opqDOOOOOOOHHHN
666666h'-ihhhhh
cm cm cm cm cm cm cm cm cm cm cm cm cm
wcboooococo'^^'^^^^'JJ
NNNgg2gg^
-(( lO O N 00 -.
05OCJOOC5
O9699O
(6666cot>t-t>^i>NN
m hi c^ H to m + + *o w->vo
t
A - Latitudes, or Horizontal Dis-
40 Beff * tances for Difference of Levels
114
TABLE III.
Degree
TANGENTIAL ANGLES FOR
Tangent
Cotangent
o o-
00000
Infinite
6V
CIRCULAR CUE
i
2
00029
00058
34377460
718-8730
'%
400 feet \
3
4
00087
001 16
145-9150
859-4363
%
4 chains [
Radii.
5
00145
687-4588
55
40 metres /
6
00175
572-9572
54
7
00204
491-1060
53
Bends.
8
0023 3
429-7175
52
9
10
00262
00291
381-9709
343*7737
5i
50
In one 66 feet chain 6 inches
ii
00320
312-5213
49
Rails 18 lengths If
12
00349
00378
286-4777
264*4408
48
47 <
In one 100 chain 9f
4
15
00407
00436
245-5519
229-1816
46
45
Rails 18 lengths lfV
16
*7
00465
00495
214-8576
202-2187
44
43
Superelevation op Rails.
18
19
00524
00553
190-9841
180-9322
42
4i
66 feet chain, 20 m.
per hour 6"
20
21
00582
0061 1
171-8854
163 7001
40
39
100 feet chain, 20 m.
per hour 3|"
22
2-1
00640
00669
156-2590
149-4650
38
24
00698
143-2371
36
Left-hand
No. of
Right-hand
25
26
00727
137-5075
35
Reading
Chains
Reading
00756
132-2185
34
27
00785
127-3213
33
356 25-1'
i
1
3 34-8'
28
29
00814
00844
1227739
118-5401
32
3i
352 50-3
7 9-7
30
00873
114-5886
30
349 15-4
1*
10 44-6
31
32
33
00902
00931
00960
110*8920
107-4264
104-1709
29
28
2 l
345 40-5
342 5-7
2
14 19-4
17 54-3
34
35
00989
01018
101*1069
98*2179
26
*5
338 308
3
21 29-1
36
01047
95-4894
2 4 .
334 56-0
H
25 4-0
37
01076
92*9084
*3
331 21-1
4
28 38-9
38
39
01 105
01135
90*4633
88*1435
22
21
327 46-3
4*
32 13-7
40
01 164
85*8397
20
324 11-4
5
35 48-6
4i
42
ci 193
01222
83.8435
81*8470
19
18
320 36-5
&i
39 23-4
43
01251
79*9434
*l
317 1-7
6
42 58-3
44
45
01280
01309
78*1263
76*3900
16
15
313 26-8
H
46 33-2
46
01338
74*7291
H
309 52-0
7
50 8-0
47
48
49
01367
01396
01425
73-1389
71*6150
7 -I 533
13
12
11
306 17-1
302 42-2
7J
8"
53 42-9
57 17-7
5o
01455
68*7500
10
299 7-4
9
60 52-6
5 1
52
01484
01513
67*4018
66*1054
9
8
295 32-5
64 27-5
53
54
55
01542
01 571
01600
64*8580
63-6567
62*4991
I
5
291 577
288 22-8
10
68 2-3
71 37-2
56
01629
61*3829
4
284 47-9
101
75 12-0
57
58
01658
01687
60*3058
59*2658
3
2
281 13-1
11
78 46-9
59
01716
58*2611
I
277 38-2
12
121
82 21-7
60
01746
Cotangent
57*2899
Tangent
89 O
274 3-4
270 28-5
85 56-6
89 31-5
89 Degrees
- w 2
TABLE III.
115
1 Degree
TANGENTIAL ANGLES FOR
1 o'
Tangent
01746
Cotangent
57-2899
60'
CIRCULAR CURVES.
I
01775
56-3505
59
2
01804
55*4415
58
500 feet
3
4
01833
01862
54"56i3
537085
u
5 chains
Radii.
5
01 891
52-8821
55
60 metres
6
01920
52-0806
54
7
01949
51-3031
53
Bends.
8
01978
50-5485
51
9
10
02007
02037
49-8157
49-1038
5i
50
In one 66 feet chain 5 inches
ii
02056
48-4120
49
Rails 18 lengths If
12
02095
02123
477395
47-0853
48
4 Z
In one 100 chain 7
14
15
02153
02182
46-4488
45-8293
46
45
Rails 18 lengths 1
16
*7
0221 1
02240
45*2261
44-6385
44
43
Superelevation of Rails.
18
02269
44-0661
42
19
20
02298
02328
02357
43-5081
42-9640
42-4334
4i
40
66 feet chain, 20 m. per hour A\ n
21
39
100 feet chain, 20 m. per hour 3"
22
02386
02415
4i*9"57
41-4105
38
24
02444
40-9174
36
Left-hand
No. of
Right-hand
25
02473
40-4358
39-9654
35
Reading
Chains
Reading
26
02502
34
27
02531
39-5058
33
357 81'
1
2 51-9'
28
29
02560
02589
39-0567
38-6177
32
3i
354 16*2
2
1
5 43*7
30
02619
38-1884
30
351 24-4
H
8 35*6
31
3*
02648
02677
37-7686
37*3578
29
28
348 32-5
2
11 27-5
33
02706
36-9560
Z l
345 40*6
H
14 19-4
34
35
02735
02764
36-5626
36-1775
26
*5
342 48-7
3
17 11'3
36
02793
35-8005
24
339 56-8
31
20 3-1
37'
02822
35-4312
2.3
337 50
4
22 55*0
38
39
02851
02881
35-0695
34*7151
22
21
334 13*0
H
25 46-9
40
02910
34*3677
20
331 21-2
5
28 38*8
4i
4 2
02939
02968
34-0273
33-6935
19
18
328 29*3
2
31 30-6
43
02997
33-3661
'I
325 37-4
6
34 22-5
44
45
03026
03055
33*0451
32-7302
16
15
322 45*6
6J
37 14-4
46
03084
32-4212
14
319 53-7
7
40 6*3
47
48
49
03 1 14
03143
03172
32-1180
31-8205
31-5283
13
12
11
317 1*8
314 9*9
8
42 58-2
45 50*1
5o
03201
31-2415
10
311 18-1
H
48 419
5i
5 Z
03230
03259
30-9599
30-6833
9
8
308 26*2
9
51 33*8
5?
03288
30-4115,
I
5
305 34*3
H
54 25-7
54
55
03317
03346
30-1446
29-8822
302 42*4
10
57 17-6
56
03 3 7 6
29-6244
4
299 50-5
10J
60 9-4
59
03405
29-3711
3
296 58-7
11
63 1*3
03434
03463
28-8770
\
294 6*8
ni
65 53-2
60
03492
28-6362
88
291 14-9
12
68 45*1
Cotangent
Tangent
288 23-0
12i
71 36*9
88 Degrees
z
116
TABLE III.
2 Degrees
TANGENTIAL ANGLES FOE
2 O'
Tangent
03492
Cotangent
28-6362
6d
CIRCULAR CURVES.
I
2
03521
03550
28-3993
28-1664
59
58
600 feet \
3
4
03579
03609
27-9372
277117
11
6 chains [
Radii.
5
03638
27-4898
55
60 metres f
6
03667
27-2714
54
7
8
03696
03725
27-0565
26-8449
53
5*
Bends.
9
IO
03754
03783
26-6366
26-4316
5i
50
In one 66 feet chain 4| inches
n
03812
26-2296
49
Kails 18 lengths 1
12
03842
26-0307
48
"
13
03871
25-8348
A l
In one 100 chain 6| ;;
*4
is
03900
03929
25*6418
25 '45 1 7
46
45
Rails 18 lengths \%
16
03958
25-2643
44
7
03987
25-0797
43
Superelevation op '.
18
04016
24-8978
42
19
zo
04046
04075
247185
24-5417
4*
40
66 feet chain, 20 m. per hour 3f "
21
04104
24-3675
II
100 feet chain, 25 m.
)er hour 4"
22
04133
24-1957
*3
04162
24*0263
l l
24
041 91
23-8592
36
Left-hand
No. of
Bight-hand
^5
26
04220
04250
04279
04308
04337
23-6945
35
Reading
Chains
Reading
27
28
29
23-5320
23-3717
23-2136
23-0576
34
33
32
3i
357 36-8'
355 13-5
2
1
2 23-2'
4 46-5
30
04366
22-9037
30
352 50-3
H
7 9-7
3i
32
04395
04424
227518
22*6020
29
28
350 27-0
2
9 32-9
33
04454
22-4540
27
348 3-8
2^
11 56-2
34
35
04483
04512
22*3080
22-1639
26
25
345 40-6
2
3
14 19*4
36
04541
22-02I7
24
343 17-3
H
16 42-7
37
38
04570
04599
21-8812
21-7425
23
22
340 54-1
4
19 5-9
39
04628
21-6056
21
338 30-8
H
21 29-1
40
04658
21-4704
20
336 7-6
5
23 52-4
4i
42
04687
04716
21-3368
21-2049
*9
18
333 44-4
H
26 15-6
43
04745
21-0746
I7 <
331 21-1
6
28 38-9
44
45
04774
04803
20-9459
20-8118
16
"5
328 57-9
6J
31 2-1
46
04833
20-6932
H
326 34-6
7
33 25-3
47
48
04862
04891
20-5691
20-4464
*3
12
324 11-4
7 1
'2-
35 48-6
49
04920
20-3253
11
321 48-2
8
38 11-8
50
04949
20-2055
10
319 24*9
8*
9
40 35-1
5i
5*
04978
05007
20-0871
19-9702
9
8
317 1-7
42 58-3
53
54
55
05037
05066
05095
19-8545
19-7402
19-6272
I
5
314 38-4
312 15-2
10
45 21-5
47 44-8
56
05124
19*5155
4
309 52-0
101
50 8-0
57
58
05153
05182
19-4051
19-2959
3
2
307 28-7
11
52 31-3
I 9
05212
19-1879
I
305 5-5
1U
54 54-5
60
05241
Cotangent
19-0811
Tangent
87 O
302 42-2
300 190
12
57 17-7
59 41-0
87 Degrees
TABLE III.
117
3 Degrees
TANGENTIAL ANGLES FOR
Tangent
Cotangent
3 d
05141
19-0811
60'
CIRCULAR CURVES.
i
'05270
*8-9755
59
2
05299
18-8710
58
700 feet \
3
4
05328
05357
187677
18-6655
2
7 chains [
Radii.
5
05387
18-5644
55
70 metres '
6
05416
18*4644
54
7
8
05445
05474
18-3655
18-2676
53
52
Bends.
9
IO
05503
05533
18-1708
18-0749
5i
50
In one 66 feet chain 3 inches
II
IZ
05562
05591
17-9801
17-8863
49
48
Rails 18 lengths %
13
05620
177934
4 l
In one 100 chain 5|
IS
05649
05678
177015
17-6105
46
45
.Rails 18 lengths y|
16
05708
17-5205
44
17
05737
I743I3
43
Superelevation of
18
05766
*7"343i
42
19
20
05795
05824
17-2558
17-1693
4i
40
66 feet chain, 20 m. per hour 3"
21
05853
17-0837
39
100 feet chain, 25 m. per hour 3"
22
*3
05883
05912
16-9989
16-9150
38
3 Z
24
05941
16-8319
36
Left-hand
No. of
Right-hand
25
05970
167496
35
Reading
Chains
Reading
26
i6*668i
34
33
32
27
28
05999
06029
06058
16-5873
16-5074
357 57-2'
1
2 2-8'
29
06087
16-4282
3i
355 54-4
1
4 5-5
30
061 16
16-3498
30
353 51-7
1*
2
6 8-3
3i
3 2
06145
06175
16*2721
16-1952
29
28
351 48-9
8 11*1
33
06204
16-1189
Z l
349 46-1
3
10 13-8
34
35
06262
16-0434
15-9686
26
25
347 43-4
12 16-6
36
06291
15-8945
24
345 40-6
H
14 19-4
06321
06350
15-8211
157483
23
22
343 37-8
4 .
16 22-2
39
06379
15-6762
21
341 35-0
U
18 24-9
40
06408
15-6047
20
339 32-3
h
20 27-7
41
42
06438
06467
15*5339
15-4638
19
18
337 29-5
H
22 30-5
43
06496
15-3942
3
335 26-7
6
24 33*3
44
45
06525
06554
15*3253
15-2570
16
15
333 24-0
*h
26 36-0
46
06584
15-1893
14
331 21-2
7
28 38-8
47
48
06613
06642
15-1222
i5'o557
13
12
329 18-4
71
30 41-6
49
06671
14-9897
11
327 15-6
8
32 44*3
50
06700
14-9244
10
325 12-9
8J
9
34 47-1
51
5*
06730
06759
14-8596
147953
9
8
323 10-1
36 49-9
S3
54
55
06788
06817
06847
147316
14-6685
14-6059
I
5
321 7-3
319 4-5
10
38 52-7
40 55-4
56
06876
14-5438
4
317 1*8
10J
42 58-2
57
58
06905
06934
14-4822
14-4212
3
2
314 59-0
11
45 1-0
59
06963
14-3606
1
312 56-2
14
12
47 3-7
60
06993
14-3006
86
310 53-5
49 6-5
Cotangent
Tangent
308 50-7
124
51 9-3
86 Degrees
Ait
118
TABLE III.
1
4 Degrees
j
TANGENTIAL ANGLES FOR
Tangent
Cotangent
4 of
06993
14*3006
60'
CIRCULAR CURVES.
i
07022
14-2411
59
z
07051
14-1820
58
800 feet \
3
4
07080
071 10
14-1235
14-0654
U
8 chains Radii.
5
07139
14-0078
55
80 metres-
6
07168
13-9507
54
7
8
07197
07227
13-8940
13-8378
53
52.
Bends.
9
IO
07256
07285
13-7820
13-7267
5i
50
In one 66 feet chain 3^ inches
ii
12
07314
'7343
13-6718
13-6174
8
Rails 18 lengths f
n
07373
13-5633
A l
In one 100 chain 4f
14
15
07402
07431
13-5097
134566
46
45
Rails 18 lengths ^
16
07461
13-4038
44
7
07490
I3-35I5
43
Superelevation of Rails.
18
07519
13-2995
42
J 9
20
07548
07578
13-2480
13-1968
4i
40
66 feet chain, 25 m. per hour 4a"
21
07607
13-1461
39
100 feet chain, 25 m. per hour 3"
22
07636
07665
13-0957
38
*3
1 3 -0457
3 Z
24
07695.
12*9961
36
Left-hand
No. of
Right-hand
2 5
26
07724
07753
07782
07812
12-9469
12-8980
12-8495
12*8014
127536
35
34
33
32
Beading
Chains
Reading
27
28
358 12-6'
1
t
1 47-4'
29
07841
3i
356 25-1
1
3 34-8
30
07870
12*7062
30
354 37-7
1*
2
5 223
32
07899
07929
12-6591
12-6123
29
28
352 50-3
7 9-7
33
34
35
07958
07987
08017
12-5659
12-5199
12-4742
26
25
351 2-8
349 15-4
H
3
8 57-1
10 44-6
36
08046
12-4288
24
347 28-0
H
12 32-0
37
38
08075
08104
12-3837
12-3390
23
22
345 4-5
4
14 19-4
39
08134
12-2946
21
343 531
5
16 6-8
40
08163
12-2505
20
342 5-7
17 54-3
4i
42
08192
08222
12*2067
12-1632
19
18
340 18-3
H
19 41-7
43
44
45
08251
08280
08309
I2-I200
I2'077I
12-0346
15
338 30-8
336 43-4
6
21 29-1
23 16-6
46
08339
II-0923
14
334 56-0
7
25 4-0
2
08368
08397
II-9503
II-9086
13
12
333 8-5
71
26 51-4
49
08427
II-8672
11
331 21-1
8
28 38-9
50
08456
II-826I
10
329 33-7
8J
9
30 26-3
51
52
08485
08514
1 1 7853
1 1 7447
9
8
327 46-3
32 13-7
53
54
08544
08573
11-6644
I
325 58-8
H
34 1-2
55
08602
11-6247
S
324 11-4
10
35 48-6
56
08632
11-5852
4
322 24-0
10-J-
11
37 360
57
58
08661
08690
11-5460
11-5071
3
2
320 36-5
39 23-4
12
08720
11-4684
1
318 49-1
Hi
12
41 10-9
60
08749
Cotangent
11-4300
Tangent
85
317 1-7
42 58-3
315 14-2
124
44 45-7
85 De
gbees
TABLE III.
119
5 Degrees
TANGENTIAL ANGUS ;
Tangent
Cotangent
5 o'
08749
11-4300
60'
CIRCULAR CURVES.
i
z
08778
08807
n-39'8
11-3539
59
58
900 feet \
3
4
088 j 7
08866
11-3163
11-2788
U
9 chains [ Radii.
5
08895
11-2471
55
90 metres''
6
08925
11-2047
54
7
8
08954
08983
11-1680
HM316
53
52
Bends.
9
IO
09013
09042
11-0954
11-0594
51
50
In one 66 feet chain 2f inches
II
09071
11-0236
49
Rails 18 lengths
12
09101
09130
10-9881
10-9528
48
4 1
In one 100 chain 4|
14
IS
09159
09189
10-9177
10-8829
46
45
Rails 18 lengths $$
16
17
09218
09247
10-8482
10-8138
44
43
Superelevation of Rails.
18
09277
10-7796
42
19
09306
10-7456
4-
66 feet chain, 25 m. per hour 4"
20
'9335
107119
40
*
21
09365
10-6783
39
100 feet chain, 35 m. per hour 5"
22
23
09394
09423
1 0-6449
10-6118
38
24
09453
10-5788
36
Left-hand
No. of
Right-hand
*5
26
09482
10*5461
10-5136
35
Reading
Chains
Reading
095 1 1
34
27
09541
10*4812
33
358 24-5'
1
-2-
1
1 35-5'
28
29
09570
09600
10-4491
104171
3*
3*
356 49-0
3 11-0
30
09629
10-3853
30
355 13-5
H
4 46-5
3i
32
09658
09688
10-3538
10-3224
29
28
353 38-0
2
6 22-0
33
09717
10-2912
% l
352 2-5
2i
7 57-5
34
35
09746
09776
10-2602
10-2294
26
25
350 27-0
3
9 33-0
36
09805
10-1987
24
348 51-5
H
11 8-4
37
38
39
09834
09864
09893
io-i683
10-1380
10-1079
23
22
21
347 16-0
345 40-5
4
4i
12 439
14 19-4
40
09923
10*0780
20
344 5-1
5
15 54-9
4i
42
09952
09981
10*0482
0-0187
19
18
342 29-6
H
17 30-4
43
10011
9-9893
\l
340 54-1
6
19 5-9
44
45
10040
10069
9-9600
9-9310
16
15
339 18-6
6i
20 41-4
46
10099
9-9021
M
337 43-1
7
22 16-9
47
48
49
10128
10158
10187
9*8733
9-8448
9-8164
13
12
11
336 7-6
334 32-1
n
8
23 52-4
25 27-9
50
10216
9-7881
10
332 56-6
H
27 3-4
5i .
51
10245
10275
9-7600
97321
9
8
331 21-1
9
28 38-9
53
10305
97044
I
329 45-6
H
30 14-4
54
55
10334
10363
9-6768
9-6493
S
328 10-1
10
31 49-8
56
10393
9-6220
4
326 34-6
10J
33 253
3
59
10422
10452
10481
9' 5949
9-5679
9-5410
3
z
1
324 59-1
323 23-7
11
35 0-8
36 36-3
60
10510
9 , 5*43
84
321 48-2
12
38 11-8
Cotangent
Tangent
320 12-7
m
39 47-3
84 Degrees
120
TABLE III.
6 Degrees
Tangent
Cotangent
6 d
10510
9'5H3
60'
i
10540
9-4878
59
2
10569
9-4614
58
3
10599
9"435i
H
4
10628
9-4090
56
5
10658
9-3830
55
6
10687
9"3572
54
7
10716
9*3315
53
8
10746
9-3059
52
9
10775
9-2805
5i
IO
10805
9' 2 553
50
ii
10834
9-2301
49
12
10863
9-2051
48
*3
10893
9-1802
4 l
14
10922
9^555
46
15
10952
9-1309
45
16
10981
9-1064
44
17
iioii
9-0821
43
18
1 1040
9-0578
42
19
1 1070
9-0337
4i
20
11099
9-0098
40
21
11128
8-9859
39
22
11158
8-9622
38
23
11187
8-9386
n
24
11217
8-9152
36
25
11246
8-8918
35
26
1 1276
8-8686
34
27
11305
8-8455
33
28
"335
8-8225
32
29
1 1 364
8-7996
31
30
"394
8-7768
30
Ji
11423
87542
29
32
"453
87317
28
33
1 1482
87093
27
34
11511
8-6870
26
35
11541
8-6648
25
36
"570
8-6427
24
37
11600
8-6207
23
38
1 1629
8-5989
22
39
11659
8-5771
21
40
1 1688
8-5555
20
4i
II7I8
8-5340
19
42
'"747
8-5125
is
43
'"777
8-4912
17
44
11806
8-4700
16
45
11836
8-4489
15
46
1 1 865
8-4279
H
47
1 1 895
8-4070
13
48
1 1924
8-3862
12
49
'"954
8-3655
11
5o
1 1983
8-3449
10
5i
12013
8-3244
9
52
12042
8-3040
8
53
12072
8-2837
7
54
12101
8-2635
6
55
I2T3I
8-2434
5
56
12x60
8-2234
4
57
12190
8-2035
3
58
12219
8-1837
. 2
59
12249
8-1639
I
60
12278
8-1443
83
Cotangent
Tangent
83 Degrees
TANGENTIAL ANGLES FOR
CIRCULAR CURVES.
1000 feet \
10 chains \ Radii.
100 metres)
-Bends.
In one 66 feet chain 2| inches
Rails 18 lengths -f
In one 100 , y chain 3|
Rails 18 lengths
Superelevation of Rails.
66 feet chain, 30 m. per hour 5"
100 feet chain, 35 m. per hour 4a"
Left-hand
Reading
358 c
357
355
354
352
351
349
348
347
345
344
342
341
339
338
337
335
334
332
331
329
328
327
325
324
34-1'
8-1
42-2
162
50-3
24-3
58-4
32-4
6-5
40-6
14-6
49-7
22-7
56-8
30-8
4-9
38-9
13-0
47-1
21-1
55-2
29-2
3-3
37-3
11-4
No. of
Chains
n
9 l
3J
H
6
6i
7
n
8
8*
9
10
101
11"
111-
12
12J
Right-hand
Reading
25-9'
51-9
17-8
43-8
9-7
8 35-7
10 1-6
11 27-5
12 53-5
14 19-4
15 45-4
17 11-3
18 37-3
20 3-2
21 29-1
22 55-1
24 21-0
25 47'0
27 13-0
28 38-9
30 4-8
31 30-8
32 56-7
34 22-6
35 48-6
TABLE III.
121
7 Dbgbsbi
TANGENTIAL ANGLES FOR
7 C
Tangent
12278
Cotangent
8-1443
60'
CIRCULAR CURVES.
i
2
12308
12338
8-1248
8-1053
59
58
1500 feet \
3
4
12367
12397
8-o86o
8-0667
li
15 chains
Radii.
5
12426
8-0475
55
150 metres
6
12456
8*0284
54
7
12485
8-0094
*, 53
Bends.
8
12515
7-9905
52
9
10
12544
12574
7-9717
7-9530
51
50
In \ 66 feet chain If inches
ii
12603
7*9343
49
Rails 18 lengths T 7 g-
12
3
12633
12662
7-9158
7'8973
48
4 Z
In \ 100 chain 2
4
5
12692
12722
7-8789
7-8606
46
45
Rails 18 lengths &
16
7
12751
12781
7-8424
7-8242
7-8062
44
43
Superelevation of Rails.
18
12810
42
19
20
12840
12869
77882
7-7703
4i
40
66 feet chain, 35 m. per hour 4"
21
12899
77525
39
100 feet chain, 35 m. per hour 3"
22
23
12929
12958
77348
77171
38
3 Z
24
12988
7-6995
Left-hand
No. of
Right-hand
*5
26
27
28
29
13017
7-6820
7-6646
7 - 6473
7-6300
7-6128
Reading
Chains
Reading
13047
13076
13106
13136
34
33
32
31
359 2-7'
358 5-4
1
1
57-3'
1 54-6
30
13165
7'5957
30
357 8-1
1*
2 51-9
31
31
33
13195
13224
13254
7"5787
7-5617
7'5448
29
28
356 10-8
355 13-5
2
n
3 49-2
4 46-5
34
35
13284
133*3
7-5280
7'5"3
26
25
354 16-2
3
5 43-8
36
'3343
7-4946
24
353 18-9
n
6 41-1
37
13372
7-4780
7-4615
7-4450
23
352 21-6
4
7 38-4
38
39
13402
13432
22
21
351 24-3
4i
8 35-6
40
1 3461
7-4287
20
350 27-0
5
9 32-9
4i
42
13491
13521
7-4123
7-3961
19
18
349 29-7
5i
10 30-2
43
13550
7"3799
15
348 32-4
6
11 275
44
45
13580
13609
7-3638
7' 3478
347 35-1
*h
12 24-8
46
13639
7-3318
14
346 37-8
7
13 22-1
47
48
49
13669
13698
13718
7-3160
7-3001
7-2844
13
12
11
345 40-6
344 43-2
n
8
14 19-4
15 1G-7
50
13758
7-2687
10
343 46-0
8i
16 14-0
5*
52
13787
13817
7-253
7'*375
9
8
342 48-7
9
17 113
53
13847
7-2220
I
341 51-4
H
18 8-6
54
55
13876
13906
7-2066
7-1912
6
5
340 54-1
10
19 5-9
56
13935
7-1759
4
339 56-8
101
20 3-2
57
58
59
13965
'13995
14024
7-1007
7"i455
7-1304
3
2
1
338 59-5
1 338 2-2
11
ill
21 0-5
21 57-8
60
14054
7-1153
82
337 4-9
12
22 55-1
Cotangent
Tangent
336 7-6
1
in
23 52-4
|
82 Di
XJRF.ES
-**- 2
122
TABLE III.
8 Degrees
TANGENTIAL ANGLES FOR
CIRCULAR CURVES.
8 o'
Tangent
14054
Cotangent
7-1153
60'
z
14084
14113
7-1003
7-0854
59
58
2000 feet \
3
4
14143
4<7J
7-0705
7'557
s l
56
20 chains [ Radii.
5
14202
7-0410
ss
200 metres f
6
14232
7-0263
54
7
14262
7-0117
53
Bends.
8
14291
6-9971
52
9
IO
14321
i435i
6-9826
6-9682
51
50
In one 66 feet chain 5 inches
ii
14381
6-9538
49
Rails 18 lengths T -%
12
14410
14440
6-9395
6*9252
48
4 Z
In one 100 chain 7^
"4
IS
14470
14499
6*9110
6-8968
46
45
Rails 18 lengths \
16
7
14529
14559
6-8827
6-8687
44
43
Superelevation of Rails.
18
14588
6-8547
42
19
14618
6-8408
41
66 feet chain, 35 m. per hour 21 "
20
14648
6-8269
40
*
21
14677
6-8131
39
100 feet chain, 35 m. per hour 2"
22
23
14707
14737
67993
6-7856
38
3 1
24
14767
67719
36
Left-hand
No. of
Right-hand
25
26
27
14796
14826
14856
6-7583
6-7448
67313
35
Reading
Chains
Reading
34
33
358 34-1'
1
1 25-9'
28
29
14886
14915
67178
67044
32
31
357 8-1
2
2 51-9
30
14945
6-6911
30
355 42-2
3
4 17-8
31
32
14975
15005
6-6778
6-6646
29
28
354 162
4
5 43-8
33
15034
6-6514
27
352 50-3
5
7 9-7
34
35
15064
15094
6-6383
6-6252
26
25
351 24-3
6
8 35-6
36
15123
6'6i2i
24
349 58-4
7
10 1-6
37
38
39
15153
15183
15213
6-5992
6*5862
6-5733
23
22
21
348 32-4
347 6-5
8
9
11 27-5
12 53-5
40
15243
6*5605
20
345 40-6
10
14 19-4
4i
42
15272
15302
6*5477
6x350
19
18
344 14-6
11
15 45-4
43
15332
6-5223
3
342 48-7
12
17 11*3
44
45
15362
15391
6-5096
6-4971
16
15
341 22-7
13
18 37-2
46
15421
6-4845
14
339 56-8
14
20 3-2
47
48
49
i545i
1 548i
15511
6-4720
6-4596
6-4472
13
12
11
338 30-8
337 4-9
15
16
21 29-1
22 55-1
5
15540
6-4348
10
335 38-9
17
24 210
5i
52
15570
15600
6-4225
6-4102
9
8
334 13-0
18
25 47-0
53
15630
6-3980
I
332 47-1
19
27 12-9
54
55
15660
15689
6-3858
6-3737
6
5
331 21-1
20
28 38-9
56
15719
6-3616
4
329 55-2
21
30 4-8
57
58
8
15749
15779
15808
6-3496
6-3376
6-3256
3
2
328 29-2
327 3-3
22
23
31 30-7
32 56-7
60
15838
6-3137
8i
325 37-3
24
34 22-6
Cotangent
Tangent
324 11-4
25
35 48*6
81 Di
GREES
!
TABLE III.
123
9 Degrees
TANGENTIAL ANGLES FOR
9 d
Tangent
15838
Cotangent
63137
6V
CIRCULAR CURVES.
i
z
15868
15898
6-3018
6-2900
59
58
2500 feet \
3
4
15928
15958
6-2782
6-2665
3
25 chains \ Radii.
5
15988
6-2548
55
250 metres )
6
16017
6-Z432
54
7
16047
6-2316
53
Bends.
8
16077
6-220O
52
9
10
16107
161J7
16167
6-2085
6-1970
6-1855
5i
5
49
In one 66 feet chain 4 inches
ii
Rails 18 lengths ^
IZ
16196
i6zz6
6-I7 4 I
6- 1 628
48
4 7
In one 100 chain 6
*5
i6z 5 6
i6z86
6/1515
6-i4oz
46
45
Rails 18 lengths T \
16
17
16316
16346
6-1289
6-1177
44
43
Superelevation of Ralls.
18
16376
6-1066
42
19
16406
6/0955
41
66 feet chain, 35 m. per hour 2|"
zo
ZI
16435
16465
6-0844
6-0733
40
39
100 feet chain, 45 m. per hour 3"
zz
23
16495
165Z5
6-0623
6-0514
38
Z4
16555
6-0405
36
Left-hand
No. of
Right-hand
45
z6
16585
6-0296
35
Reading
Chains
Reading
16615
6*0187
34
z 7
M ^ 45
6-0079
33
358 51-2'
1
1 8-7'
z8
ZQ
16674
16704
5-997I
5-9864
32
31
357 42-5
2
2 17-5
JO
16734
5*9757
30
356 33-7
3
3 26-2
31
3*
33
16764
16794
i68z4
5-9651
5-9544
5-9438
29
z8
355 25-0
354 16-2
4
5
4 350
5 43-7
34
35
16854
16884
5-9333
5-9228
z6
25
353 7-5
6
6 52-5
36
16914
5'9 1Z 3
24
351 58-7
7
8 13
37
16944
5-9019
23
350 50-0
8
9 10-0
38
39
16974
17004
5-8915
5-8811
Z2
21
349 41-2
9
10 18-8
40
17033
5-8708
ZO
348 32-5
10
11 275
4i
4Z
43
17063
17093
171Z3
5-8605
5 - 85oz
5*8400
19
18
s
347 23-7
346 15-0
11
12
12 36-3
13 450
44
45
17153
17183
5-8Z98
5-8196
16
15
345 6-2
13
14 53-8
46
17Z13
5-8095
14
343 57-5
14
16 25
47
17243
5'7994
13
342 48-7
15
17 11-3
48
49
17Z73
17303
5-7893
5-7793
IZ
II
341 40-0
16
18 200
5
17333
5-7693
10
340 31-2
17
19 28-8
5i
52
17363
17393
5*7594
5*7494
9
8
339 22-5
18
20 37-5
53
17423
5-7395
I
338 13-7
19
21 46*3
54
55
17453
17483
5-7 2 97
57199
6
5
337 5-0
20
22 55-0
56
17513
57101
4
335 56-2
21
24 3-8
57
58
I 9
17543
17573
17603
s 'Tl
5-6906
5-6809
3
z
1
334 47-5
| 333 38-7
22
23
25 12-5
26 21-3
60
17633
5 -6 7 iz
8o
1 332 300
24
27 30-0
Cotangent
Tangent
' 331 21*2
25
28 38-8
80 Degrees
F 2
124
TABLE III.
10 Degrees
Tangent
Cotangent
io d
17633
5-6712
60'
i
17663
5-6616
59
2
17693
5-6520
58
3
17723
5-6424
S l
4
17753
5-6329
56
5
17783
5-6234
55
6
17813
5-6139
54
7
17843
5-6045
53
8
17873
5"595i
52
9
17903
5-5857
5i
IO
17933
5*5763
50
ii
17963
5-5670
49
IZ
17993
5*5577
48
I?
18023
5*5485
47
14
18053
5-5392
46
*5
18083
5-5300
45
16
18113
5-5209
44
*7
18143
5-5117
43
18
18173
5-5026
42
*9
18203
5*4935
4i
20
18233
5"4845
40
21
18263
5 '4754
39
22
18293
5-4664
38
23
18323
5*4575
3 7
24
18353
5*4485
36
25
18383
5*4396
35
26
1 8414
5*437
34
27
18444
5-4219
33
28
18474
5-4130
32
29
18504
5-4042
3i
30
18534
5*3955
30
31
18564
5*3867
29
32
18594
5-3780
28
33
18624
5*3693
27
34
18654
5*3696
26
35
18684
5'352o
25
36
18714
5*3434
24
37
18744
5*3348
23
38
18775
5-3263
22
39
18805
5*3177
21
40
18835
5-3092
20
4i
18865
5-3008
19
42
. '18895
5-2923
18
43
18925
5-2839
l l
44
18955
5*2755
16
45
18986
5-2671
15
46
19016
5-2588
14
47
19046
5-2504
13
48
19076
5-2421
12
49
19106
5*2339
11
50
19136
5-2256
10
5i
19166
5-2174
9
52
19197
5-2092
8
53
19227
5-2010
7
54
19257
5-1929
6
55
19287
5-1848
5
56
19317
5-1767
4
57
19347
5-1686
3
58
19378
5-1605
2
5 9
19408
5-1525
1
60
19438
5*1445
79
Cotangent
Tangent
79 Degrees
TANGENTIAL ANGLES FOR
CIRCULAR CURVES.
3000 feet \
30 chains Y Radii.
300 metres )
Bends.
In one 66 feet chain 3 inches
Rails 18 lengths ^\
,,
In one 100 chain 5
Rails 18 lengths -fa
Superelevation of Rails.
66 feet chain, 40 m. per hour 3"
100 feet chain, 45 m. per hour 2f "
Left-hand
Reading
359
358
357
356
355
354
353
352
351
350
349
348
347
346
345
344
343
342
341
340
339
338
338
337
336
2*7'
5-4
8*1
10-8
135
16-2
18-9
21-6
24-3
27-0
29-7
32-4
35-1
37-9
40-6
43-3
46-0
48-7
51-4
54-1
56-8
59-5
2-2
4-9
7-6
No. of
Chains
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Right-hand
Reading
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
21
22
23
57-3'
54-6
51-9
492
46-5
43-8
41-1
38-4
35-7
33-0
30-2
27-5
24-8
22-1
19-4
16-7
14-0
11-3
8-6
5-9
3-2
0-5
57-8
55-1
52-4
TABLE III.
125
11 Degrees
TANGENTIAL ANGLES FOR
11 c/
Tangent
19438
Cotangent
5"i445
5-1365
5-1286
60'
CIRCULAR CURVES.
I
2
19468
19498
59
58
3500 feet \
3
4
19529
19559
5-1206
5-1127
56
35 chains
Radii.
5
19589
5-1049
55
350 metres
6
19619
5-0970
54
7
8
19649
19680
5-o89Z
5-0813
53
52
Bends.
9
IO
19710
19740
5-0736
5-0658
51
50
In one 6G feet chain 2-g- inches
ii
19770
5-0580
49
Rails 18 n lengths T 3 g ,.
IZ
1 9801
5-0503
48
11
19832
5-0426
4 l
In one 100 chain 4^
IS
1 9861
1 9891
5'349
5-0273
46
45
Rails 18 lengths -|-
16
19921
5-0197
44
17
19952
5-0120
43
Superelevation of Rails.
18
19982
5-0045
42
19
zo
zooiz
20042
4-9969
4-9894
41
40
66 feet chain, 40 m. per hour 2| //
1
20073
4-9818
39
100 feet chain, 45 m. per hour 2|"
zz
23
20103
20133
4*9743
4-9669
38
24
20164
4*9594
36
Left-hand
No. of
Right-hand
25
26
20194
4-9520
4*9445
35
Reading
Chains
Reading
34
27
28
20254
20285
4-9372
4-9298
33
32
359 10-9'
1
49*1'
- 29
20315
4-9224
31
358 21*8
2
1 38-2
30
20345
4-9151
30
357 32-7
3
2 27-3
31
32.
20376
20406
4-9078
4-9005
29
28
356 43*6
4
3 10-4
33
20436
4-8932
27
355 54-4
5
4 5*5
34
35
20466
20497
4-8860
4-8788
26
25
355 5*3
6
4 54-7
36
20527
4-8716
24
354 16-2
7
5 43-8
37
38
20557
20588
4-8644
4-8572
23
22
353 27-1
8
6 32-9
39
20618
4-8501
21
352 38-0
9
7 22-0
40
20648
4-8430
20
351 48-9
10
8 11-1
4i
42
20679
20709
4*8359
4-8288
19
18
350 59-8
11
9 0-2
43
20739
4*8217
T I
350 10-7
12
9 49-3
44
45
'20770
20800
4-8147
4-8076
16
15
349 21-6
13
10 38-4
46
20830
4-8006
14
348 32-4
14
11 27-5
47
48
20861
20891
4*7936
4-7867
13
12
347 43-3
15
12 16-6
49
20921
4*7797
11
346 54-2
16
13 5-7
5
20952
4-7728
10
346 5*1
17
13 54-9
5i
Si
Z0982
21013
4'7659
4*7590
9
8
345 16-0
18
14 44-0
53
54
55
21043
21073
21 IO4
4-7521
4*7453
4*7385
I
5
344 26-9
343 37-8
19
20
15 33-1
16 22-2
56
2II34
47316
4
342 48-7
21
17 11-3
57
58
21 164
2II95
4-7249
4-7181
3
2
341 59-6
22
18 4
i 9
21225
471 1 3
1
341 10-4
23
18 49-5
60
21256
Cotangent
4-7046
Tangent
78
340 21-3
339 32-2
24
25
19 38 6
20 27-8
78 Degrees
126
TABLE III.
12 Degrees
TANGENTIAL ANGLES FOR
Tangent
Cotangent
12 d
21256
47046
6o /
CIRCULAR CURVES.
I
21286
4-6979
11
2
21 3 16
4-6912
4000 feet
3
4
21347
21377
4-6845
4-6778
%
40 chains
Radii.
5
21408
4-6712
55
400 metres
6
21438
4-6645
54
7
8
21469
21499
4'6S79
4-6513
53
52
Bends.
9
IO
21529
21559
4-6448
4-6382
5i
50
In one 66 feet chain 2 inches
ii
12
21590
21621
4-6317
4-6251
49
48
Rails 18 lengths ft
13
2165 1
4-6186
47
In one 100 chain 3f
*4
21682
4-6121
46
15
21712
4-6057
45
Rails 18 lengths ^
16
21743
4-5992
44
7
21773
4-5928
43
Superelevation of Rails.
18
21804
4-5864
42
9
20
21834
21864
4-5800
4*5736
4i
40
6Q feet chain, 45 m. per hour 3"
21
21895
4-5672
39
100 feet chain, 50 m. per hour 2"
22
21925
21956
4-5609
38
*3
4'5545
37
24
21986
4-5482
36
Left-hand
No. of
Right-hand
*s
22017
4'54 x 9
35
Beading
Chains
Reading
26
22047
22078
22108
4*5356
4-5294
4-5231
27
28
34
33
32
359 17-0'
1
43-0'
29
22139
4-5169
3i
358 34-0
2
1 25-9
30
22169
4-5107
30
357 51-1
3
2 8-9
3i
32
22200
22231
4*5045
4-4983
3
357 8-1
4
2 51*9
33
34
35
22261
22292
22322
4-4921
4-4860
4-4798
3
25
356 25-1
355 42*2
5
6
3 34-9
4 17-8
36
22353
4*4737
24
354 59-2
7
5 0-8
37
38
22383
22414
4-4676
4-4615
23
22
354 16-2
8
5 43*8
39
22444
4*4554
21
353 33*2
9
6 26*7
40
22475
4*4494
20
352 50-3
10
7 97
4i
42
22505
22536
4*4433
4*4373
19
18
352 7-3
11
7 52*7
43
44
45
22567
22597
22628
4*4313
4*42.53
4*4193
15
351 24*3
350 41-4
12
13
8 35*7
9 18'6
46
22658
4*4133
14
349 58-4
14
10 1-6
47
48
22689
22719
4*4074
4-4015
13
12
349 15-4
15
10 44-6
49
22750
22781
2281 1
22842
4*3955
4-3896
4-3838
4*3779
11
348 32-4
16
11 27*5
50
5i
5*
10
I
347 49*5
347 6-5
17
18
12 10-5
12 53-5
53
54
22872
22903
4-3720
4-3662
I
346 23-5
19
13 36-5
55
22934
4-3604
5
345 40-6
20
14 19-4
56
22964
4*3545
4
344 57-6
21
15 2*4
57
58
22995
23026
4*3487
4*3430
3
2
344 14-6
22
15 45*4
I 9
23056
4*3372
I
343 31*6
23
16 28*3
60
23087
Cotangent
4*33*4
Tangent
77
342 48-7
342 5*7
24
25
17 11-3
17 54-3
77 Di
GREES
TABLE III.
127
13 Degrees
TANGENTIAL ANGLES FOB
CIRCULAR CURVES.
13 o'
Tangent
23087
Cotangent
4'33i4
60'
2
23 1 17
23148
4*3257
4-3200
59
58
4500 feet \
3
4
23179
23209
4-3142
4-3085
S
45 chains
Radii.
5
23240
4*3029
55
450 metres
6
23271
4-2972
54
7
8
23314
23332
4-2915
4-2859
53
52
Bends.
9
IO
23363
23393
4-2803
4*2747
5i
50
In one 66 feet chain 2 inches
ii
23424
4-2691
49
Rails 18 lengths
12
13
23455
23485
4-2635
4'2579
48
4 7
In one 100 chain 3
14
15
23516
23547
4-2523
4-2468
46
45
Rails 18 lengths *fa
16
7
23578
23608
4-2413
4-2358
44
43
SUPERELEVATION OP RAILS.
18
23639
4-2302
42
19
23670
4-2248
4i
66 feet chain, 45 m. per hour 2$"
20
23700
4-2193
40
21
23731
4-2138
39
100 feet chain, 50 m. per hour 2"
22
23
23762
23793
4-2084
4-2029
38
3 l
24
23823
4-1975
36
Left-hand
No. of
Eight-hand
25
26
27
28
29
23854
23885
23916
23946
23977
4-1921
4-1867
4-1813
4-1760
4-1706
35
Beading
Chains
Reading
34
33
32
31
359 21-8'
358 43-6
1
2
38-2'
1 16-4
30
24008
4-1652
30
358 5-4
3
1 54-6
31
32
24039
24069
4* 1 599
4*1546
29
28
357 27-2
4
2 32-8
33
24100
4' '493
% l
356 49-0
5
3 11-0
34
35
241 3 1
24162
4-1440
4-1387
26
25
356 10-1
6
3 49-2
36
24193
4'*335
24
355 32-6
7
4 27-4
37
38
39
24223
24254
24285
4-1282
4-1230
4-1177
23
22
21
354 54-4
354 16-2
8
9
5 5-6
5 43-8
40
24316
4-1125
20
353 38-0
10
6 22-0
4i
42,
'24347
24377
4-1073
4-1021
19
18
352 59-8
11
7 0-2
43
24408
4-0969
\l
352 21-6
12
7 38-4
44
45
24439
24470
4-0918
4-0866
16
15
351 43-4
13
8 16-6
46
24501
4-0815
14
351 5-2
14
8 54-7
47
48
24532
24562
4-0763
4-0712
13
12
350 27-0
15
9 32-9
49
24593
4-0661
11
349 48-8
16
10 11-1
50
24624
4-0610
10
349 10-6
17
10 49-3
5i
52
24655
24686
4-0559
4-0509
9
8
348 32-4
18
11 27-5
53
24717
4-0458
I
347 54-2
19
12 5-7
54
55
24748
24778
4-0408
4*0357
6
5
347 16-0
20
12 43-9
56
24809
4-0307
4
346 37-9
21
13 22-1
57
58
24840
24871
4-0257
4-0207
3
2
345 59-7
22
14 0-3
I 9
24902
4-0157
1
345 21-5
24
14 38-5
60
24933
Cotangent
4-0107
Tangent
76
344 43-3
344 5-1
25
26
15 16-7
15 54-9
76 Degrees
128
TABLE III.
14 Degrees
TANGENTIAL ANGLES FOR
J
Tangent
Cotangent
1 *4 C
!
24933
24964
4*0107
4*0058
60'
59
CIRCULAR CURVES.
2
24995
4 , ooo8
58
3
25026
3-9959
s l
5000 feet \
4
5
25056
25087
3-9909
3*9860
56
55
50 chains \
Radii.
6
25118
3*9811
54
500 metres >
7
25149
3-9762
53
8
25180
3-9713
52
9
2521 1
3-9665
51
Bends.
IO
25242
3-9616
50
ii
25273
3-9568
49
In one 66 feet chain 2 inches
12
13
25304
253H
3*95'9
3-947I
48
4 Z
In one 100 chain 3
14
25366
3-9423
46
15
25397
3*9375
45
16
25428
3-9327
44
Superelevation <
)F Rails.
17
25459
3-9279
43
18
*9
25490
25521
3-9231
3-9183
42
41
66 feet chain, 50 m.
per hour 2f "
20
25552
3-9136
40
100 feet chain, 50 m.
per hour 2"
21
25583
3-9089
39
22
25614
3-9041
38
23
25645
3-8994
n
24
25676
3-8947
36
Left-hand
No. of
Right-hand
15
26
27
28
29
25707
25738
25769
25800
25831
3-8900
3-8853
3-8806
3-8760
3-8713
35
Reading
Chains
Reading
34
33
32
31
359 25-6'
358 51-2
1
2
34-4'
1 8-7
30
25862
3-8667
30
358 16-9
3
1 43-1
31
32
25893
25924
3-8620
3-8574
29
28
357 42-5
4
2 175
33
25955
3-8528
z i
357 8-1
5
2 51-9
34
35
25986
26017
3 -8482
3-8436
26
25
356 33-7
6
3 26-3
36
26048
3-8390
24
355 59-3
7
4 0-6
11
26079
261 10
3-8344
3-8299
23
22
355 25-0
8
4 35-0
39
26141
3-8253
21
354 50-6
9
5 9-4
40
26172
3-8208
20
354 16-2
10
5 43-8
4i
42
26203
26235
3-8162
3-8117
19
is
353 41-8
11
6 18-1
43
26266
3-8072
l i
353 75
12
6 52-5
44
45
26297
26328
3-8027
3-7982
16
15
352 33-1
13
7 26-9
46
26359
37937
14
351 587
14
8 1-3
47
48
26390
26421
3-7893
3-7848
13
12
351 24-3
15
8 35-7
49
26452
3-7803
11
350 50-0
16
9 10-0
50
26483
3 '7759
10
350 15-6
17
9 44-4
5i
5*
26546
37715
3-7670
9
8
349 41-2
18
10 18-8
53
54
55
26577
26608
26639
3-7626
3-7582
37538
I
5
349 6-8
348 32-4
19
20
10 53-1
11 27-5
56
26670
3-7494
4
347 58-1
21
12 1-9
57
5
26701
26733
37451
3-7407
3
2
347 23-7
22
12 363
I 9
26764
37363
1
346 49-3
23
13 10-7
6q
26795
Cotangent
3-7320
Tangent
75
|
346 14-9
345 406
24
25
13 45-0
14 19-4
75 De
GUEES
1
TABLE III.
129
15 Degrees
GLES FOR
Tangent
Cotangent
TANGENTIAL AN
i S o'
i
Z6795
z68z6
3732o
37277
60'
59
CIRCULAR CURVES.
z
Z6857
37233
58
3
z6888
37190
55
5500 feet \
4
5
zfyzo
Z6951
37H7
37104
55 chains J-
Radii.
6
Z098z
37061
54
550 metres'
7
Z701J
37018
53
8
9
27044
^7076
3-6976
3 '693 3
52
5i
Bends.
10
Z7107
3-6890
50
ii
IZ
Z7138
Z7169
3*6848
3-6806
49
48
In one 6G feet chain If inches
13
14
Z7Z01
z 7 z 3 z
3-6763
3-6721
46
In one 100 chain 2f
*5
Z7z6j
3-6679
45
16
27294
Z7jz6
3-6637
44
Superelevation of Rails.
'7
3-6595
43
18
19
27357
z 73 88
3-6553
36512
42
4i
66 feet chain, 50 m.
3er hour 2"'
zo
27419
3-6470
40
100 feet chain, 50 m.
3er hour 2"
ZI
27451
3*6428
39
zz
23
z 74 8z
27513
36346
38
3 Z
z 4
27544
\'%f
36
Left-hand
No. of
Right-hand
25
z6
z 7
z8
z 9
27576
Z7607
27639
Z770I
3-6263
3*6zzz
3-6181
3-6140
3-6099
35
Reading
Chains
Reading
34
33
32
3i
359 28-7'
358 57-5
1
2
31-2'
1 2-5
30
27732
3-6058
30
358 26-2
3
1 33-7
3i
3Z
27764
27795
3 '6018
3-5977
29
28
357 55
4
2 5-0
33
Z78z6
3-5937
Z7
357 23-7
5
2 36-3
34
35
Z7858
Z7889
3-5896
3-5856
26
25
356 52-5
6
3 75
36
Z79ZI
3-5815
24
356 21-2
7
3 38-7
37
38
27952
27983
3-5775
3*5735
23
ZZ
355 50-0
8
4 10-0
39
'Z8015
3-5695
3-5655
21
355 18-7
9
4 41-3
40
28046
20
354 47-5
10
5 12-5
4i
42
28077
28109
3-5615
3-5576
19
18
354 16-2
11
5 43-8
43
28140
28172
28203
3-5536
3-5496
3-5457
15
353 45-0
12
6 15-0
44
45
353 13-7
13
6 46-3
46
Z8Z34
Z8266
28297
3-54I7
14
352 42-5
14
7 17-5
47
48
3-5378
3-5339
13
IZ
352 11-2
15
7 48-8
49
28329
3-5300
II
351 40-0
16
8 20-0
50
28360
3-5260
10
351 87
17
8 513
5i
52
28391
28423
3-5221
3- 5 i8z
9
8
350 37-5
18
9 22-5
53
54
55
28454
28486
28517
3-5I44
3-5105
3-5066
I
5
350 6-2
349 34-9
19
20
9 53-8
10 25-0
56
28549
3-50Z7
4
349 3-7
21
10 56-3
57
58
28580
28612
3-4989
3-4950
3
2
348 32-4
22
11 27-5
I 9
28643
3-49I2
348 1-2
23
11 58-8
60
28675
Cotangent
3-4874
Tangent
74
347 29-9
346 58-7
24
25
12 300
13 1-3
74 De
GREES
F 3
130
TABLE III.
16 Degbees
TANGENTIAL ANGLES FOR
Tangent
Cotangent
i6 d
28675
3*4874
60'
CIRCULAR CURVES.
i
28706
3'483S
59
z
28738
3*4797
58
3
28769
3 "4759
5 I
6000 feet -
4
5
28801
28832
3-4721
3*4683
56
55
60 chains
Radii.
6
28864
3*4645
54
600 metres -
7
28895
3-4608
53
8
28927
3*457
51
9
28958
3*4531
51
Bends.
IO
28990
3*4495
50
ii
29021
3*4457
49
In one 66 feet chain If inches
IZ
M
29053
29084
291 16
3-4420
3-4382
3*4345
48
46
In one 100 chain 2\
IS
29147
3-4308
45
16
Z9179
3-4271
44
Superelevation op Rails.
17
Z9210
3*4134
43
It
9
29242
29274
3*4197
3-4160
42
41
66 feet chain, 50 m. per hour 2"
zo
Z9305
3-4113
40
100 feet chain, 50 m. per hour 2"
ZI
19337
3-4086
39
zz
13
29368
29400
3-4050
3-4013
38
3 l
Z4
29432
3*3977
36
Left-hand
No. of
Right-hand
*S
z6
Z8
z 9
19403
3*394
35
Reading
Chains
Reading
29495
29526
Z9558
Z9S9
3'394
3*3867
3-3831
3*3795
34
33
31
31
359 31-3'
359 2-7
1
2
28*6'
57*3
30
29621
3*3759
3
358 34-1
3
1 25*9
31
3*
19653
29685
3*3713
3-3687
19
z8
358 5*4
4
1 54-6
33
29716
3-3651
Z7
357 36-7
5
2 23-2
34
35
29748
29780
3-3615
3-3580
26
15
357 8*1
6
2 51-9
36
2981 1
3*3544
14
356 39-5
7
3 20*5
37
38
29843
29875
3-3508
3*3473
13
22
356 10-8
8
3 49-2
39
29906
3*3437
ZI
355 42-2
9
4 17*8
40
29938
3*3401
ZO
355 13-5
10
4 46-5
4*
42
29970
30001
3-3366
3*3331
19
18
354 44-9
11
5 15-1
43
44
45
30033
30065
30097
3-3296
3-3261
3-3226
16
15
354 16-2
353 47-6
12
13
5 43-8
6 12-4
46
30128
3-3191
14
353 18-9
14
6 41-1
47
48
30160
30192
3-3156
3-3121
13
IZ
352 50-3
15
7 9-7
49
30224
3-3086
II
352 21-6
16
7 38-4
50
30255
3-3052
IO
351 53-0
17
8 7-0
5i
52
30287
30319
3-3017
3-2982
9
8
351 24-3
18
8 35*6
53
54
55
30351
30382
30414
3-2948
3-2913
3-2879
I
S
350 55-7
350 27-0
19
20
9 4-3
9 33-0
56
30446
3-2845
4
349 58-4
21
10 1-6
57
58
30478
30509
3-2810
3-2776
3
z
349 29-7
22
10 30-2
12
30541
3-2742
1
349 1-1
23
10 58-9
60
30573
Cotangent
3-2708
Tangent
73
348 32-4
348 3-8
24
25
11 27-5
11 56*2
73 Degrees
TABLE III.
131
17 Degrees
TANGENTIAL ANGLES FOR
Tangent
Cotangent
i 7 d
30573
3-2708
6b'
CIRCULAR CURVES.
i
30605
3-2674
59
z
30637
3-2640
58
3
30669
3-2606
TL
6500 feet \
4
5
30700
30732
3-2572
3-2539
56
55
65 chains \
Radii.
6
30764
30796
3-2505
54
650 metres '
7
3-2471
53
8
30828
32438
52
9
30860
3-2404
51
Bends.
IO
30891
3-2371
50
li
30923
3-2338
49
In one 66 feet chain l inches
IZ
'30955
3-2304
48
H
30987
3-2271
4 7
In one 100 chain
14
31019
3-2238
46
15
31051
3-2205
45
16
31083
3-2172
44
SUPERELEVATION OP RAILS.
7
18
19
31114
3 1 146
31178
3-2139
3-2106
3-2073
43
42
41
66 feet chain, 50 m. per hour 2"
zo
31210
3 -2040
40
100 feet chain, 50 m. per hour 1 \"
ZI
31242
3-2007
39
zz
31274
31306
3-I975
38
23
3*1942
3 7-
Z4
31338
3-1910
3-1877
36
Left-hand
No. of
Right-hand
*5
31370
35
Reading
Chains
Reading
z6
31402
31434
31466
3-1845
3-1812
3-1780
34
33
32
z 7
z8
359 33-5'
1
26-4'
z 9
31498
3-1748
31
359 7-1
2
52-9
3
31530
3-I7I5
30
358 40-7
3
1 19-3
3i
32
31562
31594
3-1683
3-1651
29
28
358 14-2
4
1 45-8
33
34
35
31626
3165
31690
3-1619
3-1587
3-1555
z6
25
357 47-8
357 21-3
5
6
2 12-2
2 38-7
36
317"
3-1523
24
356 54-9
7
3 5-1
37
38
31754
31786
3-1492
3-1460
23
zz
356 28-4
8
3 31-5
39
31818
3-1428
ZI
356 2-0
9
3 58-0
40
31850
3*1397
3-1365
3-1334
zo
355 35-5
10
4 24-4
4i
4Z
3188Z
31914
31946
31978
32010
19
18
355 9-1
11
4 50-9
43
44
45
3-1302
3-1271
3-1239
15
354 42-7
354 16-2
12
13
5 17-3
5 43-8
46
32042
3-1208
14
353 498
14
6 10-2
47
48
32074
32106
3-1177
3-1146
13
12
353 23-3
15
6 36-7
49
32139
3-1115
II
352 56-9
16
7 3-1
50
32171
3-1084
IO
352 30-4
17
7 29-5
5i
5*
32203
32235
3-1053
3-1022
9
8
352 4-0
18
7 56-0
53
54
55
32267
32299
32331
3-0991
3-0960
3-0929
I
5
351 37-6
351 11-1
19
20
8 22-4
8 48-9
56
32363
3-0899
4
350 44-7
21
9 15-3
57
58
32396
32428
3-0868
3-0837
3
2
350 18-2
22
9 41-8
s
32460
3 -0807
1
349 51-8
23
10 8-2
60
32492
Cotangent
3-0776
Tangent
72
349 25-3
348 58-9
24
25
10 34-6
11 1-1
72 Degrees
132
TABLE III.
18 Degrees
TANGENTIAL ANGLES FOR
Tangent
Cotangent
i8 o
i
32492
32524
3-0776
3-0746
60'
59
CIRCULAR CURVES.
2
32556
3-0716
58
3
4
32588
326x0
3-0685
3-0655
9
7000 feet \
5
32653
3-0625
55
70 chains \ Radii.
6
32685
3-0595
54
700 metres )
7
32717
3-0564
53
8
32749
3'0534
52
9
32782
3-0504
51
Bends.
lO
32814
3 '0474
50
ii
32846
3'Q445
49
In one 6Q feet chain If inches
12
T 3
32878
3291 1
3-0415
3-0385
48
4 7
In one 100 chain 2
*4
32943
3*0355
46
15
32975
3-0325
45
16
33007
3-0296
44
Superelevation of Rails.
17
33040
3-0266
43
18
19
33072
33104
3-0237
3-0207
42
41
66 feet chain, 45 m. per hour l"
20
21
33136
33168
3-0178
3-0148
40
39
100 feet chain, 50 m. per hour 1"
22
33201
3-0119
38
23
33233
3-0090
37
24
33266
33298
33330
3*oo6i
36
Left-hand
No. of
Right-hand
25
26
3-0031
3-0002
2-9973
2-9944
35
34
33
32
Reading
Chains
Reading
27
28
33363
33395
359 35-4'
1
24-5'
a*
33427
2-9915
31
359 11-0
2
49-1
30
33460
2-9886
30
358 46*3
3
1 136
3i
32
33492
33524
2-9857
2-9829
29
28
358 21-8
4
1 38-2
33
34
35
'33557
33589
33621
2-9800
2-9771
2'9743
26
25
357 57*2
357 32'7
5
6
2 2-8
2 27-3
36
33654
336S6
33719
2-9714
24
357 8*1
7
2 51-9
37
38
2-9685
2-9657
23
22
356 43-5
8
3 16-4
39
33751
2-9628
21
356 19'0
9
3 41-0
40
33783
33816
33848
2-9600
20
355 54*4
10
4 5-5
4i
42
2-9572
2-9543
19
18
355 29*9
11
4 30-1
43
44
45
33881
339 J 3
33945
2-9515
2-9487
2-9459
M
15
355 5*3
354 40*8
12
13
4 54-6
5 192
46
33978
2-9430
14
354 16-2
14
5 43-8
47
48
34010
34043
2*9402
2-9374
13
12
353 51-7
15
6 8-3
49
50
34075
34108
2-9346
2-9318
11
10
353 27'1
353 2-5
16
17
6 32-9
6 57-4
51
52
34140
34173
2-9290
2-9263
9
8
352 38-0
18
7 22-0
53
54
34205
34238
2-9235
2-9207
I
352 13-4
19
7 46-5
55
34270
2-9179
5
351 48'9
20
8 11-1
56
34303
2-9152
4
351 243
21
8 356
57
58
'34335
34367
2-9124
2-9097
3
2
350 59-8
22
9 0-2
I 9
60
34400
"34433
Cotangent
2-9069
2-9042
Tangent
71
350 35-2
350 107
349 46-1
23
24
25
9 24-8
9 49-3
10 13-9
71 Di
GREES
TABLE III.
133
!
19 Degrees
i
Tangent
Cotangenl
19 o'
34433
2-9042
60'
I
34465
2-9014
59
I
34498
2-8987
58
?
34530
2-8959
57
4
34563
2-8932
56
5
34596
2-8905
55
6
34628
2-8878
54
7
34661
2-8851
53
8
34693
2-8824
2-8796
52
9
34726
51
IO
'34758
2-8769
50 '
ii
34791
2-8743
49
12
34823
2-8716
48
13
34856
2-8689
47
'4
34889
2-8662
46
15
34922
2-8635
45
16
34954
2-8608
44
17
34987
2-8582
43
18
35020
2-8555
42
19
35052
2-8528
4i
20
35085
2-8502
40
21
35"8
2-8475
39
22
35150
35183
2-8449
2-8422
38
z 3
37
24
35216
2-8396
36
25
35248
2-8370
35
26
35281
2-8343
34
27
353H
35346
2-8317
33
28
2-8291
32
29
35379
2-8265
31
30
35412
2-8239
30
31
35444
2-8213
29
31
35477
2-8187
28
33
355io
2-8161
27
34
35543
2-8135
26
35
35576
2-8109
25
36
35608
2-8083
24
37
35641
2-8057
23
38
35674
2*8031
22
39
35707
2-8005
21
40
35740
2-7980
20
4i
35772
27954
19
42
35805
2-7928
18
43
35838
2-7903
17
44
35871
27877
l6
45
35904
2-7852
15
46
'35937
2-7826
14
47
35969
2-7801
13
48
36002
27776
12
49
36035
2-7750
II
So
36068
27725
IO
5i
36101
27700
9
52
36134
27674
8
53
36167
2-7649
7
54
36199
2-7624
6
55
36232
2-7599
5
56
36265
27574
4
57
36298
27549
3
58
36331
2-7524
2
I 9
36364
2-7499
1
60
36397
2-7474
70
<
Cotangent!
Tangent
70 De<
SREES
TANGENTIAL ANGLES FOR
CIRCULAR CURVES.
7500 feet \
75 chains l Radii.
750 metres-'
Bends.
In one 66 feet chain 1 inches
In one 100 chain 2
SUPERELEVATION OF RAILS.
66 feet chairi, 45 m. per hour 1"
100 feet chain, 50 m. per hour 1"
Left-hand
Reading
No. of
Chains
359 c
359
358
358
358
357
357
356
356
356
355
355
355
354
354
353
353
353
352
352
351
351
351
350
350
37-1'
14-2
51-2
28-3
5-4
42-5
19-6
56-6
33-7
10-8
47-9
25-0
2-1
39-1
16-2
53-3
30-4
7-5
44-5
21-6
58-7
35-8
12-9
50-0
27-0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Right-hand
Reading
1
1
1
2
2
3
3
3
4
4
4
5
5
6
6
6
7
7
8
8
8
9
9
22-9'
45-8
8-7
31-7
54-6
17-5
40-4
3-3
26-3
49-2
12-1
35-0
57-9
20-8
43-8
6-7
29-6
52-5
15-4
38-4
1-3
24-2
47-1
10-0
32-9
134
TABLE III.
20 Degrees
TANGENTIAL ANGLES FOR
Tangent
Cotangent
top of
36397
a*7474
6V
i
36430
27449
3
CIRCULAR CUR
2
36463
27425
3
36496
27400
s l
4
5
'< 9
36562
*737S
27350
56
55
Radius 80 chains.
6
36595
27326
S4
7
36628
27301
S3
Bends.
8
36661
27277
5*
9
IO
36694
36727
27252
27228
5i
5
In one 66 feet chain 1 inch
ii
12
36760
36793
27203
27179
49
48
In one 100 chain 1|
1J
36826
27154
4 7
4
36859
27130
46
IS
36892
27106
45
Superelevation of Rails.
16
36925
27081
44
*7
IB
36958
36991
27057
27033
43
42
66 feet chain, 50 m. ]
)er hour 1"
19
20
37024
37057
27009
2-6985
4i
40
100 feet chain, 50 m. per hour 1"
21
37090
2-6961
39
22
*3
37123
37157
2-6937
2-6913
38
24
37190
2-6889
36
Left-hand
No. of
Right-hand
*s
26
37223
37256
2-6865
2-6841
35
Reading
Chains
Reading
34
27
37289
2-6817
33
359 38-5'
1
21-5
28
29
37322
*3735S
2-6793
2-6769
3*
3i
359 17-0
2
430
30
37388
2-6746
3
358 55-5
3
1 4-4
3
32
37422
'37455
2-6722
2-6698
2 2
28
358 34-1
4
1 25-9
33
37488
2-6675
z l
358 12-6
5
1 474
34
35
37521
'37554
2-6651
2-6628
26
15
357 51-1
6
2 8-9
36
37687
2-6604
24
357 29-6
7
2 30-4
37
38
39
37620
37654
37687
2-6581
2-6557
2-6534
23
22
21
357 8-1
356 46-6
8
9
2 51-9
3 13-4
40
37720
2-6510
20
356 25-1
10
3 34-9
4i
42
'37754
37787
2-6487
2-6464
\l
356 3-6
11
3 56-3
43
37820
2-6440
l l
355 42-2
12
4 17-8
44
45
37853
37887
2-6417
2-6394
16
15
355 20-1
13
4 39-3
46
37920
2-6371
14
354 59-2
14
5 " 0-8
47
48
37953
37986
2-6348
2-6325
13
12
354 37-7
15
5 22-3
49
38020
2-6302
11
354 16-2
16
5 43-8
50
38053
2-6279
10
353 54-7
17
6 5-3
51
52
38086
38120
2-6256
2-6233
9
8
353 33-2
18
6 26-7
53
54
55
38153
38186
38220
2-6210
2-6187
2*6164
I
5
353 11-8
352 50-3
19
20
6 48-2
7 9-7
56
38253
2-6141
4
352 28-8
21
7 31-2
57
58
38286
38320
2-6118
2-6096
3
2
352 7-3
22
7 527
I 9
38353
2-6073
1
351 45-8
23
8 14-2
60
38386
Cotangent
2-6050
Tangent
69
351 24-3
351 2-8
24
25
8 35-7
8 57-1
69 Degrees
TABLE III.
135
21 Degrees
TANGENTIAL ANGLES FOR
Tangent
Cotangent
21 O'
38386
38420
2*6050
2-6028
60'
59
CIRCULAR CURVES.
z
38453
2 '6005
58
3
38487
2-5983
57
4
38520
2-5960
56
Radius 85 ch
ains.
5
38553
2-5938
55
6
38587
2-5915
54
7
8
38620
38654
2-5893
2-5870
53
52
Bends.
9
38687
2-5848
51
IO
38721
2-5826
50
In one 66 feet chain 1 inch
ii
IZ
38754
38787
2-5803
2-5781
49
48
In one 100 chain If
J
38821
2*5759
4 Z
14
38854
2*5737
46
IS
38888
2-5714
45
Superelevation of Rails.
16
38921
2-5692
44
7
18
38955
38988
2-5670
2-5648
43
42
66 feet chain, 50 m. per hour 1"
9
ZO
39022
39<=55
2-5626
2-5604
4i
40
100 feet chain, 50 m. per hour 1"
ZI
39088
2-5582
39
2Z
23
39122
39156
2-5560
2-5538
38
37
Z4
39186
2-5516
36
Left-hand
No. of
Right-hand
25
z6
39223
39256
2*5495
35
Reading
Chains
Reading
2'5473
34
z 7
39290
2-5451
33
359 39*8'
1
20'2'
28
29
39324
39357
2-5429
2-5408
32
3 1
359 19-5
2
40 4
30
39391
2-5386
30
358 59-3
3
1 0-6
3i
3*
39425
39458
2-5364
2*5343
29
28
358 391
4
1 20*8
33
39492
2*5321
27
358 18-9
5
1 41-1
34
35
39526
'39559
2-5300
2-5278
26
25
357 58-7
6
2 1-3
36
39593
2-5257
24
357 38-4
7
2 21-5
37
39626
2-5235
23
357 18-2
8
2 41-8
38
39
39660
39694
2-5214
2-5192
22
21
356 58-0
9
3 2-0
40
39727
2-5171
ZO
356 37-8
10
3 22-2
4i
42
39761
'39795
2-5150
2-5128
19
18
356 17-5
11
3 42-4
43
39829
2-5107
l l
355 57*3
12
4 2-6
44
45
39862
39896
2-5086
2-5065
16
15
355 37-1
13
4 22-9
46
39930
2*5044
14
355 16-9
14
4 431
47
39963
2-5022
13
354 56-7
15
5 3-3
48
49
'39997
40031
2-5001
2-4980
12
II
354 36-4
16
5 23-5
50
40065
2*4959
IO
354 16-2
17
5 438
51
52
40098
4C132
2-4938
2-4917
9
8
353 56-0
18
6 4-0
53
40166
2-4896
7
353 35-8
19
6 24-2
54
55
40200
40234
2-4875
2-4854
6
5
353 15-6
20
6 44-4
56
40267
2*4834
4
352 55-3
21
7 4-7
57
40301
2-4813
3
352 35-1
22
7 249
58
59
40335
40369
2*4792
2-4771
z
352 14-9
23
7 45-1
60
40403
2*4750
68
351 54-7
24
8 5*3
Cotangent
Tangent
351 34-3
25
8 25-5
68 Di
"GREES
ia6
TABLE III.
22 Degrees
23 Degrees
24 Degrees
Tangent
Cotangent
Tangent
Cotangent
Tangent
Cotangent
o*
40403
2-4750
42447
2-3558
44522
2*2460
60
i
40436
2-4730
42481
2*3539
44557
2-2442
59
2
40470
2-4709
42516
2-3520
44592
2-2425
58
J
40504
2-4688
42550
2-3501
44627
2*2407
57
4
40538
2-4668
42584
2-3482
44662
2-2390
56
5
40572
2-4647
42619
2-3463
44697
2-2372
55
6
40606
2-4627
42653
2*3444
44732
2-2355
54
7
40640
2-4606
42688
2-3425
44767
2-2337
53
8
40673
2-4585
42722
2-3406
44802
2-2320
52
9
40707
2-4565
42756
2-3388
44836
2-2303
5i
IO
40741
2*4545"
42791
2*3369
44871
2-2285
50
ii
40775
2-4524
42825
2-3350
44906
2-2268
49
\%
40809
2.4504
42860
2-3331
44941
2-2251
48
13
40843
2-4483
42894
2-3313
44976
2-2233
47
*4
40877
2-4463
42928
2-3294
4501 1
2-22l6
46
15
4091 1
2-4443
42963
2-3275
45046
2-2I09
45
16
40945
2-4422
42997
2-3256
45081
2'2l8l
44
7
40979
2-4402
43032
2-3238
45116
2*2l64
43
18
41013
2-4382
43066
2-3219
45151
2-2147
42
19
41047
2-4362
43 1 01
2*3201
45186
2-2I30
4i
20
41 08 1
2-4342
43135
2-3182
45221
2*2113
40
21
41 1 15
2-4322
43170
2-3164
45256
2-2006
11
22
41 149
2-4301
43204 .
2-3145
45291
2-2079
23
41183
2-4281
43239
2-3127
45326
2*200I
3 Z
24
41217
2-4261
43273
2-3108
45362
2-2044
36
*5
41251
2-4241
433o8
2-3090
45397
2-2027
35
26
41285
2-4221
43342
2-3071
45432
2-20IO
34
*7
41 3 19
2-4201
'43377
2-3053
45467
2-1993
33
28
41353
2-4181
43412
2-3035
45502
2*1976
32
29
41387
2-4162
43446
2-3016
'45537
2-1959
3i
30
41421
2-4142
43481
2-2998
45572
2-1942
30
?i
4H55
2-4122
43515
2-2980
45607
2-1926
29
3*
41489
2-4102
43550
2-2961
45642
2-1909
28
33
41524
2-4082
43585
2-2943
45678
2*1892
27
34
41558
2-4062
43619
2*2925
45713
2*1875
26
35 *
41592
2-4043
43654
2-2907
45748
2-I858
25
36
41626
2-4023
43688
2-2889
45783
2-I84I
24
37
41660
2-4003
43723
2-2870
45818
2-I825
23
38
41694
2-3984
43758
2-2852
45853
2-1808
22
39
417^8
2-3964
43792
2-2834
45889
2*1791
21
40
41762
2*3944
43827
2-2816
45924
2*1774
20
4i
41797
2-3925
43862
2-2798
45959
2-1758
19
42
4183 1
2-3905
43896
2-2780
"45994
2-1741
18
43
41865
2-3886
43931
2-2762
46030
2-1724
l l
44
41899
2-3866
43966
2-2744
2-2726
46065
2-1708
16
45
41933
2-3847
44001
46100
2-1691
5
46
41968
2-3827
44035
2-2708
46135
2-1675
14
47
42001
2-3808
44070
2-2690
461 7 1
2*1658
13
48
42036
2-3789
44105
2-2673
46206
2-1641
12
49
42070
2-3769
44140
2-2655
46241
2-1625
11
50
42115
2-3750
44174
2-2637
46277
2-1608
10
5i
42139
2-3731
44209
2-2619
46312
2-1592
9
51
42173
2-3711
44244
2-2601
46347
2-1576
8
53
42207
2-3692
44279
2-2584
46383
2-1559
7
54
42242
2-3673
44313
2-2566
46418
2-1543
6
55
42276
2-3654
44348
2-2548
46453
2*1526
5
56
42310
2-3634
44383
2-2530
46489
2-1510
4
57
42344
2-3615
44418
2-2513
46524
2*1494
3
58
42379
2-3596
44453
2-2495
46559
2*1477
2
f 9
42413
2-3577
44488
2-2477
46595
2*1461
1
60
42447
2-3558
44522
2*2460
46630
2*14-1-5
Cotangent
Tangent
Cotangent
66 De
Tangent
GREES
Cotangent
Tangent
67 Degrees
65
Degrees
1
TABLE III.
137
25 Degrees
26 Degrees
27 Degrees
Tangent
Cotangent
Tangent
Cotangent
Tangent
Cotangent
d
46630
2-1445
48773
2*0503
50952
1-9626
60'
i
46666
2*1428
48809
2*0487
50989
1-9612
59
z
46701
2*1412
48845
2*0472
51025
1-9597
58
3
46737
2*1396
48881
2*0457
51062
1-9583
57
4
46772
2*1380
48917
2*0442
51099
1-9569
56
5
46807
2*1363
48953
2*0427
'53S
1-9555
55
6
46843
2*1347
48989
2*0412
51 172
1-9541
54
7
46878
2*1331
49025
2*0397
51209
I-9527
53
8
46914
2*1315
49061
2*0382
51246
1-95I3
52
9
46949
2*1299
49097
2*0367
51282
1-9499
51
10
46985
2*1283
49133
2*0352
51319
1-9485
50
ii
47020
2*1267
49160
49206
2*0337
51356
i'947i
49
12
47056
2*1251
2*0322
51393
1-9457
48
I?
47091
2*1235
49242
2*0307
51429
1-9443
47
14
47127
2*1219
49278
2*0292
51466
1-9430
46
IS
47163
2*1203
493H
2*0277
51503
1-9416
45
16
47198
2*ii87
4935o
2*0263
51540
1-9402
44
17
47234
2*1171
49386
2*0248
51577
1-9388
43
18
47269
2*1155
49423
2*0233
51613
1-9374
42
19
47305
2*1139
49459
2*0218
51650
1*9360
41
20
4734o
2*1123
"49495
2*0203
51687
1-9347
40
21
47376
2*1107
49531
2*Ol89
51724
1*9333
39
22
47412
2*1091
49567
2*OI74
51761
1-9319
38
2.3
47447
2*1075
49604
2*OI59
51798
1-9305
3 Z
24
47483
2*1059
49640
2*OI44
51835
1-9291
36
25
47519
2*1044
49676
2*OI30
51871
1-9278
35
26
'47554
2*1028
49712
2*0115
51908
1-9264
34
27
47590
2*IOI2
'49749
2*OIOO
51945
1-9250
33
28
47626
2*0996
49785
2*O086
51982
1-9237
32
29
47661
2*098l
49821
2*007I
52019
1-9223
31
30
47697
2*0965
49858
2*0056
52056
1-9209
30
3i
'47733
2*0949
49894
2*0042
52093
1-9196
29
32
47768
2*0934
49930
2*0027
52130
1-9182
28
33
47804
2*09l8
49967
2*OOI3
52167
1-9168
27
34
47840
2'0902
50003
1*9998
52204
1-9I55
26
35
47876
2*0887
50039
1*9984
52241
i-9'4i
25
36
4791 1
2*087I
50076
1*9969
52278
1-9128
24
37
'47947
2*0856
501 12
1-9955
52315
1-91I4
23
38
47983
2*0840
50149
1*9940
52352
1-9101
22
39
48019
2*0824
50185
1*9926
52389
1-9087
21
40
48055
2*0809
50221
1*9911
52426
1*9074
20
41
48090
2*0793
50258
1*9897
52464
1*9060
19
42
48126
2*0778
50294
1*9882
52501
1*9047
18
43
48162
2*0763
50331
1*9868
52538
1*9033
l l
44
48198
2*0747
50367
1*9854
52575
1 '9020
16
45
48234
2*0732
50404
1-9839
52612
1*9006
15
46
48270
2*0716
50440
1*9825
52649
1-8993
14
47
48306
2*0701
50477
1*9810
52686
1 -8980
13
48
48341
2-o685
50513
1*9796
52724
1*8966
12
49
48377
2*0670
50550
1*9782
52761
1-8953
11
50
48413
2*0655
50586
1*9768
52798
1-8939
10
5i
48449
2*0640
50623
1*9753
52835
1*8926
9
52
48485
2*0624
| '50659
1*9739
52872
1-8913
8
53
48521
2*0609
| -50696
1*9725
52910
1*8900
I
54
48557
2-0594
i "50732
1*9711
52947
1*8886
6
55
48593
2*0578
i -50769
1*9696
52984
1*8873
5
56
48629
2*0563
! '50806
1*9682
53021
i*886o
4
57
48665
2*0548
50842
1*9668
53059
1*8846
3
58
48701
2*0533
50879
1*9654
53096
1*8833
2
5 Q
48737
2*0518
50915
1*9640
-53133
1*8820
1
60
'48773
2*0503
| -50952
1*9626
53170
1*8807
Cotangent
Tangent
Cotangent
Tangent
Cotangent
Tangent
64. Degrees
63 Degrees
62
Degree
s
138
TABLE III
28 Degrees
29 Degrees
30 Degrees
Tangent
Cotangent
Tangent
Cotangent
Tangent
Cotangent
o*
53170
1-8807
55430
1*8048
'57735
17320
60-
i
53208
1-8794
55468
1*8025
57773
17308
59
z
53245
1-8780
55506
1*8013
57812
17297
58
3
53282
1-8767
55545
i*8ooi
57851
17285
S Z
4
5332o
1-8754
55583
1*7998
57890
17274
56
5
'53357
1-8741
55621
1*797
57929
17262
55
6
53395
1-8728
55659
1*7966
57967
17250
54
7
53432
1-8715
55697
17954
58006
17239
53
8
53469
1-8702
"55735
17941
58045
17227
52
9
53507
1-8689
'55773
17929
58084
1-7216
5i
IO
53544
1-8676
558"
1 79i 7
58123
1-7204
50
ii
53582
1-8662
55849
1*7905
58162
17193
49
14
53619
1-8649
55888
1*7892
58201
17181
48
IJ
53656
1-8636
55926
1*7880
58240
1 71 70
47
4
53694
1-8623
55964
1*7868
58279
17158
46
15
53731
i-86io
56002
17856
58318
17H7
45
16
53769
1-8597
56040
17844
58357
17135
44
17
53806
i-8;84
56079
17831
58396
17124
43
18
53844
1-8572
561,7
17819
58435
17112
42
*9
53881
1-8559
56i55
17807
58474
17101
41
20
53919
1-8546
56193
17795
58513
17090
40
21
53957
1-8533
56232
17783
58552
17078
39
22
53994
1-8520
56270
17771
58591
17067
38
23
54032
1-8507
56308
i'77S9
58630
17055
37
24
54069
1-8494
56347
i'7^7
58669
17044
36
*5
54107
1-8481
56385
17735
58708
17033
35
26
54H5
1-8468
56423
17723
58747
1 702 1
34
27
54182
1-8456
56462
17710
58787
1 7010
33
28
54220
1-8443
T6500
17698
58826
1-6999
32
29
54257
1-8430
56538
1-7686
58865
1*6987
3i
30
54295
1-8417
56577
17674
58904
1*6976
3o
Ji
54333
1*8404
* 5 ? IS
1-7662
58943
1-6965
29
32
54370
1-8392
56654
17650
58982
1-6954
28
33
54408
1-8379
56692
17639
59022
1-6942
27
34
54446
1-8366
56730
1-7627
59061
1*6931
26
35
54484
1-8353
56769
17615
59100
1 '6920
25
36
54521
1-8341
56807
17603
59139
1*6909
24
37
'54559
1-8328
56846
17591
59179
1-6897
23
38
54597
1-8315
56884
17579
59218
1-6886
22
39
54635
1-8303
56923
17567
59257
1-6875
21
40
54672
1-8290
56961
17555
59296
1-6864
20
4i
54710
1-8277
57000
1*7543
59336
1-6853
11
42
54748
1-8265
57038
17531
"59375
1-6841
43
54786
1-8252
57077
17520
59415 1
1-6830
17
44
54824
1*8240
571 16
17508
59454
1-6819
16
45
54861
1-8227
*57 J 54
1*7496
'59493
1*6808
15
46
54899
1*8215
5793
17484
'59533
1-6797
14
47
54937
1-8202
57231
17472
59572
1*6786
13
48
54975
I-8I89
57270
1*7460
5961 1
1*6775
12
49
55013
I-8I7 7
57309
17449
59651
1*6764
11
5o
55051
1*8164
'57347
17437
59690
1*6752
10
5i
55089
I*8l52
57386
17425
59730
1*6741
9
52
55127
1*8139
57425
17413
59769
1*6730
8
53
55165
1*8127
57463
17402
59809
1*6719
I
54
55202
1*8114
57502
17390
59848
1*6708
55
55240
I*8l02
57541
17378
59888
1*6697
5
56
55278
1*8090
'57579
17367
59927
1-6686
4
57
55316
1*8077
57618
17355
59967
1-6675
3
58
'55354
1-8065
57657
17343
60006
1-6664
2
5
55392
1*8052
57696
i'7332
-60046
1-6653
1
60
5543o
I '8040
'57735
17320
60086
1-6642
Cotangent
Tangent
Cotangent
Tangent
Cotangent
Tangent
61 Degrees
60 Degrees
59 Degrees
TABLE III
139
31 Degrees
32 Degrees
33 Degrees
Tangent
Cotangent
Tangent
Cotangent
Tangent
Cotangent
o'
60086
1-6642
62486
1*6003
64940
1-5398
60'
i
6012s
1-6631
62527
1-5992
64982
1-5388
59
z
60165
1-6620
62567
1-5982
65023
'5379
58
3
60204
1-6609
62608
1-5972
65064
65106
1-5369
57
4
60244
1-6599
62648
1-5961
i"5359
56
5
60284
1-6588
62689
1-5951
65147
i'5349
55
6
60323
1-6577
62729
1-5941
65189
1-5339
54
7
60363
1-6566
62770
1-5931
65230
I-5330
53
8
60403
1-6555
62810
1-5920
65272
1-5320
5*
9
60442
1-6544
62851
1-5910
65313
1-5310
5*
IO
60482
1-6533
62892
1-5900
65355
1-5301
50
ii
60522
1-6522
62932
1-5889
65396
1-5291
49
IZ
60562
1 -651 1
62973
1-5879
65438
1-5281
48
13
60601
1-6501
63013
1-5869
65479
1-5271
47
14
60641
1-6490
63054
1-5859
65521
1-5262
46
15
60681
1-6479
63095
1-5849
65562
1-5252
45
16
60721
1-6468
63135
1-5838
65604
1-5242
44
"7
60761
1-6457
6,176
1-5828
65646
1-5233
43
18
60800
1-6447
63217
1-5818
65687
1-5223
42
*9
60840
1-6436
63258
1-5808
65729
1-5213
4 T
zo
60880
1-6425
63298
1-5798
65771
1-5204
40
21
60920
1-6414
63339
1-5787
65812
1-5194
3
zz
60960
1-6404
63380
1 '5777
65854
1-5185
*3
61000
1-6393
63421
1-5767
65896
i*5*75
37
24
61040
1-6382
63461
1 '5757
65937
1-5165
36
25
61080
1-6371
63502
1*5747
65979
1-5156
35
26
61120
1-6361
63543
1*5737
66021
1-5146
34
27
61 160
1-6350
63584
1-5727
66063
i-5'37
33
28
61200
1-6339
63625
1-5717
66104
1-5127
3*
29
61240
1-6329
63666
1-5706
66146
1-5117
3*
30
61280
1-6318
63707
1-5696
66188
1-5108
30
31
61320
1-6307
63747
1-5686
66230
1-5098
29
32
61360
1-6297
63788
1-5676
66272
1-5089
28
33
61400
1-6286
63829
1-5666
66314
1-5079
27
34
61440
1-6275
6387c
1-5656
66356
1-5070
z6
35
61480
1-6265
6391 1
1-5646
66397
1-5060
25
36
61520
1-6254
63952
1-5636
66439
1-5051
24
37
61560
1-6244
63993
1-5626
66481
1-5041
23
38
61600
1-6233
64034
1-5616
66523
1-5032
22
39
61640
1-6223
64075
1-5606
66565
1*5022
21
40
61680
1-6212
64116
1-5596
66607
1-5013
zo
4i
61721
1 -6201
64157
1-5586
66649
1-5003
*9
4z
61 761
1-6191
64198
1-5576
66691
1-4994
18
43
61 801
1-6180
64239
1-5566
66733
1-4984
5
44
61 841
1-6170
64281
1-5556
66775
''4975
16
45
61881
1-6159
64322
1-5546
66817
1-4966
*5
46
61922
1-6149
64363
1-5536
66859
1-4956
14
47
61962
1-6138
64404
1-5526
66902
'4947
13
48
62002
1 -6128
64445
1-5516
66944
T, 4937
IZ
49
62042
1-6117
64486
1-5507
66986
1-4928
II
5o
62083
1-6107
64527
1*5497
67028
1-4919
IO
5i
62123
1-6096
64569
1-5487
67070
1-4909
!
5^
62163
1-6086
64610
1 '5477
671 12
1-4900
53
62204
1 -6076
64651
1-5467
67155
1*4890
I
54
62244
1-6065
64692
1 '5457
67197
1-4881
6
55
62284
1-6055
64734
1 "5447
67239
1-4872
5
56
62325
1-6044
64775
1-5437
67281
1-4862
4
57
62365
1-6034
64816
1-5428
67323
1-4853
3
58
62406
1-6024
64858
1-5418
67366
1-4844
z
I?
62446
1-6013
64899
1-5408
67408
1-4834
1
62486
1-6003
64940
1-5398
67450
1-4825
Cotangent
Tangent
Cotangent
Tangent
Cotangent
Tangent
I
58 Degre
ES
57 Degrees
06 Degrees
140
TABLE II]
34 Degrees
35 Degrees
36 Degrees
Tangent
Cotangt
Tangent
Cotangent
Tangent
Cotangent
d
67450
1-4825
70020
1*4281
72654
1-3763
60
i
67493
1-4816
70064
1-4272
72698
i'3755
59
z
67535
1-4807
70107
1-4263
72743
1-3746
58
3
67577
1 "4797
70150
1-4254
1-4246
72787
1-3738
57
4
67620
1-4788
70194
72832
1-3730
56
5
67662
1 "4779
70237
1-4237
72876
1-3721
55
6
67705
1-4769
70281
1*4228
72921
1*37*3
54
7
67747
1.4760
70324
1-4219
72965
1-3705
53
8
67789
1-4751
70368
1-4210
73010
1-3696
52
9
67832
1-4742
7041 1
1 -4202
73055
1-3688
5i
IO
67874
1-4732
70455
1-4193
73099
1-3679
50
ii
67917
1-4723
70498
1-4184
73144
1-3671
49
IZ
67959
1-4714
70542
'4175
73188
1-3663
48
ij
68002
1-4705
70585
1-4167
73233
1-3654
47
4
68045
1-4696
70629
1-4158
73278
1-3646
46
15
68087
1-4686
70673
1-4149
73323
1-3638
45
16
68130
1-4677
70716
1-4140
73367
1-3629
44
*7
68172
1-4668
70760
1-4132
73412
i'362i
43
18
68215
1-4659
70803
1-4123
73457
1-3613
42
*9
68258
1-4650
70847
1-4114
1-4106
73502
1-3605
4*
zo
68300
1-4641
70891
73546
1-3596
40
21
68343
1-4632
70935
1-4097
7359 1
1-3588
39
2Z
68386
1 -4622
70978
1-4088
73636
1-3580
38
23
68428
1-4613
71022
1 -4080
73681
1-3571
37
24
68471
1-4604
71066
1-4071
73726
1-3563
36
25
68514
1 '4595
71110
1-4062
7377*
'3555
35
26
68556
1-4586
7**53
1-4054
738i6
1*3547
34
27
68599
1*4577
71 197
1-4045
73861
1-3538
33
28
68642
1-4568
71241
1-4036
73906
**3530
32
29
68685
'"4559
71285
1 '4028
73951
1-3522
3i
30
68728
1-4550
71329
1-4019
73996
**35*4
30
31
68770
1-4541
7*373
1-4010
74041
1-3506
29
3*
68813
i"453i
71417
1-4002
74086
''3497
28
33
68856
1-4522
71461
3993
741 3 1
1-3489
27
34
68899
'45'3
71505
1-3985
74176
1-3481
26
35
68942
1-4504
71548
1-3976
74221
**3473
25
36
68985
'4495
71592
1-3967
74266
1-3465
24
37
69028
1-4486
71636
"3959
743"
1-3456
23
38
69071
**4477
71681
1-3950
74356
1-3448
22
39
691 14
1-4468
71725
1-3942
74402
1-3440
21
40
69157
'"4459
71769
'3933
74447
1-3432
20
4i
69200
1-4450
71813
1-3925
74492
1-3424
*9
42
69243
1-4441
71857
1-3916
74537
1-3416
18
43
60286
1-4432
71901
1-3907
74582
1-3407
*7
44
69329
1-4423
7 "945
1-3899
74628
''3399
16
45
69372
1-4414
71989
1-3890
74673
1-3391
*5
46
69415
1-4405
72033
1-3882
747*8
1*3383
H
%
69458
J'4397
72078
1-3873
74764
**3375
*3
69501
1-4388
72122
1-3865
74809
1*3367
IZ
49
69544
'4379
72166
1-3856
74854
1*3359
11
50
69588
1-4370
72210
1-3848
74000
i'335*
10
51
69631
1-4361
72255
1-3839
74945
-3342
9
5*
69674
1-4352
72299
1-3831
7499*
'3334
1*3326
8
53
69717
'4343
7*343
1-3822
75036
7
54
69760
'"4334
72387
1-3814
75082
I-33I8
6
55
69804
1-4325
72432
1-3806
75127
1*3310
5
56
69847
1-4316
72476
1-3797
75*73
1-3302
4
57
69890
1-4308
72521
1-3789
75218
1-3294
1-3286
3
58
69934
1-4299
7*565
1-3780
75264
z
59
69977
1-4290
72609
1-3772
75309
1-3278
1
60
70020
1-4281
7. 26 54
1-3763
75355
1-3270
Cotangent
Tangent
Cotangent
Tangent
Cotangent
Tangent
55 Degrees
54 Degrees
53 Degrees
TABLE III.
141
37 Degrees
38 Degrees
39 Degrees
Tangent
Cotangent
Tangent
Cotangent
Tangent
Cotangent
d
75355
1*3270
78128
1-2799
80978
1-2348
DO*
i
75401
1*3262
78175
1-2791
I*2 7 L
1*2776
81026
1-2341
59
2
75446
1*3254
1-3246
78222
81074
1*2334
1*2326
58
3
75492
78269
81123
5 7
4
'75537
1-3238
78316
1*2768
81171
1-2319
56
5
75583
1-3230
78363
1*2761
81219
1*2312
55
6
75629
1*3222
78410
1-2753
81267
1-2304
54
7
75675
1-3214
1-3206
78457
1*2745
81316
1-2297
53
8
75720
78504
1*2738
81364
1*2290
52
9
75766
1-3198
78551
1*2730
81412
1*2283
5i
IO
75812
1-3190
78598
1*2722
8 1 461
1*2275
50
ii
75858
1-3182
78645
1-2715
81509
1*2268
49
12
75904
M!B
78692
1-2707
81558
1*2261
48
11
75949
78739
1-2700
81606
1*2253
4 7
14
75995
1-3158
78786
1-2692
81654
1*2246
46
15
76041
1-3150
78833
1-2684
81703
1-2239
45
16
76087
1-3142
78880
1 -2677
81751
1-2232
44
17
76133
^3134
1-3126
78928
1-2669
81800
I '2224
43
18
76179
78975
1-2662
81849
1*2217
42
9
76225
1-3118
79022
1-2654
81897
I*22IO
4i
so
76271
1*3111
79069
1-2647
81946
I-2203
40
21
76317
1*3103
791 1 7
1-2639
81994
1-2195
39
22
76363
1-3095
79164
1 -263 1
82043
1-2188
38
2J
76409
1-3087
7921 1
1 -2624
1*2616
82092
I*2l8l
H
24
76455
1-3079
79259
79306
82140
1*2 166
36
25
76501
1-3071
1*2609
82189
35
26
76548
1-3063
79353
1*2601
82238
1*2159
34
27
76594
1-3055
79401
1*2594
82287
1*2152
33
28
76640
1-3047
79448
1*2586
82335
1*2145
32
29
76686
1-3040
79496
1*2579
82384
1*2133
3i
30
76732
1-3032
79543
1*2571
82433
1*2130
30
?i
76778
1-3024
1-3016
79591
1*2564
1*2556
82482
1*2123
29
32
76825
79638
82531
I*2Il6
28
33
76871
1*3008
79686
1*2549
82580
1*2109
Z l
34
76917
1*3000
79733
1*2541
82629
1*2102
26
35
76964
1-2993
79781
1*2534
82678
1*2095
25
36
77010
1-2985
79828
1*2526
82727
1*2087
24
37
77056
1-2977
79876
1*2519
82776
i *2o8o
23
38
77103
1-2969
79924
1*2511
82825
1*2073
22
39
77149
1-2961
79971
1*2504
82874
1*2066
21
40
77195
1-2954
80019
1*2496
82923
1*2059
20
4i
77242
1-2946
80067
1 '2489
82972
1*2052
19
42
77288
1-2938
801 1 5
1*2482
83021
1*2045
18
43
77335
1-2930
80162
1*2474
83070
1*2037
x z
44
77381
1-2922
80210
1*2467
83119
1*2030
16
45
77428
1-2915
80258
1*2459
83169
1*2023
15
46
77474
1-2907
80306
1*2452
83218
1*2016
14
47
77521
1*2899
80354
1-2444 |
83267
1*2009
13
48
77567
1-2891
80402
1*2437
83316
I *2002
12
49
77614
1-2884
80449
1*2430
83366
i*i995
II
50
77661
1-2876
80497
1*2422
83415
1-1988
IO
5i
77707
1-2868
80545
1*2415 ;
83464
1-1981
9
52
77754
1-2860
80593
1*2407
83514
1*1966
8
53
77801
1-2853
80641
1 -2400
83563
J
54
77847
1-2845
80689
1 '2393
83612
1*1959
6
55
77894
1-2837
80737
1-2385
83662
1*1952
5
56
77941
1-2830
80785
1-2378
837"
1-1945
4
57
77988
1-2822
80834
1-2371
83761
1-1938
3
58
78o34
1*2814
80882
1*2363
83810
1-1931
2
5
78081
1*2807
80930
1*2356
83860
1-1924
1
60
78128
1-2799
80978
1*2348
83909
1-1917
Cotangent
Tangent
Cotangent
Tangent
Cotangent
Tangent
52 Degrees
51 Degrees
50 Degrees
142
TABLE III.
40 Degrees
41 Degrees
42 Degrees
Tangent
Cotangent
Tangent
Cotangent
Tangent
Cotangent
o'
83909
1*1917
86928
1-1503
90040
1*1106
60'
i
83959
1*1910
86979
1-1496
90093
1*1099
11
2
84009
1-1903
87030
1-1490
90145
1*1093
3
84058
1-1896
87082
1-1483
90198
1*1086
57
4
84108
1-1889
87133
1-1476
90251
1*1080
56
5
84158
1-1882
87184
1-1469
90304
1*1073
55
6
84207
1-1875
87235
1-1463
90356
1*1067
54
7
84257
ri868
87286
1-1456
90409
1*1060
53
8
84307
1-1861
87338
1-1449
90462
1*1054
5*
9
84357
1-1854
87389
i*i443
90515
1*1047
51
10
84406
1-1847
87440
1-1436
90568
1*1041
50
ii
84456
1-1840
87492
1-1429
90621
1*1034
49
IZ
84506
1-1833
87543
1-1422
90674
1*1028
48
13
84556
1-1826
87594
87646
1-1416
90727
i* 1022
4 Z
14
84606
1-1819
1-1409
90780
1*1015
46
15
84656
1-1812
87697
1-1402
90833
1*1009
45
16
84706
1-1805
87749
1-1396
90886
I'I002
44
17
84756
1-1798
87800
1-1389
90939
1*0996
43
It
84806
1-1791
87852
1-1382
90993
1*0989
42
19
84856
1-1784
87903
11376
'91046
1-0983
4i
20
84906
I-1777
87955
1-1369
91099
1*0977
40
21
84956
1-1770
88006
1-1362
91152
I-0970
39
22
85006
1-1763
88058
1-1356
91205
1*0964
38
23
85056
1-1756
88110
1-1349
91259
1*0957
3 Z
24
85106
1-1749
88161
1-1342
91312
1*0951
36
as
85156
1*1743
88213
1-1336
91365
1*0945
35
26
85207
1-1736
88265
1-1329
91419
1-0938
34
27
85257
1-1729
88317
1-1322
91472
1*0932
33
28
85307
1-1722
88368
1-1316
91526
1-0925
3*
29
85357
1-1715
88420
1-1309
91579
1-0919
31
30
85408
1-1708
88472
1-1302
91633%
1-0913
30
31
85458
1-1701
88524
88576
1-1296
91686
1-0906
29
3a
85508
1-1694
1-1289
91740
1*0900
28
33
85559
1-1687
88628
1-1283
91793
1-0893
27
34
85609
1-1680
8868c
1-1276
91847
1-0887
26
35
85659
1-1674
88732
1-1269
91901
I-088I
*5
36
85710
1-1667
88784
1-1263
91954
1-0874
24
37
85760
i- 1660
88836
1-1256
92008
1-0868
*3
38
85811
1-1653
88888
1-1250
92062
1*0862
22
39
85861
1-1646
88940
1-1243
921 1 5
1*0855
21
40
85912
1-1639
88992
1-1266
92169
1 '0849
20
4i
85962
1*1632
89044
89096
1-1230
92223
1*0843
19
42
86013
1-1626
I-I223
92277
1*0836
18
43
86064
1-1619
89148
I-I2I7
92331
1*0830
l l
44
861 14
1-1612
89201
I-I2IO
92385
1*0824
16
45
86165
1-1605
89253
I-I204
92439
1*0817
15
46
86216
1-1598
89305
1-1197
92493
ro8n
14
47
86266
1-1591
89357
1*1190
92547
1*0805
13
48
86317
1-1585
89410
1*1184
92601
1*0799
12
49
86368
1-1578
89462
1*1177
92655
1*0792
11
50
86419
1-1571
89515
1*1171
92709
1*0786
10
51
86470
1-1564
89567
1*1164
92763
1*0780
9
51
86520
1*1557
89619
1*1158
92817
1*0773
8
53
86571
1-1551
89672
1-1151
92871
1*0767
7
54
86622
1-1544
89724
1*1145
92925
1 -0761
6
55
86673
1*1537
89777
1*1138
92979
1*0755
5
56
86724
1-1530
89829
1*1132
93034
1-0748
4
57
86775
1-1523
89882
1*1125
93088
1 -0742
3
58
86826
1-1517
89935
1*1119
93142
1-0736
2
I 9
86877
1-1510
89987
I*III2
93197
1 -0729
1
60
86928
1-1503
90040
1*1106
93251
1-0723
Cotangent
Tangent
Cotangent
Tangent
Cotangent
Tangent
49 Degrees
48 Degrees
47 Degrees
TABLE III.
143
43 Degrees
44 Degrees
Tangent
Cotangent
Tangent
Cotangent
d
93251
1-0723
96568
10355
6o'
i
93305
1-0717
96625
1 -0349
59
2
93360
1*0711
96681
1 -0343
58
3
934H
1-0704
96737
1*0337
57
4
93469
1-0698
96793
1-0331
56
5
93523
1-0692
96850
1-0325
55
6
93578
1-0686
96906
1-0319
54
7
93632
1-0680
96963
1-0313
53
8
93687
1-0673
97019
1-0307
52
9
93742
1-0667
97076
1*0301
5i
io
93796
ro66i
97132
1*0295
50
II
93851
1-0655
97189
1*0289
49
12
93906
1-0648
97245
1*0283
48
*3
93961
1-0642
97302
1*0277
4 7
*4
94015
1-0636
97359
1*0271
46
*5
94070
1-0630
97415
I *0205
45
16
94125
1-0624
97472
1-0259
44
17
94180
1-0617
97529
1-0253
43
t 18
94235
i-o6ii
97585
1-0247
42
x 9
94290
1-0605
97642
1 '0241
4i
20
94345
1-0599
97699
1*0235
40
21
94400
1-0593
97756
1*0229
39
22
94455
1-0587
9781 3
1*0223
38
23
94510
1-0580
97870
1*0217
3 7
*4
94565
1 -0574
97927
1*0211
36
25
94620
1-0568
97984
I '0205
35
26
94675
1-0562
98041
1*0199
34
*2
9473o
1-0556
98098
I*OI93
33
28
94785
1-0550
98155
I*Ol87
32
29
94841
1*0543
98212
1*0181
3i
30
94896
1-0537
98269
1*0176
30
31
9495i
1-0531
98326
1*0170
3
32
95007
1-0525
98384
1 '0164
33
95062
1-0519
98441
1-0158
27
34
95117
1-0513
98498
1 -01 52
26
35
95173
1-0507
98556
1-0146
25
36
95228
1*0501
98613
1 -0140
24
37
95284
1-0494
98670
1-0134
23
38
95339
1 -0488
98728
I'OI28
22
39
95395
1 -0482
98785
I*OI22
21
40
9545o
1 -0476
98843
I*OII7
20
4i
955o6
1-0470
98900
I'OIII
19
42
95562
1 -0464
98958
I*0I05
18
43
95617
1-0458
99015
I-0099
l l
44
95673
1-0452
99073
I-0O93
16
45
95729
1*0446
991 3 1
I-0087
15
46
95784
1*0440
99188
1-0081
14
47
95840
1*0433
99246
1*0075
13
48
95896
1*0427
99304
1*0070
12
49
95952
1*0421
99362
1-0064
11
50
96003
1-0415
99419
1-0058
10
5i
96064
1-0409
'99477
1-0052
9
51
96120
1-0403
99535
1 '0046
8
53
96176
1*0397
99593
1*0040
I
54
96232
1-0391
99651
1-0034
55
96288
1-0385
99709
1*0029
5
56
96344
i*o379
99767
1*0023
4
57
96400
1*0373
99825
1*0017
3
58
96456
1*0367
99883
I*OOII
2
P
96?'.-.
7*0361
99941
1*0005
I
60
96568
1*0355
1*0000
i-oooo
Q
Cotangent
Tangent
Cotangent
Tangent
46 Degrees
45
Degrees
J
144
TABLE IV.
ANGLES, RADII, AND DISTANCES FOR RAILWAY CROSSINGS.
Pitch of
Crossing
Angle
Radius
Distance of
Point of
Switch from
Point of
Crossing
Cross-over Road
Distance of Point of Switch from
Point of Recurvature, or Half-length
of Road
For 6 feet
between
Roads
For 7 feet
between
Roads
For 8 feet
between
Roads
1 in 5
1 in 6
1 in 7
1 in 8
1 in 9
1 in 10
1 in 12
Deg. Min.
11 26
9 32
8 10
7 10
6 21
5 44
4 46
Feet
237
341
464
603
768
938
1361
Ft. In.
47
56 7
65 10
75 2
84 11
93 8
113 1
Feet
51
61
72
82
92
102
123
Feet
53
64
75
85
96
106
129
Feet
55
67
78
89
100
111
135
145
SETTING OUT CURVES WITHOUT A
THEODOLITE,
ON THE PRINCIPLE OF TANGENTIAL ANGLES, BY TANGENTS AND
CORRESPONDING OFFSETS, CALCULATED FOR FIELD USE FROM
THE SINES AND VERSINES OF THE ANGLES AT THE CENTRE.
To many, even good practical engineers, there is an insuperable objection
to the use of the Theodolite. For the purpose of setting out curves with-
out this instrument, the annexed tables have been calculated, so that
the work may be done on the principle of tangents and tangential
angles, merely by setting off the offsets from given distances on the
tangents, such distances corresponding to the proper chainage on the
curve. There are many engineers who still adhere to the old, very old,
system of ranging curves by short chords of a chain in length, and then
offsetting to the curve, and thus bending round at the length of every
chain ; but all those who have actually done much field work, know how
tedious and uncertain the system, and no one better than the writer,
who used it some twenty-five years ago, in setting out many miles of
curves in a very hilly country. The tables here given do away with all
uncertainty, and the work may be done rapidly and with accuracy.
In the accompanying diagram, p. 146, let a b represent a chain's length
on any circular curve, and let b c be a second chain's length on such curve;
let d a be tangent to the curve at the point a, and let e be the centre
of the curve. The angle at the centre b e a is equal to twice the angle
bad, and, similarly, the angle c e a is equal to twice the angle cad; b f
is the sine of the angle b e a, and f a is the versine of the same angle ;
and c g is the sine of the angle c e a, of which g a is the versine.
The sines b f and c g are parallel to the tangent a d, and the versines
fa and g a are at right-angles to ad.
On ad, set off a h, equal to f b, and also h 1 , equal to G e ; now, if from
h we set off the right-angled offset h b, equal to a f, and from h 1 , the
right-angled offset h 1 c, equal to a g, we get two points on the curve, viz.,
b and c, each one chain's length from the other ; for b a and c a are each
equal to one chain. In the right-angled parallelogram b a, b h is equal to
the versine fa of the angle bea; and also in the right-angled paral-
lelogram Ci, h'c is equal to the versine a g of the angle c e a. Any
g2
146
SETTING OUT CURVES
other number of points on the curve might have been obtained in the
same manner. In the tables here given, the tabular ' tangents ' all cor-
respond to a h, a h 1 , a h 2 , and a h s , &c. ; and the tabular offsets all cor-
respond to hb, h'c; h 2 c 1 , h 3 c 2 , for different radii of curves, and
for points along the curve distant half a chain each from each, so that a
curve of any radius given in the tables may set out on the ground, with-
out theodolite, with the greatest facility and with perfect accuracy by
any one who can chain with care and set off a right-angled offset, both
simple operations, which even a good ganger is perfectly competent to
accomplish, so that, with the tangent starting point, and the direction
of the tangent being given on the ground, much time may often be saved.
As an example, we will take a curve of 10 chains radius ; referring
still to the last figure, and to Table IV., let a b be the first chain, b c
the second, and c c 1 the third chain, &c. &c. ; leaving the half chains out
of the question for the present, we find the length of the first tangent to
be 99-8, to which make a h equal ; make a h 1 equal to 198*6, the length of
the next tangent in the table ; chaining still on in the direction ad, make
WITHOUT A THEODOLITE. 147
AH* equal to 295-5 for the length of tangent for the third chain h 2 , and
then on to h 3 , leaving a mark at 389-4 for the fourth chain at h 8 , &c, &c.
Keferring now to the column of offsets, make h b equal to 5*0 links,
which will give the length and direction of the first chain ab; from h 1 set
off h 1 c at right angles to a d, and mato h 1 c equal to 19*9 links ; this will
give the length and the direction of the second chain h 1 c. In the next place,
from h 2 set off h 2 c at right-angles to a d ; from the column of offsets in
the table, take out 44*7, the length of the offset due to the third chain, to
which make h 2 c 1 equal ; this will give the length and the direction of
the third chain cc 1 , and so on until we change the direction of the
tangent. We now come to the operation of setting out a curve from one
tangent to the other, as shown in fig. 2 on the next page, in which we
will suppose the radius of the curve to be still ten chains. It may be
observed here, as regards the actual meaning of the words ' chain,' and
' link,' that the' length of chain may be 100 feet, or 100 links = 66 feet,
or 100 decimetres, it being only necessary, according as we are working
on one or the other system, to have a chain of the proper length, and a
ten feet, ten link, or ten decimetre rod, with each unit properly divided
into tenths, so as to be able to do the work with sufficient accuracy. If,
for instance, we have a ten ' chain ' curve, then we shall use the ordinary
66 feet chain and a ten link staff, properly divided ; and if we have a
curve of 1,000 feet radius, then we shall use the 100 feet chain, and a
ten feet staff divided into feet and tenths, &c, &c.
In the figure now referred to, it will be seen that it is here proposed
to illustrate the two methods of setting out, that is, with and without
theodolite, both systems being applications of practical mathematics in
the field : in the one system we set out by angles and chords, and in the
other by the lineal measurements of the angles only ; both systems will
bring about exactly the same results if properly carried out. Commencing,
then, at the very beginning of the work, we measure the angle a c b, and
divide it by 2, which gives the angle ago; deduct this from 90 and we
get the angle c o a, to which a c is the tangeftt.
Let the angle b c a measure 79 36', half of which is 39 48', equal
too c a ; subtract this from 90, and we shall have 50 12', equal to the
angle c o a, to which c a is the tangent. The first point we require
is a; to find this we take out from Table III. the natural tangent
of 50 12', which is 1*2002 ; this, multiplied by the radius of the curve,
gives the length of ca, which, measured off from c, fixes the point a; in
the present case, 1-2002, multiplied by 10, gives 12*002, which, measured
off along the tangent c a, fixes the point a.
This preliminary settled, we may proceed with our work of setting out.
The direction of a c having been carefully determined already, we have
only to chain on from A to 1', equal to 99-8, leaving there some small
pig. (as of course we are supposed to do all along), and on to 2', equal
to 198*6, and to 3', equal to 295-5, and so on to 6', equal to
148
SETTING OUT OUBVES
Fig. 2.
\*
X:
Stf.
TO.
-AN
I" \- IV
l lALrT
- i !\ Vr ' i?
t t !\ ,\6 i $
WITHOUT A THEODOLITE.
149
564-6. We are here getting into obstructions of bushes and broken
ground, and we will therefore set out a new tangent. Before doing this,
however, we must set out the offsets which will determine the points on
the curve.
From 1' set out l'l, equal to 5'0 ; from 2' set out 2'2, equal to 19*9 ;
from 3' set out 3'3, equal to 44 - 7 ; and so on to 6', where the
offset 6'6 will be 1745. It will be unnecessary to observe that the line
A 6' must be chained perfectly straight, and in line with the tangent a c,
of which it forms a part, and that each point must be carefully set out
at its correct length ; also that the offsets must be set off perfectly square
to the tangent, which should be done with the cross-staff, and, of course,
that the length must be accurately set out.
With regard to turning the straight line, or getting a new tangent :
the setting out has been stopped at the 6th chain, then set the cross-
staff on the last tangent at 3', and through the point 6 sight out the
line from 3', through 6, on and beyond 14', according to the distance
Fig.Z.
we intend to run out. The chaining is now to be recommenced from
the point 6; 6, 7', is made equal to 99-8 ; 6, 8', is made equal to 1986 ; 6,
9', is made equal to 295'5; and so on until we get to 14',
where the length is made equal to 717*4. The tabular offsets are set off
in the same manner as already explained, until we get to 14', 14, where
the length of offset is 235-2.
Here we propose again to set out a new tangent, and this is done in
the same way as we did it last ; this time, however, we have set out 8
additional chains on the curve, therefore set up the cross-staff at 10', and
sight the new tangent through the point marked 14.
150
SETTING OUT CUEYES
It is, of course, understood that the measurements given above, for the
lengths of tangents and offsets, are taken from the tabular numbers given
in the columns of tangents and of offsets in the Table, prepared for a 10
chain curve, and that these tabular numbers have all been calculated
from the sines and versines of the angles at the centre of the curve.
It is a very common occurrence, when setting out work, to meet with
obstructions on the ground. We have an illustration at fig. 3, where the
tangent runs into and along the bank of a river. Set out the work from
1 and 2 as before, and from a, set out a d exactly at right-angles to the
tangent, and make ad some 8 or 10 feet, as convenient ; in the next
place, from any point b (carefully sighted on the tangent), set off b c,
exactly equal to a d ; from 2 set off 2 e, exactly equal to a d and to b c ;
set up the cross-staff at d, and see that d, e, and c are all three exactly
in line. From point e we can now set off from e to 3, 4, 5, &c. ; the off-
sets set off from these points will merely be 8 or 10 feet shorter than they
would have been otherwise. If the cross-staff is true, and the work is
Fig. 4.
carefully done, there will be no error. This method may also be adopted
where the tangent runs along, or on the wrong side of a fence.
In fig. 4, we have an illustration of a case requiring even more care
than the last. Both the curve and the tangent run for 2 or 3 chains
across a river. From 1, 2, and 3, set out the offsets as before. From 3
set out 3 b, exactly at right angles to a 8, and observe both the angles
b 3 a and b 3 8 to ensure that b 3 is really square to the tangent, as other-
wise the work will be valueless. Make 3 b some 2 or 3 full chains long, so
that it may be somewhere about equal to 3 c. Having done this, measure
WITHOUT A THEODOLITE. 151
the angle 3 b c with the box sextant ; enter the observation in the field
book, and then measure the angle 3 c b : the two together should make
up 90 ; if otherwise, the work has been badly done.
Let the angle 3 b c measure 52 26', and let 3 b be exactly 2 chains.
From p. 141 (Table III.), take out the natural tangent of 52 26', equal
to 1*300, and multiply it by 2, and we shall have 260 for the exact length
of the line 3 c.
Now, let us suppose that we are setting out a 15 chain curve. By re-
ferring to the proper Table, it will be found that for a 3, the length of the
tangent set out, we have 298, which, added to the above 260, gives 558
for the length from a to c. The next chainage on our tangent is, by
the Table, equal to 584*1, and the difference between this and 558 is
equal to 26-1 ; and if on the ground we set out this 26*1 in continuation
from c, we get the point 6, from which we may set off the offset due to
the curve, which is 118*4. Through 3 and 6', we shall be able to set
out a fresh tangent.
The theory of setting out curves by tangential angles, or by the
offsets given in the Tables, is very simple ; but in practice, some discretion
is required in applying the theory, so as to obtain the best results in the
easiest way.
In setting out with the theodolite, it is very desirable not to have to
remove the instrument oftener than is absolutely necessary, and there-
fore stations should be selected, from which as many stumps as possible
may be set out at once.
In the subjoined figure, p. 152, we select a case in point. Curves gene-
rally run along the sides of hills, so as to diminish the depths of cut-
tings and heights of embankments ; in the example given, we suppose
the line to be in cutting. Let a and d be the points of junction with the
tangents, a being the point from which the curve is to be run towards
d. Now it will be perceived that a is at the foot of the hill, and that
there are five hedges to intersect, each of which will considerably impede
the view, if the instrument be set up at a, unless gaps are cut for every
stump to be set out ; and this kind of work always occasions a great
deal of loss of time, unless very tall ranging rods are used, which we
object to, because they are never held sufficiently upright.* But if,
instead of being in the hollow at a, the instrument were placed on high
ground, we should be able to look back, and down upon the work,
so as to see over the hedges. If, for instance, the instrument were
placed at b, at the higher ground-level, not only should we be able to
do this, but obtain also an unimpeded view towards d, and thus, after
fixing the point b, range out the whole of the curve from one single
point.
* The writer, in his practice of setting out works, hardly ever uses ranging rods,
but prefers short pieces of white lath, which he always intersects close to the ground
with the cross-hairs of the diaphragm of the theodolite.
G 3
152
SETTING OUT CURVES
From the plan we take into the field, we can easily ascertain whether
this point, b, is at 8, 9, or 10 chains on the curve it does not matter
which. "We will suppose that we select the 10th chain, and what we
have now to do is to fix the point b, on the ground, from the point of
junction a, which is at, say, 23 chains and 60 links.
Now if from this point we can set out the line a b correctly in length
and direction, point b will be correctly fixed on the. ground. Since the
junction, a, is at 23 -60, the length of curve, from a to b, should be
exactly 10-40.
Fig. 6.
For a curve of ten chains radius, the tangential angle for 1 chain is
equal to 2 51-9' (Table III., p. 120); then for a length of 10-40 on
the curve, the angle cab, to be set out, will be 2 51*9' x 10-40 =
29 47'6'. This angle will accurately fix the direction a b ; therefore
set up the theodolite at a, and set out this angle of 29 476'; and as, in
doing this, we shall be working from right to left on the instrument,
the reading on the limb will be 3600' minus 29 47'6', equal to
330 12-4' the instrument being set up with o in the direction of c.
We now want the length of the straight line a b, which is the chord of
that portion of the curve. Now, the chord of an angle, or arc, is equal
to twice the sine of half the angle subtended by such arc, or chord ;
and the angle at the centre, which is the angle subtended by our arc or
portion of curve b a, is equal to twice the angle 29 47*6', and we
have therefore to take twice the sine of this angle. At page 83, we find
WITHOUT A THEODOLITE. 153
the sine of 2947' = '49672, and for 2948' = -49697 ; the mean of
which (more than near enough for our work) will be -49684, equal to
the sine of our tangential angle, or to the sine of half the angle sub-
tended by the arc or chord ; and twice this sine multiplied by 2
equal to '99368, and this multiplied by the ten-chain radius of curve,
equal to 993"68, 993 links and f. According to the care observed in
chaining this distance, or the line a b, so will the point b be more or
less accurately set out on the curve ; and as from this single point, the
18 stumps on the curve may all be set out without removing the instru-
ment, it is worth while to measure out this distance as carefully as
possible.
We will therefore suppose this portion of the work accomplished, and
only further remark that it may be carefully carried out in the field in
a much shorter time than it will take to read this explanation, when
once the method is well understood. The half-chains have been left
out in order to avoid confusion in the diagram, but for sharp curves
these should always be set out.
The instrument may now be removed to -point b, with the vernier
clamped to 29 47*6', and the telescope turned on to a. The tangential
angle, 2 5 19' x -40 (the distance from point A to stump 24), equal to
1 8-7', and this deducted from 29 47*6' equal to 28 38'9', which is
the reading for 10 chains (page 120), equal to the distance on the
curve, from b to 24. To this angle therefore the instrument is set,
and peg 24 driven at the end of the chain from 23 to 24 ; the in-
strument will now be set at 27 13' (9| chains), and peg 24| driven
at the end of 24| chains. The vernier is next set at 25 47' (9 chains),
and peg 25 driven in line with the centre of the telescope and at the
end of chain from 24 to 25. The vernier is next made to read 24 21'
(8| chains), and peg 25| is driven in the line pointed out by the in-
strument, and at the end of 25| chains, &c, "until we come to reading
1 25'9', which will fix the stump between 33 and 34 ; and finally the
vernier is brought to zero, which will fix the direction of the tangent
to the curve at the point b.
The telescope is now reversed, or turned over in its standards to set
out the remainder of the curve. We are now going to read from right
to left, and we take the column headed ' Left-hand Beading.' The first
tabular number is 358 341' (| chain), and this will fix the peg at
34| chains; the next reading is 357 8-1' (1 chain), which will fix ther
direction at the end of 35th chain, and so on to the end of the curve.
It will very often be found convenient to set out the whole of a curve
with the theodolite from a single point in the middle of a curve, which
may be done in the following manner.
Keferring to the diagrams at p. 148, it will be seen that c o is the
secant to either of the equal angles A o c, b o c ; multiply the radius of
curve by this natural secant, deduct radius, and the remainder will be
154 SETTING OUT CURVES WITHOUT A THEODOLITE.
the distance from c, the intersection of the tangents, to the middle of
the curve ; set np the instrument at c, and lay out a line in the direction
c o, by dividing the angle acb exactly in two ; on c o, set off the dis-
tance found, from c to the middle of the curve. This part of the work
may be very accurately tested, for each of the angles of deflection from the
middle of the curve to the tangential points a and b, should be found
equal each to each, and their sum should be equal to the total angle
of deflection acb, equal to half the external angle at c, which has
always to be measured in order to set out the points a and b, from
which the curve begins to deflect from each of the tangents.
The total angle of deflection, cab, divided by the tangential angle
for 1 chain, is equal to the length of the curve. We have now all that
is required to enable us on many occasions to range from the middle of
the curve every stump towards a and b. As an example, let the radius
of a curve to be set out = 20 chains ; angle of deflection cab, equal to
half the external angle at c, = 25-21'-226, half of which equal to
12 40''613 = angle of deflection from the middle of the curve to either
point of junction, A or b.
Tangential angle for 1 chain = 1718 9 = l -25'945, and 12 ~ 40 '' 613
& 20 l-25'-945
= 8*85 chains = half length of curve.
Let the distance from the last full chain stump to the commencement
of curve measure 60 links ; then we shall have 40 links of curve up to
the next full chain stump, and the half length of curve = 8 1 85 (0*40 + 8)
= 0*45 = the distance from point 8 to the middle of the curve.
The tangential angle due to 40 links = 85''945 x 0'40 = 34'-4.
8 chains . . = ll-27'-56,
the sum of which, deducted from the above 12 40' - 613, will leave 38' - 6
for the tangential angle due to the 45 links from point 8 to the middle
of the curve.
Now plant the theodolite at the point ascertained as the middle of the
curve, set the vernier to the angle of 12 40'*5, and bring the glass to
bear on the stump at the commencement of the curve ; unclamp and set
to 12-6'-2 (12-40'-6-34'-4) for the next stump, and then to
10 40'*2, for the following stump ; and so on to the end of the curve.
TABLE V.
TABLE FOR SETTING OUT CURVES WITHOUT THEODOLITE, ON
THE PRINCIPLE OF TANGENTIAL ANGLES, BY TANGENTS AND COR-
RESPONDING OFFSETS, CALCULATED FOR PRACTICAL FIELD USE,
FROM THE SINES AND VERSINES OF THE ANGLES AT THE CENTRES
OF THE CURVES.
O
^ w
%
p
W
O}
W
H
fM
ga
73
L
pq.
pq
H
H
w
W
to
w "S
ts. vi vn m
w-> On J^ t* - N rovO MNOO "S
| | NO
O VT) M *
c 02
a N ON N ON'- f>. fv i On ON ^ U
*B
3 N tnvo OO 11 ^00 N r-j
M _ _ _ N a
8
O
10 rd
<^ 2
3-9
CO*
t3
CO ON
rt k
M
n3
9
-s ' ' '
3 s 2
co
e-t
*-i O
'gbvbvN^bvNNOOMO *
5-s '
a
5 <*- On rb ON ^CO N + ONN a,
r d
W M
H
83 S
5 a .1
.0 - fl s
10 rj
fl'S
O
'S
angl
ntre
le at
03 _q
^Sg>:
6 g
ingenti
Qgle at
ne of a
ursine
CO
1
of <4 9
3*92!
He* H<m He* h|m He* .S -S
** N N r<">c<->T}-T$-u-\ '
H<3tCr>
S IT fi
11
^H's
r^ 'd-
TS^^
" <* "<* S 2
c ^
c3 ON c3
l 7 +w
10
e23
w n Thoo 00 vp m\D On y^oo g M ^
M
to
.
m ft Js
w a e3
13
.
g XrQ
g
... 'o "^ rt
r^ 2" "3
>"H . . . .
^^S-S
5
...-.
09
1=1 fl
ui a
-t->
a
On On ^00 O no vp OnnO -f^
fl ON OO NO ^- N t^sb O ON ^'i^
ft '3
p
to
M M 2 2
pi
5 ^-ON'^-ON'^ot^o r<->No r^> 3 ^
<j -
fl
fl
fl =!
^^
' 3 ^ >S
83 (3,3
> ON+3
r-H P fcC
c3
c3 w (3
O.g -
ingenti
ngle at
ne of a
ersine
10
.9
'3
He* He* H<* Hn Hm ' " ^
,J3
5
E-KjCGr""
o M -+00
Y^m si.
1 7 2z
CQ
moo p 7*"N *<-> n n J^t* poo t^r^.
00
B * t^^O OO +WNm Os. L-n b
$tt
"3 i-i N -^-\0 00 * to t^, O -"*-00 N
1 1 _ _ _ N N N t <->
....
o
00
p
t-l . .
5
. - . .
00
a t
B
a>
bD
B
0\0 00 N t^ OvO u-nvO un w i^o
'rt ON O\00 t^- rh O loOO O\00 io Q\ O On
LJ B "
"3 -^ON^-ONH-ON^r^.- to On N NO OO
c3
-^ s
c3 B^
3 a
T3 43 c3
b << 2
&>2 .S
00
B
'efl
He He He Hw H^ He He
1- - N N CO tO T$- T+- LT\ ITNVQ vO t^.
R 5P2 S
03 B . g
H<i&ot>
o ON0O VO
oilrP
05
43
CD
-CO
jo tovo O MJ^N u-n p iaO\ m OnO
B N 00 OO to '-* to O\0O m\o + t^OO -+
-3 m WlflN^NVO ONMONMyO
1-1 - <- N N to to
....
m
P . . . ,
y
9
B
0/
ON^f to00 NiAOpp\wifl
a On Onoo vb n NO h b\ tHvo isb <
B
"3 -^- 0\ "oy CT\ ^oo fnNO t*- N i-i to un
" h n n N w n >+ + tJ- w UN un
3
H ~ 2
EH
^ * >- .
p n s
"feJQ 2 "3
fl -p
c3 B,2
aSp 8
is +2 3
IL* .9
B
'1
He He He He He He He
B P 2 Sh
rB
5
i-" i-i N N KN. M + tJ- UN ir>vQ VO N
H^cc>-
O O ON t*^
" 1
11-8
CO
to tJ-i^i^n ijman ^J-N W OvNNCO
tovo " "
.03
r a u^n n ^-bsKr^b ^N N ^*-oo
fc
,J 3 i-i N m -^-vo 00 <- covO On N w-%
H M M M m ^ N
....
o
US.
M
. . . .
CO
1 1 . .J
d
b0
03 ON00 MN00 ir\ *r> O U-N f- rf- U"v On l/^
"d on On OnOO "O rH t^ ^-<) vb ^
3' "
s
3 "<* On rh On <+ On -^-oo f^N ur\ On <*">
13
W w
H
O b .|
ON** s
o
cj c eg
-a s g> *
'-B tS 3
CO
o se c
A
ange
ngle
ne o
ersir
'3
He H He H <! He He
rd
5
* i-i N n fn w+t)-i^ lovo no r^
H<5{>
00 NNO
O to
CO
.03
m t-n N O OO t->-vO tn On N N l^"0 On r*
fl *" VO ^~ rt-00 iy-i Lr\ f^ r<-> m ^-O0 f^
fcl
M m -i -. N N N
....
o
GQ
P
V 1 ....
1
...
S *3 R 8 S
3
d
bfl
a
o\n^ n ono on y* , o r 1 i^ r^ r^ P
d OnOnOnI^l^n'-'OO msO OO N i^O "+"
3 ^ On -^- On ^VO t*">00 N NO O **-oo -
M _ ,-, m m to ro rt- -4" u- u-n utnnO
<j 't
3
W -
H
o *
o = d ..
angl
ntre
le at
H9i.
d S3 =
to
d
ange
ngle
ine o
ersin
'S
He* He He He He He He
,d
Q
i- -" N N t<N W^-Tf-UN U-NNO "O l>*
H<^ cot>
* M H
^ i* 3^3
??"&
ta 00 r<-> itn c>00 ON NO O "O t^ "J-NO *"t"\0 w
l 1 p p
03
"a O wtsfn b 'ob wnn onoo 00 b fnob
5tt
*9 im M N tJ- l^nq 00 ON ~ ro^O 00 O
M m - n
....
O
GO * * * '
P
(1
P . . . .
3
co
15 CHAINS
e for 1 chain
centre
B
03
6D
co pNpsr^^-oo f^N tnoovo oooo *- vp
B C?\ On On OnOO 00 no 1^ w O t^^-t^Vj-ONN
B
3 ^-ONrhON^ONTf-ON'^-ON c->00 N N-O
S3
'bb g "3
5 -s
S ^ s
CJ O *
B * 4H 2
05
B
11 a; a
g"bbg"g
'8
He* H<n H H H^ H <h| H
rB
>- N N cr>rr )T J--r}-ur\ vtnvO NQ f^ l^ 00
b*<>
o\oo rj- r^
CO
co N O N On - l^^O ON y"N ^J" ^" ^N ON N J ^
1 1 p
a ">
03
.CO
*a M irH O* ** ^HOob ON N t^rj-tn w-\O0 r<">
te
.9 _ -. cr> rf vO N ON N -+ t^ O rnNO O
....
1-1 MMi-iNNNro
CO * '
9
tf
1
0)
bD
a
co
5 .9
1
co OnOO i^\vp rr y^ On 7$- O **\ r^^O N N Np r}-
"a On On OnOO r^ ur\ n on ^n On N ^" ifl + < t^
3 "+ On tJ- On ^ On ^00 mnn\o O -t-oo ~
03
EH
2 s " -
M 03
1pg"3
c,2
-h be r.
ea B
i
Tangenti
Angle at
Sine of a
Versine
01
a
'3
nta H H<n H -H H h| H<n
1-1 N N m ^ tJ- tJ- u^ ur>NO VO t^ t^OO
W V)00 ON
^S8
1 O O
05
wiyso ^O wo ON "^-oo t^vo -" mvO On
'O O N rhOO NM rH ~ O ON O rht-s.VO
&8
M H N Wrj- Tt-sO J>-00 ON " N
O
CO
p
M
5
CO
3
Pi
ao ON OnOO NW^On r^so VOO NVO O\00 m->
be
fl ON ON ON ON Os OSOO OO t^NO u-s. rf- N O M VQ
<| ^ 5 S K
B i
pi
"3 Tt-ON , =l-ON'!hON-<*-Os-^-ON-^-0\^}-ON ^N00
eS
H
C3 fl r5
r^ S> M S
cs a
mgenti
ngle at
ne of a
ersine
'c3
.h|<n H<n H h h<m h H<N - t|M
i-i N N co to -*}- -^- u-s iosO so NN00
H<jtoi>
OS Osoo 'o
^ ^ OS N
7 ?*2
1 1 o o
-l-J
00 NO L/-NNO O ^O H" >-^iOO -r}-N <-> WN n 00
M rt *
ab Nu->b i^N b b\b N i^sbs^h ONO-
SH
i- i-i N c<-> c<"> u-sso t^.00 O N to un
o
m ' ' ' '
to
i i
9
Ph
cc ' * * *
H 9 *.
bD
JJ on onoo t^7*-t->.^ WNO0 N psp r> io00
n "on on on on bsoo oo t-^^b ^t- <o i- oo i^\N oo
<< ^ - ~ "
Vj Tj-Os-^-ON^t-ONThON^-OsrhOs mOO r<-> t^
PJ H
o3
O H
H -+=> >
til
cs a,2
oS w O
# J3 c3
a
O S
ej C S
'3
H|N H<N H<M rt|M >h|n H Hn H
5
*" - N N CO to *<4- t}- Ws. LrsNO sQ t^ 1^00
H<Jboi>
M f)VO M
1 1 p p
1
jo co tJ- N N OvOn V^QO OnnO **"> N O O O
o *
tZi
O O h ro inOO n NNO0 u~,rn O ON O **
o
^ ""- N N m tJ- lonq \0 G\
QQ
3
11 ... .
525 .2
H S s s
<* A - - -
JO
OB
03 ChpN ONOO t^ t^>- ^*- nh 00 N t^-O ?">?"> 7* O
^ C\ ON ON b\ OS OS ON ONOO O0 - f^NO to ^J- rrj
9 Tt-ON-^-ON^-ON'^-ON'^-ON'^-aN'^-OS'^-ON
i-3 >
c3
^
<2 = g ?
!?| *
1
<s c ,2
g3*p s
"43-^03
fl * w 2
09
m O H
Tang
AngL
Sine
Versi
*8
Hn H H H '-'Iff' H<n H H<x
r3
n 1-1 N N WtO + 'tW U-nNO no r^. t-^oo
cnvo o />
1 , po
' o o
03
jq c<->no r^vp t*- p rj-vp r^vp n 00 n ppn
o o
f M
a b covb b in b no cnf^b b\ *- ** rnNb
....
o
wi-"NNrr>Tj-u->Lo t^oo Os O
QQ
p
H
3 ' ' " '
2 _
iz5 .a
d
OX)
w On OnOO 00 N|ANM fOK ONON OnNO N u-\
S3 On On On On ON ON OnOO 00 t^NO in ^h m N O
3 ,-s3 ~ * "
*g ^t-ON'^-ON^t-ON'^-ON-^-ON^ONTt-ON-^-Ov
l-i ^-iNNmmTt-"5j-u-i m\0 NO O. t-^
KH
3
H
<& "
CO
T" 1 +
0J3 C3
3 a r^
lis 8
1 fl - M
Tange
Angle
Sine o
Versin
'3
h|n h|w H H H hm Hei h
* -" N N W + tJ- in inVQ VO tN. t^QO
r3
r}" t*> io
i i p p
O O HI
m rr> m tJ- tH ON ON^O t^ U"> t^ JA p\O0 *"> t">00
'rt n ^->o ON *<"> > N f^ rn ON'O ^j- n b
o
*2 ii h N N mw^ ur\SO t^
US.
M . . . .
9
. . , . .
99
45 CHAINS
e for i chain
centre
1
09 c> on on onoo op ^y^r^P^P r'S 3 r* r** *>
a b\ On Os On On On b\ C\ On 0\00 OO f^ t^"0 iA
a
angl
ntre
le at
a
genti
;le at
>of a
sine
00
.5
'S
H* H* H* H* H H H H<
i-i - N N m c*"> **- tJ- u- u-*vO ^O t^ C^OO
O Osoo i-
as
an wnoo o op r^r^P^r^r y^p^r^r* r* *>
1 1 o p
O O w '
,91
A O *, N Lr I"-* *- u-\ b\ ^<"> ~ 00 +N ~ b C?\
e
8 H h m n criwf uo^o r^ t>-
o
Hi
....
US.
1 1
- ....
M
05
02 J
B
P3 H
PI
09 P^P^pNONt^r^y^T^p t^. pOO ~ rrj unvp
be
'S b\ b\ on b\ bs b\ b\ b\ onoo oo t^ f^.vo i^ tH
3 '^-o\'i-ON'=l-ON'<i-ON"^-a\^ON ,: *-ON'r}-a\
a
O <*5 (X)
* o
'Sogta
S S m
ed 0,2
h- g fcD S
S fl
p e^
o g
CD r r < r . "53
09
|
!
He* H' H* H* H H H* H
fa 1
H<Td3fc>
O
M m H N trj m rh tJ- ur> u->vO VO t^ t^.00
i
n m t-.vo
,
1 o o
o
M
aiN On O o vp n n y^7*"r^y^|^7hp O w
3
'a O O N <"> LOOO tJ-00 N N N OO lr\ It 00
50
S -Hi-iNNroto-t-i/^L^
....
o
M
CO
1 1 . . . .
a
M . . . .
CO
fe .9
^ 3 > - .
<J r^3 " " 2
a
a
to On ON On On OnOO r^vp *0 t*"> 00 vO 0*0 **
'a On b\ On On On On On On On On OnOO 5O0 nn
ca
S M &
H
* S
*
Tig 3
8 *2 m
a a ju
e3 a
genti
jle at
s of a
sine
a
'3
Hoj -i|n H-< He H - i iw -!* H-'
03 G .3 >
,c3
cj
* tt N N W M tj- tj- ir> uivO >0 t^ t>.00
E-i<2;>
*4- i^-oo o
rlo?
oa
mNONpsNTj-NpNONpSNON^OO
"
r"i
O O "- 1 N Vnvb On N NO O i^b uoNOOvb ^
o
N N N WMTt-Tt" U-\VO
CQ
to
n
5 '
OQ
fc .9
to
co O, On On OnOO 00 NO u-\ -rf- N OO ^ T" t^N u-
'a OnOnOnOnOnOnonOnOn onoo ob oo f-^ t^o
3 g * s s
a
* ^ON'^-On-^-On-^-On-^-O^-OnH-OntJ-On
M h h n n tn tfi t}- T^- ia u-\vO ^O NN
o M S
O CJ
^
a
angl
ntre
leat
03
P3
a, o C
'3
He* H Hm H H H He* H
s fi.2
m f N N c"> m * rh m u->sO O NN
"* ON OS t*
*4.fe5S
| | O o
+3
o o '
tn
fe
H>-iNNtOtn^-Tt-
....
O
. .
m
P
I ~ . . .
iff"*'
m
d
j Os On OS On O\00 00 CO N ^-\p N OVO H" ON
^ J s S S
p
p CJ\ONOnOnCT\OiC?\c5\OnO\ON onoo oooo n
F-l *2
10 ,o P -
ts
5 r2
^sp**
mgenti
ngle at
ne of a
ersine
.9
mm H h) M<n H>i H 1 ^ Hm H
is
"-" - N N WW^-t^ Li-v'O so t^ t^OO
H<lcKf>
>C WN'j-
1 1 o o
02
w N 00 00 m N U-, N m QsOO N * 00 OO t">
o o ' *
q O O M Mi^NO e^sO O J-s O ^ O ^O tn
o
Mi-i 1^ NN m wf +in
....
OQ
P
H . . .
9
...
a
g a
On ON On On CnOO ^-^^7*"^ O t~^ 7*- O t^
fcD
*s bsbsbNb\ONc5sb\bNb\QNbN cnoo oo oo f>*
W M
P
3 -tJ-0>' ; ^ON , ^-ON"^ - ON' , ^-0\-^Oi^1-C\-^-0
3
s s i
O ~g 8
VO a, S
angl
ntre
ie at
%%^'
genti
Je at
i of a
sine
m
.2
^-tjo <H<n H He Hn He H^ Hn
6
1-1 1-1 N N *> tn rj- -<*- u-s uo>0 vO NNX
1
WlO H
N ^ M O
| I o o
5
9 +fl pNVO NOVO N ON^O ^J-VO - O
a O O * N cniot^.O N ioOO N no b *-* b
o o
a>
o
mmmtmii Nnnr
m
g
i-i
9
Ph
m L ' ' '
5
d
a
a 6nO\0\0\ OnOO OnOO OnOO tJ- tJ- <*"> p 00 t^
* .9
3 1 * * *
W M
"rt On On On On On On On On On On On On On ONOO ob
"1 Tj-ON"^"OS"^-ON^"ON'^l-0\"^-ONrhON'<J'ON
a
H
o *<
ft -s
" ** 5 <U r
||-a
03 fl
as* -
l*5ji
09
a
'3
He* h|n H** He He H H<h h|s
a Jp2 S
cs a g
J9
o
ii n N N M W + t)- i/^ uovO \0 NNOO !
H<l02f>
o O o O
1 1 o o
jg <> t^vo onltn^I-oo tJ-unoovo r^ o w t^.
o o o
i
o
2 0'-'^ ^-^b oo h ^-n iao i^b io
....
^ M M H N MM'+'t
od
to
H
p . . . .
3
M
...
tn
I i ri
j On On On On OnOO On t^ r^CO tJ- j* On On j"> f">
O On ON On On On ON On* On On On On Onoo do 6o oo
34**1
as
Vj ^-On^OntJ-On^J-On'^-OntI-ON'^-ON'^-On
OS
O . f-i
s-l +2
angl
ntre
le at
n &p s
.2
a *< 2
09
ange
ngle
ne o
ersir
"e3
H H<n He* H<n Hn h|n H He*
rd
O
-" i-i N N ntnTf-rJ-i^i iy\\0 O t^ t^.O0
H<lco!>
166
CONTRACT EARTHWORK TABLES AND
MEASURING UP.
The accompanying Earthwork Tables have been prepared with a view
of sparing labour and economising time in computations not only of
great length, but always of considerable importance in railway, road, and
other contracts, always requiring a great amount of checking before the
calculations are considered as satisfactory. Having been worked out for
every six inches in depth, they will be found to produce more accurate,
and, in contract matters, more satisfactory results, than are usually ob-
tained. During the last eighteen months the writer has had to take out
contract quantities of earthwork on some long and heavy lines, and the
contractors particularly requested that the calculations should be made
on this system. The tables in ordinary use only give quantities for
every foot in depth ; those now submitted give the quantities for every
six inches in depth : and when it is considered that in cuttings, say from
30 to 35 feet deep, for every six inches in depth the quantities for the
slopes only are upwards of 180 cubic yards, and for earthworks at 2 to
1, and for the same depths, the differences are 250 cubic yards, it is not
surprising that there has almost always been so much dissatisfaction
in contract matters about earthwork calculations.
To make this plainer, and at the same time explain the use of the
tables, let the following few depths of cutting, from portion of a contract
section, serve as an example. It is not that the most perfect accuracy
of the tables in ordinary use is questioned ; but they are not carried
far enough, nor sufficiently detailed.
#
Formation, 20 feet ; slopes
1| to 1 ; 100 feet chain.
i.
n.
ni.
IV.
3190\
32-40/
8059-3
8059-3
3205
34-50
8496
8716-2
33-45
38-20
10109
10105-1
36-35
42-43
11859
12112-5
40-31
46-68
14309
14297-7
44-65
52-30
17281
17279-2
49-49
49-42
17904
18227-8
50-82
49-30
16968
17279-2
106077-0
49-56
In the above, Column I. gives the depths of the cutting in feet and
CONTRACT EARTHWORK TABLES. 167
decimals, and Column II., the quantities in cubic yards, from the tables
in ordinary use. Column III gives the quantities in cubic yards, taken
from the accompanying tables, and due to the mean heights given in
Column IV. Thus, 31-90 and 32-40 in Column I. give 32-0f> for a mean
depth in Column IV., and the tabular number in Table VI., for a forma-
tion width of 20 feet, with 32 feet depth, gives 2370-4 cubic yards ; for
the slope of 1| to 1, Table VII. gives 5688-9 cubic yards, at the same
depth of 32 feet, and these two numbers, added together, 8059*3 cubic
yards, entered in Column III.
It will be observed of these tables, that the writer has adopted the
plan of separating the quantities due to the formation width from those
due to the slopes ; this has enabled him to bring within a very small
compass tables calculated for every six inches in depth up to 80 feet,
for 10 different widths at formation, and for 8 different slopes; there is
no other trouble in making use of them, than to pick out the tabular
numbers and add them up, and the circumstance of their being calcu-
lated to half a foot, makes them, in actual contract practice, much more
accurate than tables calculated by the prismoidal formula for only every
foot in depth, it being, of course, understood that in making use of these
tables, it is to be done chain by chain of 100 feet along the length of
section.
It is also to be observed that the plan adopted of separating the forma-
tion quantities from the slope quantities, offers great facilities in adjust-
ing the balance of earthworks ; that is, of widening embankments for the
disposal of excess of cutting, or vice versa : and also where it is advisable
to resort to side cutting in the formation of embankments in preference
to extra cutting from the excavations, all allowance being made for the
long haulage of empty waggons over steep gradients, which are now the
rule instead of the exception.
Every engineer knows the importance of cross sections in order to
arrive at practically and satisfactorily accurate results in determining
the quantities in heavy earthworks ; he knows also that to obtain these
results great care is required in plotting the cross sections of cuttings
and embankments. Though the operation is exceedingly simple, he is
equally well aware of the amount of time occupied in calculating the
areas, and in checking the work. The Earthwork Tables here given will
materially assist in reducing the time and care required in these opera-
tions to a minimum. In the annexed figure, is a cutting in sidelying
ground 35 feet deep at centre stump, but at a the depth scales only
30-75 ; set off b a equal to 30*50, and the tables at once give the quantity
in cubic yards due to the area ai/cd, leaving merely the area of the
triangle a d e to calculate. If the area ab'cd is calculated from the
esoss section, the quantities from the tables will prove if a b', b c, and
c d have been correctly plotted, and the area accurately calculated ; the
work will be safe from all chance of error.
H
.168
CONTRACT EARTHWORK TABLES
In heavy earthworks, we are all aware that in preparing the quantities
for the monthly certificates, the work of squaring up from measurements
taken on the ground always occupies considerable time. Table I. of
Earthworks will be found to save much time in making these calculations,
or in checking them, as the annexed figures will show. In fio\ A, let a
be 12 feet wide and 15 feet high, then, by Table VI., we have 666-7
cubic yards due to this area; let b be 30 feet mean width, and 10 feet
Fig. A.
mean height ; twice 15 = 30 ; on the 10 feet in column 30 we have 555'6
cubic yards, and this, multiplied by 2, gives 11112 cubic yards for the
portion b ; let the portion c be 65 feet mean width, and 9 feet mean
height ; we may take twice 24 plus 17 = 67 by 8, and we shall have
71M
711-1
503-7
1925-9
And for the whole area of A we shall have
Cubic yards.
a= 666-7
6 = 1111-2
c = 1925-9
3703-8 = A.
AND MEASURING UP.
169
At the next point of measurement determined on, let the cross section
be as in fig B. Let a be 12 feet wide and 161 feet high ; for this first
portion we get from Table VI., opposite 165, 733-0 cubic yards ; for b let
the mean width agreed to be 50 feet, and depth 20 ; then 24 plus 26 being
equal to 50, we take out from opposite 20 feet deep 17778 cubic yards,
Fig. B.
and 1925*9 cubic yards = 3703 4 7 cubic yards ; for portion c let the mean
width and mean height be 98 feet and 10 feet ; then for width we shall
hare four times 20 and 18 = 98, which will give from the tables 2962-8
and 666-7, equal to 3629-5 cubic yards. For the whole due to area B,
we shall have
a= 733-3
6 = 3703-7
c = 3629-5
8066-5 cubic yards = B.
The mean of 3703-8 and 8066*5 is equal to 5885 cubic yards, being
the quantity upon a length of 100 feet. But let us suppose that it is 190
feet instead of 100 ; then we take the 90 as a decimal, and we shall have
5885
1-9
5296-5
5885
11181-5 cubic yards.
We will conclude by an apology to engineers for the details above
given ; but they will be so good as to remember that these pages will
come into the hands of students, and even of working men, and that,
necessarily, explanations must be full and simple.
ft
* a
s
S
o
Pi
S
OB
P
<J g
h a
D g
1
M
NO
**
CO
>-c
O
00
t^ Tj- CM
ON00 NO vn
CO
r 1
p
on r^NO
-+
co
io t-v
C\
hH
CO
Vj-vb o<
O
CM
!*>
o
ts
ON 1-1
CO
in
t^do
o
b
*
O
no
O
n
SO
M
^O
r--
N
si
CM
l^
CM oo
CO
COOO
t+- on
4
CO
CM
CM
CM
CO
T+- ^ V) U->V> NO
t^
t^-00 oo
On On
o
o
rl
43
CO
t}-vO
NO\p
ci
CO
tOND 00
Cn
H
c)
ri- y-) t^oo
p
CO
tJ-nO
>b
i
cm
b oo
l-
n
CO
'_
On r-.
1*1
Vt- N
b do no
+
CO
M
b\ K,
NO
CN
C\ sf-oo
CO
co
cooo
CM
(M
t^.
CM
r-^ i-i
NO
NO
NO
o
NO
CM
>-i
M
CM
CM
CO
CO
T+- r+- NO IONO
VO
r^ t^oo oo
ON
CN O
o
M
N
"
N
On cooo
H
h
H
NO
o
rj- ON
tr.
90
J*
t
W NO
i'
On COOO
CM
l>
00
r/n
r>
b
^b
H
IO
o
*
oo
'co
t^
CM
b
i-l NO
b
'>+
do
CO
t>
CM NO
CO
<o
t>.
O
o
q-oo
^c
1-1 u->
o
~z-
CO
co
I>~
CM
NO
SI
cm
cM
CO
CO
^ <*-
'*-
uri
ND
o
l>- t^oo
CO
oo
On On
o
cm
1-1
I
to cm
p
t- ^- cm
On t^ +
ON NO
#
O NO
CO
M
00
NO
CO
O 00
m
cl
'i
CO
4
>o
no no
r^
04
do
ON
b
H
M CM
CO
-h
4 No^b
K
ts.
00
c)
no
o
oo
CM
o
o
00
Cl
f>.
ON
CO
h*
o\
CO
1-
CM
CM
cl
cM
CM
CO
CO
^- "*
^r
UO
W1NO NO NO
t> Cv
CO
CO
CO
On O
1
l
N
Cm
cM
CO
CO
CO
-*+ .*
u-,
Wl 1/-IV NO
1^ t^
t-^00
CO
CN
CN
4
' m
00
o cm
CN
NO
CO
b
t- rj-
L,
do
li-l CM CNNO
CO
b
r--
'-J-
',_,
CO
r^
rhOO
CM
NO
CN CO t>- O
T+-0O
U-l
ON CM
NO
o
*
t^
NO CO
2
M
M
m
cl
CM
H
CO
CO
^- *
NO VTNNO NO
f-
ts
t>-oo
CO
00
F
04
q
o
H
g*
t^
o
MNO
CO
h
O
CO
r^
o
CO
r-^
o
WNO
CO
t^ o
co
r^
p
i
vb
b
covb
O
CO
o
b
CO
<h
b
CO
o
b
covb
o
CO
NO
o
CO VO
b
H
no
o
CO NO
O
CO
o
o
CO NO
.o
CO
NO
o
CO NO
o
CO
NO
o
o
o
Pi
o
ft
CO
I-l
M
c)
M
M
CO
CO
CO
^f- w, vr> ONO NO
NO
c^ i-^ 1^00
.
O
<
p*
^ 0\ rjr
ON COOO
rooo
CO
t->
c)
r~* r*
r>
NO
NO
N
VO
<o
i*i
I-,-
ir-
r-
BO
O
M
CO
r}-NO
r>
"">>
b
CM
CO NOVO OO
b>
H
CM
^*
ij~
NO
Cn cm
NOOO
cl
oco
^- t~^ O
$
O CONO
CN
CM
NO
On CM
r-
Cl
CM
M
CO
CO
co tJ-
+
NO VO
NO NO
NO
r-- t^
g
wosyN
CO
*
O
r^
CO ON NO
H
00
+
M J~~
CO
p
NO
H
On vo m
S
onoo do oo
C-.
t^
f-vb NO
wo
vr>
!n
It
$
rj- CO
CO
co
iM
CM
M
M
n
M
NO 00
>-i
* t^
CO NO
ON N
vooo
t^ o
covo
CN
rl
NOOO
I-H
M
CM
cm
CM
n
CO
CO
co
Tj- T+- Th Wl
NO
NO
VONO NO NO
t>
4J
NO
CO
ON tx tJ"
cl
O OO NO
CO
<-t
On r-x + p
O oo
NO
CO
ON t--
<D
lr>
CO
OO
NO
>*
is
b
N vim
M
do
NO
j-c*
b
r^
o
CO
do no
U-lOO
CO NO
C\
cl
U-l
r^.
O
CO NO
oo
>tNO
CM
>o oo
CO
s
(S
cs
d
CO
Tj- <*
NO NO
O VONO NO
r+- t^ O
co to
M
O
CM
*. ON
>-l
rovo 00
o
CM
+ r-~ On
N
CO
8
4o
CO
' M
co
NO
t^
b
CM
T+-ND do
M
CO
NO t^ O
is
i*
NO oo
'n
CO
<A
T+-VD 0<
c<~
U1
t^
N
T+-ND 0O
CO
NO 1-^
q
CM
*
NO 00
M
C<~
<M
H
cs
Cl
H
Cl
CM
CO
CO
CO CO
T+- T+-
#
^h
tf
NO NT
Q.S
OvoO*^Oyo O)^popo
mmcmcmc^co it <* in novo *b
OvoOnoOno OnoOnoO
t^ Kdo 00 ON ON O O h h ()
O
on tsvo
+
ro
O
00
K
O
<* d
M
OMM
vo
o
co
d
O 0\N
vo
tJ- co
H
o
On
CO
o
1-1 co vo ts
rs
_
co
**VO
oo
o d
+ IOSO\
_,
CO
to tsoo
O
d
"J-vO 00
o
-(
-+
vo O >n
*et
vo
vo
Is d
Is d
Is
ri
OO
cooo
COOO
*
ON t>- ON tj-
vo
^- '*
ifi
rs
isoo
OQ
ON
On O
O
11
N
d
co
"i
tJ. rj. vo
vovO VO
tsoo
00
m d
M
N
C)
d
d
d
d d
ci
d
d d
d
Tl
d
On O m co r}-vo tsONOdcovovpooONMd;+ |fl (nM O h M
n O OO >i) ^ f< O M N ifl ( m ON k io rj- fl O 00 VO Vj" CO hi ON
vo O ^t- On t4- on ^-OO MOO COOO d Is d Is d is mW m^ m ui
N mcim"t^ vo vovo vo t - ts OOOOOnOnOO hi i-i d d co co
MHI-IMMM MMMMMMMMMI-lrttf d d d <S Cl Cl
rJ-NO |Sp H
tvi^MM O 00
O vo O vo O ^J"
*)-*$- vo v~ vo VO
d d d d rt d
no O -4- On cooo d ts m vo O ;+ On cooo d Is
in O t)-oo ci K t)iM^b+ooMtsrii
vo o <3-oo wn d vo m vo o <*-
m d d d co co "4- ^J- vo vovo vo
VO O tJ- On cooo
vo O rj-oo co is
vo O ^oo co Is
On O O O M 1-1
m N tl M rt
() N m vp O +
Cl VO W "NO V*-
d >u vn o +
d d co co ^J- tJ-
d d d d d d
cop NVif) p is t}- d p\ts +
On bbwd co co ^j- vo vovb Is
vi O *4-00 d vo O TfOO d vo O
OMMMdd cococotJ-vj-vo
00 00 ON O w M
rj-oo d ts m vo
vo nvo vo ts Is
vo co w oo vo co
d co ^4- rh invb
C\M ts M vo ON
tsoo 00 ON On ON
O 00 vo CO p Is
t^tsOO On O O
ro is w vo O tJ*
O O w w d d
d d d d d d
O O O hi m m ddcococOT}- -^ tJ- vo vo vovo
M O N rh h M vo'd ONVO CO b is + h M vi rt
vOOcotsn^-ood 1 '. Ovcots O tJ- c
OnOOOmw w d d d co co ^1-^^
VO ts Is IsOO oo
ONVO CO O Is rj-
>r, ON dvOO^-tsw
VO vo VOVO ts ts tsOO
On on On O O
hm vo co O
voce d vo O
OO 00 On On O O
_ M tt h. d d
CO
co ts O co vo
ts p
vb b covb b co
VO O covo O co
OO On On On O O
OcotsOco tsOcotsOco
b covb b co vb b covb b co
OcooOcovoOcovoOco
HMiHdd dcococorj-^4-
tspcotsoco t^pr^r^pr^
vbb co vbbco vbb covooco
vC O covo O CO vo O covo O co
rj- vo vo iovd vo
vo ts ts r-~oo oo
vo O
OO O M CO rjr vo
1-1 VOOO M <j- N
OO 00 00 On On ON
cooo co is d
voo^-ps ^1-ONThON cooo
isob b^coij-vbtsbNbdco
O co ts O covo On d vo On d vo
O O O hi m m hi d d d co co
vovo oo On hi d
OO HI Tj- tS M ^1-
co -^- -^ tJ- vo vo
m vo O vo O vn
rj- vo tsoo b h
t}- O no co on vo
O O ON OnOO 00
t O d vooo hi
CSOO 00 00 00 ON
M 00 r}- O ts CO ONVO d 00 r}-
00 ts ts tsVO VO vo vo vo rj- tJ-
+ NO COVO ON d VOOO HI t$-
OnOnOOOO H.M-dd
(SCOOVOdON ^HltSTj-pVO
co co co d d m. m m b O O bi
O covo ONdvoooHiTf-tsOd
COCOCOCO^}-tJ- ri-vovo vovo VO
dooovocoM ONtsrj-dofs y>poHioNts^i- f'pr^^r^r* f^h^." P*
dbtsvoco-i oovb'-^-'dbis vocoMoovb^}- dbtsvocoi-i oovoTJ-dois
d vo ts o covo oo h tNO *^oo w covo On d vo ts o covo oo m < ts O d
is ts tsOO 0000 OOONONONOO OOwhihi^ dddcOCOCO COT^-T^-Tt-vovo
oo O _d ^ Is On hi covo oo O
isb d V(-vboo hi covotsb
is O d '4-vo oo
vovo vo vo vo vo
tJ- Is On m covo 00 O
rJ-tsON HtcovoooO
rj-vb 00 hi co vo Is O d 'i-vO OO hi co vo Is O
..covotsOd ^-vooohicovo tsOd'+vooo wcovotso
Is Is Is tsOO OO OOOOOOOnOnON OnOOOOO wHiWMd
OvoO^nOvo pvoovopvo O wp yiO |0 p
iorOrl-^t-vovovbvbtstsOOOO ON ON OO him d
MM |_HHII-|-HIHIMIHIM HtHldddd d
voO^iOvo Ovopvoovo
d co co tj- "4-
d d d d d
J-nVO ^- co m 00 NJO^t) M
M^NO\h co ij-vo oo O d tJ-
O vo O vo h. vo m vo m r- d r^
0\0 Ohm fl rt mto^^
O p\ t>vo Th CO
t^oo Q d W-vb
Onoo *o v>mn
<ONO\M CO vo
NHOO COOO COOO tf- ON rj- ON
VO vovO VO r-~ c-< 0000 O\O\0 O
MMMPlCim WWW W<^i"
d co vovo oo On
co r}-vo no\o
* ffi Ooo n o w m b\ is >o
ON ^ ON tJ-00 CO 0O COOO d f. d
vo r-. t^oo oo on onoommn
d d d d d d C) COMMWm
M Jl ^Vl t-^00 p M CO Tj-VO tN
^- "t< O 00 vb ^- W M b\ tv <o M
NH Nmvo m vo m vo O >o O
d co co <+ tJ- vo vovo VO r-^ r>.00
CO CO CO CO CO CO CO CO CO CO CO CO
p\ cooo d r-% m vp o ^i- On cooo
oo w ts ' i m io b ij-oo tn ts
OO MNMiO m vo O ^"OO CO l>
r*- >o OVO vo t^ r-oo oo oo on on
fl H rt fl M tl M
d y^ m r o yr
d vb w vo b
d t>*
On poo
V 00 CO t-s d vo M
d VO hi vo O *$ OO MNMVO m
O O - fl f> M wm^rHvi
eocococococo co co co co co to
n fi o n -t f< p^r^r^r 1 P^*
hi d CO CO ^- vo iovb t^OO 00 ON
oo d vo o Tj-oo nvo o 'i-oo d
d CO CO rf- r}- ** vo OVO VOVO N
d d d d d d d d d d d d
tJ- m CNVO CO hi OO VO CO
O M M fl Mtj- V}- wivb
tsM iOO\fON hi vo ON
N0O00 0O 0\0\ OOO
H M (I M fl M cococo
r-."r>.0O
co r- m
m h- d
CO CO CO
m m m fi fi m r r r*" ^ ?* ? y^^p *p "p r* r- r*^ on on
Tj-MOoiocJO\vocoOr-~Tj-M oo io ji b\vo co b i>. rh '*- oo '
r-> M rj-00 d vo on co t^. O -d-oo m mo\ti^ O ^C^mh vooo
O M hi hi r* d d CO CO <*<$ tJ- vo vo o vo vo r-* N NOO OO 00
fl fl fl M fl tl rlSflflfl fl fl fl fl fl tltl ft fl fl fl fl
vOOcot-^Oco NO W N O
vb b covb b co vb b covb b co vb
vo O covo O co vo O covo O co vo
ooonononoO o hi hi hi d d
bbcovbbcovbb covb b co
O covo O co vo O covo O co
co co rf- tJ- tJ- vo >o vovo vo
MMMMfin fi ti ti fi d fi ft ei fi ft fi ti n n n fl d d
p tJ- On ^- ON tj-
CO rj- vo K-OO O
ON CO 00 COOO CO
hi CO r|-vb t^ ON
VOOO w -<4- t^ O
ON ON O O O
M HI f| fl fl d
b d co vovb oo
t}- k>. O covo ON
m m d d d d
d d d d d W
On m d "3- vo r^
d vo on d vooo
co co co rj- ^- <$
d d d d d d
coonvohiootI- o Nw Onvo d
b\oo oo oo. K 'ts t>.vb vb vo vo vo
v^O0 hi *J- c-> O COVO ON d vi-)00
vo vo r^ r^ r-oo oo oo oo on on on
oo rh m t^ to p
ij- t1- tJ- co co co
hi ^- t> O ovo
O O O "H h hi
d d d d d d
vo d On vo hi r>
M M t)>
On d w-ioo
hi d d d co co
d d d d d d
VOCOMpNt-sTj- d O 00 VO CO M
VO CO HI 00 VO ^}* d O tMOMM
VOOO HI COVO ON d vo t-^ o covo
vo >ovo vo vo vo t^ t-. c-.oo oo oo
on r>. *j- d p oo
ooi ^-'d b tv
oo m rj- t>. O d
OO ON ON ON O O
VO CO
d d
p\t -+
o co hi oo vb ^h
VOOO HI COVO ON
O O HI hi HI
d d d d d d
tJ-nom r^^p oo p d +f><^
TJ-vb OO M CO vo t^ b d r}-vb oo
=j-vo oo H, co vo i- O d rj-vo oo
dddcococo cot}-t1-t}-^}-t1-
m co jooo p d
HI MVfltsO d
m mmtso d
vo o vo vovo vo
covo
-4-vp ON I
ifrvb 00 hi co io
^vo oo hi co o
vo vo vo r- t-^ t-
fi
OVOQVOQVO OvoOvoQvo OvoQvoOvo OvOOvoQvo
en
M O On tsNO rj-
00 O "i MU1N
* O >n O m O
n S H to to *
^ * f + "* 4
to -t p oo ts u-i
ON "n to rj- NO 00
in H VO "H NO 1
r+- in inNO NO Is
4 <* ^" -4- "+ "+
^h rt w ONOO vo
O is rj- in r^ ON
t-~ s r>- s t^ m
t~-00 OO ON On O
<* * * -4- -4- v>
UNMf) O OS t^
Ii to in Km b
oo moo tooo *
O i t S to
in w-> m in in in
NO rh to m p On
*S 'tJ-NO OO O ii
ON t- On i- O vn
co tJ- tJ- invo no
u-> m in m in in
on o m tn ^vp
O 00 vq Vj- Is
w-i O st" ON *i- Cs
OO On On On O O
to to to to *J- *}-
In ON O C< CO in
b oo r-- in to i
<4-oo tooo tooo
n li S N CO CO
rj- rj- tj- ^ ^- .*-
vO M p\ h t
On t^ in '>+ "s O
s t-^ s r^ s t-
rj- t:J- us, inNO NO
4 rt- <* rh ^- ^1-
in t--oo O m to
00 no t}- to m On
h vD h VD d in
r^. 1 CO OO On OS
Tt Tj" <4" ^ T*- ^
rt-vo Np\o M
Js in to Ii b oo
O no O in O tJ-
O O w i S t)
in in> in in in in
SO O ** On tooo
in b "*}-oo to is
m o -^-00 to ts
u->nO *OvO NN
CO CO to to to to
S tsMVO O "+
<S vb It in b V*-
UNO m uiO +
OO OO On On O O
to to to co 3- rj-
On cooo H t^. m
OO CO t~^ S vb ii
oo to t^. S NO n
O i m S M to
^ ^- ^- ^- * -4-
NO O
in b
in O
to -3-
^4
O On cooo
*- OO Mis
T+-00 to is
ri- rf- in in
44 + ^
ftlNMvO O +
rt vb m in b !<
N no n in ~ir
NO NO ts tsOO 00
^- *-'* ^- 4- r}-
co O
On O
i/l O
d to
CO to
NJOJ< O
b ' Is to
tJ-OO N NO
to to >^- ^j-
to co to to
Is ^- c* Os Js t}-
to r>- in invo ts
O -^-00 t< no O
in in invo no ts
CO co to CO co to
H ONNO rj- m OS
OO 00 On O -" "i
^t-oo s t-^ w m
t^ r--oo oo cn on
to CO co to to CO
NO CO M OO NO CO
<S to t}- Vl- invo
On to t^ n in os
on o O w
to rt- rj- + tj- Tj-
O oo in to O t^
i>. tsoo bs b O
co ts m in o *
O to CO ^- r)-
't ^t- ^ tJ- 4 4
p p
co b
SO o
On O
to
OM H H
is "<* '- oo
o o -
CO co to to
c* C* CO CO CO r}-
in is ONNO to b
00 c* in On co ts
n c* M iS to co
CO co to co co to
r 1 " i* Y~> Ir^f ^P
t-. *<4- m 0*0 in *S
O ^j-oo ii in On
tJ- ^}- tJ- in in in
CO CO CO CO CO CO
VO t^ t^ t^OO 00
ONNO MO tN +
S NO O ^ t^ i
vo no t^ r^ t-^oo
CO CO CO CO CO CO
On On OS O O O
Ii oo in to b i>.
moo S no O to
00 00 On On O O
CO CO CO CO si" 'sh
t-> p
no b
NO O
vo ts
n is
to f- O to
tovO O to
tONO O tO
c-. isoo oo
rt C H N
ts O MS O co
NO O CONO b tO
NO O CONO O tO
OO On On On O O
d C H C CO CO
tNp to t-^ O to
NO O to NO O en
NO O CONO O to
O . h - rt tl
CO CO CO co to to
r* p
NO O
NO O
CO
to to
MNO M
tovb "o to
tovo O co
to to rj- rf-
co to CO CO
J-- O to t^ O to
NO O tO NO O tO
NO O tONO O tO
^J- in in invo no
to co co to to to
vo o m O O OS
OO b to ij- in
H U-lOO M H"^
m in invo no vo
M N S <S (S S
tJ- On ^- OS cooo
ts yo O m to tJ-
O wnO tovO
IS ts tsOO 00 oo
tl rt tl tl
tOOO MNt Jv
no r~. On b Is to
On vS m On M m
OO On On On O O
c H c S to co
S ISNVO HVO
invb 00 On Ii is
OO w rt- t^ w <;}.
O M i - S S
CO co to to to to
m no O *n O m
*%h in K bo b Ii
is o CONO O CO
S to to to ^- tJ-
CO to to CO co to
rj- O NO CO On in
O O ON OnOO OO
NO moo M
to ^- -4- + t}- U-.
(4 tl t) tl (<
w oo t}" O t- CO
oo is is isvb vb
tJ- Is O to no (j^
in inNO no no no
C4 M C* d C< C*
ONNO ttOO t)-m
in in in "+ "<4- Vh
H moo m rj- t~*
t^ t^ t^OO 00 00
s s s s s s
t-s to p NO C< OS
to to to 's *S M
O CONO ON S in
ON On On On O O
N d fl H WW
m m t^ + p no
hh ab b 'os
o ii ~ <-> s s
to CO CO CO CO to
H oo no to w
tS O is in to h
tl iflN O tovO
C4 tJ S to to to
c* c c< S t cl
On ts ^ S p oo
oo no "t}- Is b ts
to rj- t}- rj- in in
t) rt n t) i
NO CO M On t^. tJ-
in to ii 0*0 no V}-
inoo < tnvo On
in invo no no no
N H C< S tf
is b
N m
M c<
00 VO CO i-l
ts in co m
r-^ o cono
t-.0O 00 oo
t) S S tl
ONNtI-H o 00
oo vb '*- is b i>.
oo m + ts o n
00 On On OS O O
vS t> M C< CO CO
OO O J* ^ t" On
ts O Cl Vt-NO OO
ts O t t}-no oo
tsOO 00 00 oo oo
m to inoc O S
m to in ts O is
w to in is O S
On On On On O O
H, W M M d C<
+ novm r* 1 ^?
rt-NO oo ii to in
t^-vo oo *< to in
O o O w i -<
M tl M tl O d
00 O
K b
t-- o
N "!j- Js OS
is "st-NO oo
N ri-vo 0O
rt rt rt
rt ft M H
M CONO 00 O S
Ii tointv'o is
m to m ts o vS
to to to CO + tJ-
N H S S
O ">
b b
O m O ^o
ii 'w S S
"+ 'T + **-
O in O m O *n
to to + rf- in in
^ -4- tJ- 4 ^ 'i-
O y^ O yo O yn
no no i>- t--oo oo
^- -4- * <* ^ rj-
o y*< p y*> p y*
On On O O Ii Ii
-4- -^ w-> m in in
P y p y^ p y^
is IS CO CO tJ- Vt-
in in m in in in
i _l
o3
I'
$
fag
O
1
I
1
CO
l".VO tJ-MW p
M ifl N b\ m co
O VO O 1H VO
t^ N00 OO ON ON
tfl lO lf| >o >o lO
00 tv. vo tJ- c M
tj-vo oo b d Vj-
n m NMh
O O w w d d
VO VC v VO vO VO
CnOO kO ^iMfl
vo "t-^ ON >-l CO vo
M IsttOO COCO
co co tJ- r}- vo vo
VO VO VO VO VO VO
O On t^-vo rt- w
t^co O d 'ii-vjj
COCO -sj- ON Tj- CN
vo vo r- r>-co co
VO vo VO VO VO lO
1
to r}-vo n Ov O
i ^- btio K
On ^j- ON tJ-oo CO
d M M ^j- t)- lO
vo vovo vo vo vo
d to yovp co On
vo to l* "on t~> VO
CO COCO H N
vovo vo o- t^.co
vo vo vo vo vo vo
h d rj- yo N00
+ d b co vb rj-
t^- C) t^ M VO M
CO On ON O O w
VO vo vovo vo vo
O m co t|-vo t~^
co m on r-. vo CO
vo m vo O vo O
i d d co co rj-
VO vo VO VO vo VO
1
CM
ON MOO tNM
00 CO t^ d VO M
00 rofv VO m
CO ON ON O O w
VO O rj- ON COOO
io b rf-co to r
VO O tJ-OO to r^
HI M d d CO CO
vo vo VO vo VO VO
cj vb w vo b t*-
c vo m vo O r}-
TJ- TJ- vo vovo VO
vo vo vo vo VO vo
on toco d if J*
CO to NttvO i-h
00 MNMVOM
vo r-- r--co co On
vo vo vo vo vo VO
M
CM
yo d p (* ^- d
hi d c> to >* io
00 d VO O tJ-OO
t}- >o vovo VO VO
3- tJ- tJ- tj- t- rj-
ON t> tJ- H ONVO
vovb r>oo oo on
d vo O "i-co d
t^ r^oo oo co On
- <3" tJ- tJ- 4- Ti-
tJ- m OWO to w
O N M CJ CO 'tJ-
f~~ i-i vo ON co r^
on o o o w
rj- vo VO vo VO VO
CO vo to p OO vo
rj- vovb "r- Koo
h vo on co t^. i-
d d d co co t}-
vo vo <o vo vo vo
(M
M M 1- M d tO
^m oo vo d On
I--, ii -3-0O d to
O m m w r) r<
,4. .4. .4. 4. .4. 4.
CO CO tJ- tj- tJ- to
vb to b r^ "* m
On co r- o tJ-co
VOVO VO vo N JT^
co vo d b*va CO
M VO ON CJ VO O
vo io vovo vo r-
* -r -+ ^ <3" "sh
t-vOO 00 ON ON ON
O N '^ H 00 vo
tJ- n m vooo d
N NOO 00 OO ON
Tj- T*- Tj- Tj- Tl- Tj-
CO
N p to J>. O to
vb b covb b to
vo O covo O to
>C NN t^OO CO
to to to co to to
vo p to t>. O to
vb b tovb o to
vo O covo O co
CO ON ON ON O O
CO CO CO CO ^t - 4"
r~- p wts p to
vb o covb b co
VO O COVO O CO
O m m i-i <* d
^" -* 'i- ^ ^ tJ-
t-> O to n O co
vo b covb b co
VO O COVO O CO
cJ co co co t}- rj-
^" ^ rj- rj- rj- tJ-
O r- p\ ;* On tJ-
co r}- to "f^oo O
NO ON d VOOO C<
.4- rf- vo vo vovo
CO CO CO to to to
ON toco tooo to
m to 4-vb "t- "on
VOOO H 1-NO
vo vo t-. t-^ r^co
co to CO CO co to
b d co vovb oo
"tNO tovo ON
OO OO ON ON On On
CO CO CO CO CO CO
VO M VO M VO O
On m cl r}- vo K-
d vo on d vooo
O O O 1- M
+ ri- rj- tJ- Ti- **
-t5
to on yn hi oo ;$
ONOO CO CO t^ t^
tooo >i r}- t-- O
d d to CO CO Ti-
CO CO to CO to CO
o sw p^^p r*
r^-vo vo vo vn vo
COVO ON d VOCO
t}- tJ- tJ- vo vo vo
to to CO to CO to
00 rj- JH Jsp
tJ- Tir tJ- CO co to
M TJ-NO tOVO
VO VO vo t>- t^ t^
CO CO CO CO CO CO
vo d oo o jh jv.
d d *m "hi b
ON d VOOO hi tJ-
t-oo oo oo on On
CO CO co to to CO
1
4-1
VO mm on t-~ ri-
vo co m o vb tJ-
toOO M COVO ON
O O HI M M
CO CO CO CO CO CO
d p 00 vo to w
d O ts>^M
H vo f~~ O covO
d d d co co co
to to to to to CO
ON t- tJ- d O 0C
M vb t)- N O r-
0O >-l r}- t- O C*
CO t}- tj- tJ- vo io
CO CO CO CO CO CO
vo to m on t> rh
vo co do vo tJ-
vooo m covo On
vo vovo VO vo vo
to to CO CO CO CO
1
tJ- N ON HI COVO
tJ-VO OO HI CO VO
t}-v CO M to to
^- ^ tJ- io i^ vi
d d d d d d
J"* P ? r*" J** 9 s
r- b n T+-vb co
NO H tJ-vo CO
VOVO VO VO VO VO
H d d H t d
IH COVO 0O O C*
in co io t^. O cJ
m co vo C-- O t
n t^. r^. r>-co co
d M d d d M
tJ- r On hi covo
T}-vb oo hi to vo
rt-vo OO hi to vo
00 OO OO ON ON ON
d d d d d d
XT
A,
I
.2
y> p y> p yn
In vovo y? (n tN
vo to to VO io vo
o y> o yo p vo
O0 CO ON On O O
vo vo vo vovo VO
O vo O y*> O vo
m >-< c> d to to
vo vo vo vo vo vo
O VO O vo O JO
t}- r}- o vovb vb
VO VO VO VO VO vO
i-i O OMSNO H-
it O no o vi o
O\0 O H M M
vo fx. tx. tx. tx. t-x
CO M p 00 t^ NO
ON N CO tJ-NO OO
VO fl NO <-> NO w
d CO CO it it
tx, tx. fx. tx. tx. fx.
Nhfl M onoo no
O d Vj- lo fx. On
t> d tx. d t-x d
no no no n txoo
tx. t> tx t> r> t>.
NO CO N O ON tx
m co io rxdo b
00 COOO COOO tJ-
00 ON ON O O 1
tx. tx, fx.00 00 00
NO * CO
'o '*<&
ON it ON
fi N Ci
00 00 00
OvO h M itNO
I m booi +h
no O Tt On it ON
tJ- IO U-| VONO NO
NO NO NO NO NO NO
fx.ONpdCOVONOOOONfldlt
OOO N>T)MH ONNVi^tl b
+ x) cooo cooo d r^ n tx. d fx.
fx. fx.00 OO On On* O O m ii d d
nononononono t^t^.t^.r-N.t-^r-
NO fx.00 p W CO
do xb rf co ii on
M NO n NO H VO
CO CO it ^- NO NO
tx.tx.tx.tx.tx.fx.
itNO fx.
fx io CO
O no O
NO NO fx.
fx.tx.fx,
NO O it On WOO
<- O tJ-00 Mfs
vo O -^-oo co t-x
On O O O -
VONO NO NO NO NO
t) tNMvep^
Nvo H VlO N+
d d CO CO rj- it
NO NO NO NO NO NO
On COOO cJtx.fi
OO CO t-, ci NO M
OO CO tx C? NO >*
tJ- o nonO no fx.
NO NO NO NO NO NO
NO O ^t ON COOO
vo b xfdo co tx.
NO O -xJ-OO io t-x
tx.OO OO 0O ON ON
NO NO NC NO NO NO
dfx.fl
N NO ii
d no fi
O O n
fx.fx.tx.
On b O i-i f) M
vo O tJ-OO d no
it VO VO VONO NO
vri vo o vo vo vo
J^ Tj- H ON tx. rj-
CO Tt" NO VONO fx.
O itoo d n o
t-x tx. r--oo oo o\
NO NO U-l NO VO VO
H OnNO ^J-m ON
oo do "on b i-i h
<t-<X> N t-x i-i no
ONONO O H H
VO VONO NO NO NO
NO CO (1 00 NO CO
C) CO TJ- it VONO
C\ o fx. m vo on
m d d CO CO CO
NO Nb Nb NO NO NO
O <*> JO
tx t-xdo
CO fx. -H
it -t NO
NO NO NO
O O O M H ()
V<-> O N '^- m M
NO O CO fx. fl -<t
Cn O O O m ii
tJ- vo vo u-i vo V)
d d CO CO CO *t"
NO d ONNO co b
oo d no on co r-x
m d N N co co
NO >0 NO NO NO NO
^J- ^}- VO VONO NO
N^HOO NO N
O ^-0O i-i vo On
tJ- *t rj- vo vo NO
VO NO NO VO VO VO
NO tx. tx tx.0O 00
ONNO CO O fx. rt
N NO O Ttfx.fl
no no r-x tx. txoo
vo vo vo vo VO NO
On On On
M do NO
vooo d
00 OO ON
o vo vn
tx. O M N O CO
NO O CONO O CO
NO O COvO O CO
T+ VT1 Ul VONO no
it tJ- ^ t it it
t~x O WNO co
NO CONO O CO
NO O CONO O CO
NO r- tx. t-.oo 00
<xh rt *t it it ^-
tx. p CO t-x p CO
NO O COVO O CO
NO O CONO O CO
00 On On On O O
xj- -xh Tt + no vo
fx o co fx. p co
NO O CONO O -O
NO O COVO O CO
O H - H N N
vo vo vo vo vo vo
fx. O CO
NO O CO
vo O co
d co co
VO NO vo
y-i o y~> O *tr On
M O M MflO
M VOOO fl it t"x
d d d CO CO CO
^t "=1- it it it <*
it On it On cooo
fx.dc b >i CO if
O MNO covo
^- ^- ^4- NO NO NO
4 ^ 4 "4- <* it
CO00 CO fx. C tx.
\b fx- On O cl CO
C\ rt vo On d vo
VONO VONO NN
-xj- if ^ ^ ^" i*
t-x fl NO fl NO
vovb 00 On fi c*
00 fl rf tx. w rt
fx-OO 0O 0O On ON
M NO
*x- VO fx.
fx o co
On O O
-t NO >0
rt O no d On vo
O O "on "on do do
t-x O d VOOO
On O O O O ii
co it it it it- rj-
11 oo it O tx. co
00 f^K t-NO NO
"3" t^ O CONO On
11 d d d d
t ^t ^ ** ^ <xt
ONNO flOO rhM
vo lo vo 4 if "+
cl VOOt M 4 t~>
co co co tJ" ^- ri~
^ "xh ^ ^ 4 4
fx. CO O NO N ON
co co co c* d m
O covo On cJ no
VO "" vo VONO VO
NTNt^^^Nt
NO fl fx.
fi m b
O0 M f
NO fx fx.
Tt-t it
d OKHO CO M
d O tsio't^M
H VO tx. O CONO
fx. r- txoo oo oo
Hf co co co co co co
On fx it d O OO
00 N0 *d- h b t**
CO H tJ-NO ti
OO ON On On O O
CO CO CO CO ^" ^
NO MM ON Jx. rf
no co - oo xb t}-
VOOO Ii CONO ON
O O M M M 11
"+-+"* I*" "xi- "+
H O 00 NO CO fl
C O fx. io CO fl
H VO fx. O CONO
cl M d co co co
Ntt^Nt^ +
cjn yx, rt
do no it
OO f rt
CO rt it
OO O f) + N C\
tx. b d r}-vb oo
tx. o d "4-no oo
On O O O O O
OJ CO CO CO CO CO
M CO vooo p d
in co io tx. b d
m MU1NO d
M M M C H
CO CO CO CO CO CO
** tx. On w con
^J-NO OO 11 CO NO
^}-no oo n co vo
c< c> d co co co
CO CO CO CO CO CO
jx. O H Tt fx. ON
"fx. b d "itNO do
fx. O d itND OO
CO rt "t n- it it
CO CO CO CO CO CO
fl CONO
M co o
n CO VO
vo vo vo
O vo o >o o no
O w- o no O o
O o O ^o O no
O no O o O o
O o O
N NOO OO ON ON
VO NO NO NO NO NO
O O m n d d
NNtsrs tsts
CO CO tJ- "fr vo vo
tx.tx-tx.tx.tx.tx.
NO NO fx. fx.OO oo
fx tx tx fx fx N
ON On O
fx. fx.00
B 3
3
. w
OQ O
H H
* e
0*
l|d
51
3
S
o
g.s
C/J
O
& s
o
H
H3
5
p
n o
^ 6
W 05
H !
-4
P
a
tJ- f^\ CO f 1-*
VtO (t m NO
O0 O rj-i) CO
II U-)0O t) N
M M II H C< tO
p h ^ r* p ! f^ r- r ^ r*
to*b Vj- in b do b ^b vb bsvb
VO l-l t>- CO O VO '(M o\ t^SO
to ^- <* ''NSO so t->oo 00 Os o
^ t
t^ O n
0\>OOm
o
r^
C*
invo tJ- O t"
VO l^
t>. O
CO VOVO
00 tf OO 00
oo hi coso
o
o
to
WM O H
i-c co O *o o
co co tJ- ^1- vr
vosO VO
co O s
t>.00
VO5j-U^O\t^t^ wt^t^OVOVO ON 3" CO n O 00 o ^n MN
^boooowvb ^foi^bi u% bbi) rt-i^N cobbnvb
w M t* *J- *> r^ On ^t-vo Cs t)5 C\MNm VO m VO w so
MMMM t) f) WM^l" ^Vil VOSO VO
t- ooo ?* to ^1- to p so p to v> m to o so O
cooo ij- to to In bs *n c* t* coso m oo r-^ t^ b
H C CO ^- >flNO\M MVO 00 O coso o
MMM M tl t) t) tO
rj* CO C< 00 CO I
O do oo bs coo
t-^ O ^J-oo to I
co ^-4 ^- *o
si
Q.2
oo m tI-O O +Wi)-0 o +
M flOO NO N 00 C* M ;* O
so vb no in b t-^sb vb r-. b
covi-it^Otlio t^OcovoO'
n n m H C* c* M commtJ-
On t* ^so F^ J""* y>ip Nt)
h !tisMM3 r) b\ V-xvb vb v do
n w tf O M^ vnv t-s
On ji t^oo com oooo h o to hi
O H to indo w 'sria codo to b\
t-. h ynoo p *
b ^-00 MO k
ON O 1 CO VOVO
J n Oi N ;
in Vj- ^4- V}-sb C
oo o r) "3-so a
h tl H rt
tJ- m to On O so io h O <O(0t
O usp yip y^
w m t ii ww
n m n c< to to
p y> p yn p vn
ifr Vj- in insb vb
P 1 P ! p y*
is. Kdo do on b\
O o o m o
b b m m r
o> o
ov *3- r^vo
WtS NVN O
rt
N
t^ o
o
>>-
PI
r)
O
voN>NM
VO
t^ * Os O
ON
M
o
>H t^VO
CN
VO
VC
O 00
o
VO
J-vO
co covo
*
./^
b
OO o vo vo
OnVO
r-^
^,
n
l^
vo vovo
OV HI
<+vO
Q
in
fs
VO
vr-
n
M
4
o
IS
c
Tj- vovO
t--
OO
O
<S
**
"i
VO 00
o
rt
*
vo
t-
ON O H
5
VO 00
o
r)
*vo
c4
cl
tf
r<
ts
8
c
n
co co
co
to
o
CO ** ^
*
^rl-
VO vo vo
vo
Ox On >
o
t\
r>
vov
<* O
<
VO
VO
N
l-* O
M
On On w O
t^
C<
vovo
^-8
*
oo
r<
oo oo
o
+
IS
rt
LO
_,
o
!-i
vn N
n
^J- o
OO
00
cl
00 OO o
^+
M
r
L
o
M
ro
OO VO
VO
co
N
O
o
8
rt
co
vovo
r.o
covo O
co
C--
VO
'O
O
On O
O M
r>
co
tJ- tov
t-^oo
CN
IS
CO
"+
O
vc
'jT.
ON O N
CO
tJ-VO
NOVO
H
^
N
M
c)
ct
Cl
r)
C4
Cl CO CO CO
to
IO
CO
ro
^Th
tJ-00
*4- * ^
co
r>
+OM
o
vo
co
^J- OWO
1--
l^ I s -* O t^ f^ On
o
+VO
d
o
H
CO
t-~ co
is
vo
o
OO
0* O
<+
M
o
_
to
M
Q
O
ro
ONVO >o 00
to
n
On
M
vo
M
00
^*- O c--
*
oc
vu
ro
o
oo
t^.vc
vo
^ tJ- ^-
^ Th
<J- VOVO
i- vono
r^
,-7\
IS
lONO
t-sOO
ON ON O
IN
n
4
VO vo
VO
f-OO
Ov O
N
(O
t~-
00
H
CO
vo
r^
M
r)
is
H H t)
Cl
CJ
to
CO
ro
ro
CO
o
o
On r^ cooo
M
co
-*
co
O vo
O
wmvnwO
>0
O
CO ^j- CO f<
oo
co r^
On O
OS
VC
vo
VOOO
co
CV
00 00
^J- O
r^
t-oo
_l
vo
ro
<S
r)
VO ON vo CO CO
*
oo
CO
O
O
O
c<
r^
M t~-
woo
^- o
r^
CO
O VO
co
O oo
VO
CO
ON
r--
vo rj- CO H
o
o
o
O
VO VO
t^ t-^oo i
On O
<S
M
co
r}- -^ vovo
lx
t^OO
CvO M
O
to
3- VOVO
t oo
- d c
M
N
c*
C4
r(
n
C<
<*
W
+ o
O
+
n oo
t- O
>.
OO
S
M
<frO
O
T}- n
+ O O
*
c oo
r-, O
r-
ONVO
i ^
vo
r^
14
VO
iS
o
o
o
tf VO
_l
r^.
VO
+
tJ-vO
ON rj- o
r^
VO VO
r-
O
vo
o
VO
n
a
vo o
VO
o
vo
o
VO
VC
r> OO
rj- O VO to O <0
CO
<)
r-.
vo
r)
o
T^- VO VO VOVO VO
t-. C^<
Ov On
o
IX
c*
M
CO
"3- 4- vovo VO
r^oo
oo
ON o
cl
n
O voo ^no> MrtcJMOoo ocr^Hr^O co vovo r-~ t--vo ^ c on *o o o
co - co Onvd tJ- rJ-'^-vor^OcooO'^-OOOVONO vor^.ONr1vo c^--^-wOOO
w covo oo w tJ- r-. O covo Ocovoo^-r^>-<vo C\ w N rt vo m voovoovoo
COCOCOCO^-rj- ^vovo VOVO VC NN t^OO 00 OOOnOnOO"-" m tt H I<1 W t)-
ooo vot^covo 0-ivovO0O\ cowrJ-McoO m noo wwoo 5^r , P N ?'Pj'
ifrO M +M rt "Nfl Nwbi ^l-c>b ON00 OO OOOo'ONweovoOOcJvoOvoO
vovo 00 ON O cJ CO vovo 00 O M CO vo t^oo O cl ^J-vo 00 "I ro vo
m, m w M r) fl M WM COCOCOCO^j-Ti- tj- ^ ^- "-o vrno
Oooooo pjoooojo pvopyopyo p^opvopyo p^py^pjo
tororl-Vj-vovovbvbKr^oooo OnOnOOm-i cJricocoThrJ- vo iovo ys NiN
MM MMMm MMMI-tMI-l tHMMOHO MOHlSNN Cl fl tt tt
CO
H
K
o
g
h
o
o
3
f^vb onv vb b
O i cl -+VO ON
oo O N ^-vo oo
VOVO VO V VO VO
VO p C *-" !>. O
oo b vo V}-vb co
M VOOO N VO ->
11 CO VOOO O CO
t^ t-- t~- C-.00 00
O OM (ip>0
CO t-* tJ- vo O OO
vo n r^ co o vo
vooo o covo oo
00 00 ON ON ON ON
r. c~. covo t^ ^h
b vb vb bwb t^
rj- m on r^vo vo
w tJ-VO ON C vo
o o o o -
3
r-t
yp o t-> p w
VO V) C< Vj- b OO
co vovo oo O >h
+ ^- + 'f >o <o
ON ON w O *
oo ts oo oo o ^J-
CO 11 00 VO VO CO
CO vovo 00 O c<
lO vo vo vovo VO
c* yovp ;* p ^"
<^ h vo i b w
cl w O O O O
tJ-VO OO O C* **
V v VO t^ C^ t^>
VO VO d t^- O M
vo H C rh O 00
O w c< CO vovo
VO OO O H r}-VO
t^ t^oo 00 0O O0
3
VO *$ vo ON J>- t-
b\ b cooo vb vo
r> vo on c* vo o
vo r-^oo O " co
CO CO CO ^* ^" ^"
HM t^ M VO vp
b co b b w vo
^- ON tJ- ON tJ- Ov
tJ- vo t^OO O i
"<*- **- *- * vo vo
ON ^J- co vo O 00
m b m *+ b n
vo m t-~ co O vo
CO vovo OO O 11
vo vo vo vovo VO
O tJ- c< co t^ tJ-
00 O vo H ii CO
co h, 0O vo tJ- N
co tovO OO O C<
VO VO VO vo t- f-
2
*. cooo c* co tj-
codo r}- co co vo
O O ii H co -d-
C CO CO CO CO CO
co O vo O co vo
OVVOf) H covb
iri N Ov m CO vo
VOVO 1^ ON O w
CO CO CO CO ^* ^"
vo co O vo O co
m oo r-^ r o >*
oo O covo O co
f* ^- vovo 0O ON
^ <*" Tf -* T*- <*
t}- CO d 00 CO t--
b oo do on cooo
t-^ O 'J-oo co r~.
O O CO rJ-VO f~.
vo vo vo vo vo vo
o
60 J) M <tO O
t^vb vb t^ b ^}-
t^ VO CO w O OO
d co <^- vo vo
O N c> p< N cJ
tJ- co ^- p O ^J-
bwb tj- V vo r-
vo VO 1$- CO HI
VO f-.0O O O n
C< C* C< CO CO
M N 00 tv O t^.
m vb c b b b
m o o o o o
M co <* vovo t-^
CO CO CO CO CO CO
0O H ^ O O
N vb M Nui +
O O ii i r< co
OO ON O ts CO
CO CO ^- *} ^ TJ-
3
ON C* 3-vp t-^ t>
M "+ K * vb
vo O vo m vo c*
rj- vo vovo vo t-.
vo vo co p p*
b\ J^vb vb vb oo
r~- co on vo * r->
t-~.oo OO ON O O
_ _ _ w M rJ
t^ C JO00 w w
b *+oo co b f-^
tJ- O vo co O vo
n N d CO ^J- ^
H c< N N d
Cl f* ONVO "+
vo "<4- "sh Vj-vb on
CO O N + MO0
VOVO vo t^oo oo
d d O ri ri H
ON w t^OO CO CO
VO C 00 vo CO W
S W1NO COVO
C^ C^ I>00 00 00
MMNp WH
ON00 00 0*0 00 ON
00 M t}- t^ O CO
00 ON ON ON O O
rj- w co on O vo
O *5}-vb b co
t^ O covo O co
O W M M <o N
VO H O lOMN
K c* t-v <S do rj-
VO O MNO +
C* CO CO CO t}- tJ-
2
1
O vo O vo O vo
oo oo b\ b\ b b
H C* C* CO CO
O vo O vo O vo
M M c* C* CO CO
CO CO CO CO CO CO
O vo O vo vo
^ '+ lo iovb vb
CO CO CO CO CO CO
O vo O vo O JO
ir^ i>-do do on on
CO CO CO CO CO CO
On p
o
!* r^s 5
ro t^ r> vn p
d
H
to O
O
ts
f
p
mSNW
NO
to Tj- ON O
On
m
O
el
to no
CN
vb vb
O 00
o
VO
^vb
co covo"
*
vo
b do
O VO NO
ONVO
r-
_
o
M
loiom tovo
to
ON
Tj-VO
o
CO
to
VO
VO
CJ
OO
to
ON NO
*
c
O
O
o
OO
"i
rf- to o
CO
VO
o
covo
o
co
NO
o
WtsO
4
N
VOOO
c
ve-
o
T-O0
d no
o
d
d
d CO
CO
co
"*-^-
vo
o
vovo NO
vo
t -
t>
t^OO i
OO
On On
o
o
O
d
Cl
cl
cl
cl
d
d
ON
to
c\
r* p
Is
d
vovo tJ- O
<*
NO
to d
N
O
ON vo ONOO
O
to.
cl
vovo
"*- p
t*-
do
d 00
oo b
^
d
d
VO w
o
M
to d
el
* b
OO
do
N OO
to o
'+
"el
d
IO
i.
o
m
CO
covo O
co
to
vo O
o
to
to
CO
O vo
CO
oo
NO
vo
VO
cl
O
O
o
o
oo
CO
000
o
d
vo
to O
el
VO
r*.
o
Cl
VO 00
O
covo
oo
J
to
O
covo
on d
to
oc
ON ON ON ON O
O
o
O
cl
el
N
N
<o
CO
CO
CO
-i-
+
VO to vo VONO
VO
tJ-00
^ + rs
co
d
r}" O 00
o
VO
CO
?*" P^^P
In
w
to 00
vo to on
VO
TJ-NO
d
o
d
tsMS
COVO
Vi
b
b
MN<0 +
vb
b vb
vovo
b
to CO
'-rj-vb
M
OO
do
b
+
M
b
M
o
ONOO
rovo
VO
NO NO VO vO
tooo
CN
el
tJ-NO
ON
-1-
to
O
tJ" to
VO
O
o
VO
Ti-
vo
to ON M
CO
to
t%
ON M
CO
VO
to
o
d
rj-NO 00
co
VOOO
o
el
VO to O
Cl
vo
t^
ro
t.
to
toOO 00
cc
00
00 On On On
ON O
O
O
O
o
e)
el
M
Cl
CO
to
CO
ON o
On to cooo
f
CO
^wOvO
p
co to to CO O
VO
p
CO
el
CO
el
00
CO
to On O
On
VO VO VOOO CO
CN
oo
oo
b V*-
O
t>
to do
_l
NO
CO
el
e)
vo
On vo
CO
CO
Vj-do
co b
O
b
d
to d
to co
OO
+ o
to CO
O vo
CO
o
OO
VO
CO
CN
r^
VO
t
co
el
O
O
O
o
o
On O
M
CO "ONO
oo
o
w CO vovo
00
o
CO
vo
t*
CO
O
e)
VO 0O
o
d
rt-vo
oc
o
VONO VO NO NO NO
VO
to to to to to
tsW OO 00
00
CO
CO
On On On On On
o
O
O
O
o
m
w
rj-
CO
."* P P
*
KM NO
t*
00
el
:*p
O
;*
co
rj- On O
j-t-
w
d oo
to O
to
U-
NO
On rl- b
to
NO NO
to o
vo
b
tovb no
t-^
O
ft
ON NO
i
CO
vo
(s.
H
vb
-,
b
o
b
VONO
00 o
CO
ONO
d
VO
to o
CONO
o
CO
NO
o
CO
el
VO
vo O
vo
o
VO
VONO
NO\0
d
co vovo
l>
00
o
M
r4- vo
NO OO
On O
el
co
vovo
CO
On
d
*- ^}- ^ Ti-
vo
WO to to to to vo
VON NO NO NO vo
NO VO NO
to
to
lo
to Co to
toOO 00
O
IO O
rj- to on
M
d
d M
O OO
yo d
to
CO
!>. O
CO vovo vo
toVO
rh cl
On yo
vo
to to
CO
ONNO
$
*Tt- Vj-
"to to
b
CO
00
"4- O 00 VO NO
NO
lo-
On N NO
H
to
+
H
O
o
b
NO
CO
00 NO
d
O oo vo
vo CO
o
On tsvo
vo
*
co C<
N
O
o
o
o
o
o
ON O
M d
CO
rj- vo vovo
toOO
ON o
O
cl
CO
-t
vovo
to 00
CN
o
cl
CO
*
VO
d
CO CO
CO CO
CO
CO
CO
CO CO
CO
CO
CO
-<*<+ ^ <+
*
^- ^ ^ rj- ^i-
vo VO VO o to X">
ooo
to to co
to
p
NO NO
p
CN
CO
.+
M
CO
O
00 00
to
on d
o
d
M
oo VO
"* CO d
d
'el
d CO
"vovb
On d
lr
On codo
codo
*
CO
VO
co d
b
o
b
b
oc
Ml
On co
l>
VO
ON CO
to
to
o
rt-OO
CO
r-.
o
vO
NO
O
VO
O
to O
vo O
vo
shio>o voNO
VO
h
hs
to 00
cc
ON
On O
O
O
1-
e>
M
CO
-+
-t-
to VOVO vo
i-
to
el
cl
N
M
d
N
el
c)
e<
cl
cl
d
d
ct
cl
d
d
o
tO O
to O
vo
p
to
^ O
VO
O
to
p
to O
vo
O
vo
O
vo O
vo
to O
to p
b
b
M
w d
d
CO
CO
S*
o
VO
vb
vb
K
t-^do
do
ON ON b
b
-
'-,
d
d
c^
CO
^- -*
"* rt- rj-
^r -+
*
-* "<*
^- T*-
<* <+ ^ * * r-
^J- t4- IO vo VO VO
to to vo to to to
cd
H
Pk
o
t)
ft
o
o
1
o
M
ri- t-*VO MNN
t-*.vb cwb vb b
O w cJ rj-vo ON
+00 H vo O *}-
c4 c4 co co rj- rj-
t) rt H
to O c* M I s - O
oo b *o +VO co
ii vo00 H VO M
on co r~* H vo m
rj- vo vovO VO I s *.
O d t) d
O N M (1 O ^
COVO *!j- vo b oo
vo w S co O VO
VO O ^1- ON TJ-OO
j>.oo oo oo On On
n c< m
t** I s * covo 1-*. tj-
b vb vb onvo !>.
r}- n On r**vo to
COOO NH N
O O ii ii N
CO CO CO CO CO CO
3
vo to c* t*- p m
to c* <S rh b 00
O " r co vovO
OO m ^j- t*-. O CO
VO NN t-*00 00
ON to Ox M O I s -
O0 fl ( M O '+
OO M covo O CO
vo O covo O co
OO On On On O O
M M M M tf tf
c tovo -t O jt
is (S VO M b M
t-^ M vo O vo O
vo O mtsO +
O H. H. w H C<
H rt M t)
ifld SO w
to is N Vj- O 00
to M C^. CO o vo
r-. m ri-oo r* >o
C) CO CO CO + +
O (4 () c) c< r)
3
r-(
VO ^-lOONNts
rj- b 00 00 M<b
O VO - t>. tJ- o
O d to r-. o co
** ** * to to
r}- CO vo O vb vo
(-*>+- m Onvo +
VO00 >-i covo ON
to vovo VO vo vo
ON r}- CO to O 0O
vb b *h "vj- o i>.
r* ii on*>c f*.vo
d inNO covo
I s *. f- f*0O oo oo
p ^J- rt co t-. ^h
co b b el vb co
VO NO vO vo vo t^-
ON d tOOO ii +
OO ON On On O O
3
t*N CO00 H CO tJ-
cooo kt" co co to
O O m n m^
N rt-vO MOM
H M H M fl t(
co p vo O CO to
ON o *J C* COVO
vo r**- On m co vo
tJ-vO 00 ih ro vo
*) N C< CO CO CO
to co p VO O CO
M 00 Nt>5 r}-
00 O covo O co
I s - O C* rj" I s - ON
CO -<* + + + +
TJ- CO C 00 CO t-.
O O0 0O On cooo
r-. O "^-oo co t--.
11 tJ-VO oo CO
vo vo vo vovo VO
3
M N * O O
C* VO M K vo "<*
O vo M VO f< 00
tJ- U-) t"-00 O m
00 00 00 00 ON ON
Vhvb ON 'rj- b IN
rj- O vo co O VO
CO VOVO oo O "-"
ON ON ON ON O O
W CO00 t>* O I s *.
vb vb Kb to b
co o r-- vo r O
co vovo M O t)
O O O O w m
OO CO HI rj- o O
K vb vb K b "**
S vo co ii o oo
co vo t-* On h n
m n n n r) r>
3
ON C* +VO t>*- |"
"w ^-'nmvo "c*
O O O -i i-r C4
VO C^OO ON O M
VO VO vo VOVO VO
vo to co O I s "* H
on r-*vb vb vb oo
f) m ^" vovo r~*.
co ^- vovo r-.
VO VO NO VO vo vo
t"*. * toOO O M
O +00 WON
ON O H. CO vovo
00 O n M co rj-
VO NNtsNN
JH ft M Ol IV J^
to tJ- tJ- Vj-vb ON
oo O d "4-vo oo
vo r^OO On O hi
S I s - I s - t^OO 00
S
ON M t>00 CO CO
O U CO VO00 M
O vo O vo O vo
00 OO ON ON o o
H C) WW
00 I s * C O CO hi
tJ-0 CO00 CO ON
11 vo c* I s - cooo
M 11 C> M CO CO
CO CO CO CO CO CO
to is ONVO to CO
& O vo ii r-^ co
tJ- vo vovo vo t-.
CO CO CO CO CO CO
VO HI O to CO tv.
cJ N V k CO Vj-
On vo hi t-* co On
t-OO ON ON O O
CO CO CO CO + rj-
a
1
P
4
O to O jo p o
vo vovb i nn
vo vo vo vo "O vo
O to p to p to
do oo on on b b
to to to toVO vo
O to o to o yo
m n. is d co co
vo vo vo vo vo VO
O to p to p jo
*+ *+ to vovb vb
vo vo vo vo vo vo
On O On * (" t-
- O m "isno on
to to to vovo c-
n ts N ts pj ts
to to rj- rj- to u-i
co to to to to to
to is ts jo p j*
no no b do b *o
On hi tJ-vO O to
C) OO COOO rj- on
no no ts tsoo oo
to to co to CO CO
hi is
^-NO
tS -
rh O
On O
CO tJ-
p Nh
co tONO rh
NO H. NO P
NO M NO CJ
O HI H. N
<r * * <*
c O jo t^ t>. to
>o b do b no no
00 to hi Onno tJ-
t^ to On t- O NO
CJ CO CO J- to to
* "1- >+ 4 ^ <*
Onno r-,
c - O
H 00 *
NO NO t->
On JO On m p Js
do c* do do b r}-
CO HI OQ NO t/-| CO
On o-vo O rJ-00
tJ- to toNO NO NO
d d cJ c* d c<
H JONO Tj- p tJ-
(t fl >OH O M
m O O O O
c no O -<*-oo M
ts r-^ oo oo oo on
t) O H
NO to
to d
O HI
NO O
On O
d to
t* t-s O M
cJ tJ- b do
N co w-inO
<i-oo C NO
O O w HI
to to co to
On JO On hi O t-s
do ci do do b W-
OO HI CONO <J CO
O o ON COOO C
c M n to to 4-
to co to to to CO
N JONO
Cl M to
r^ hi to
NO M U-
rj- to to
CO CO CO
Tj-OO tJ" tJ- t-N CO
p to r-s to It V*
M WO H ^-NO
is O tJ- Is O to
O HI M M C4 t<
Cl ^- O 00 O JO
no b do d b **
oo >i co ts o co
NO O CONO O CO
d CO CO CO -"^ ^J-
d d d d ,d d
to v)r onno ts m
M b M Ifl H b
ts m i^on + ov
NO O CONO O to
t "HO tONO NO
t) H H H
t^OO hi r- t~^ On
O CO OnnO no OO
^- On -4- O no c
t^ O t|-0 m to
NO f- t- C--O0 OC
H rl O HM
JO Tj-Np
CO b ON
Onno H
oo c< no
OO ON ON
M fl t)
OnO ONN pOO
In In tndo co on
O Ntl N COOO
VO 00 HI COVO OO
no no is is is is
d co ^- to O no
do do b Vj- b is
tJ- O NMOVO
hi r}-NO On d <*
00 00 00 00 On ON
O to
IsOO
to O
ts O
On O
vo io to O
HI NO CO cJ
OO NO CO hi
C* 1000 HI
O O O hi
c< rt
NO O CO rj- CO Cl
c> to On to to to
On t^ no t}- to d
cono On c> tooo
M M HI O O Cl
oo to r^
rj-do to
MOO
c< c<
jo to 3- p p ;*
On no "rt- ij- io Is
NO *0 *j- CO M Hi
<t*-NO M O t +
C4 M CJ CO CO CO
hi COOO NO J>
hi no c n b b
m o o o o o
no oo o d si-No
to CO rj- ^J- ri- rj-
oo co
d NO
O O
oo o
+ to
H *0 O
HI K lo tJ-
M N M M
N ^J-NO 00
to o to IO
tJ- co to O O <J-
VhNO !> + b n
<r tovo oo O
O N tj-nO On hi
NO NO NO NO NO r^
hi cooo
vbi is
CO to ts
CO to f-
ts (>> ts
O JO O rj- ts ON
to Is to OnnO V}-
Hl CONO 00 M t
CO rj- toNO OO ON
00 00 00 00 00 OO
HSMO00
rj- Vj- to ts b to
ts O CONO CO
O d co -rt-vo is
On On On On On On
jo d ts d no p
oo Vh b do no no
NO O ** tS HI to
OO O hi d r$- to
On o o o o o
CO JONO t*% t^VO
VO t^ On d NO hi
On CO r- c< no hi
*COO 0\M N +
O O O HI HI HI
* H OS
k Vj- H.
to O NO
no r^oo
vooo jo Is CO JO
no do hi V*-oo ci
to hi OO tJ- o is
(t M M + t
^- ^ "<* * ^- <*
O m no no O On
is d isdo b no
CO O NO CO O NO
tONO NO tsoo 00
tl- * ^- "sv- -* "*
CO HI
Vh d
co O
ON O
rjr HI to p
b "onoo do
ts. co O t
O m fl M
hi 00 00 rh COOO
do do "on hi to to
tJ- hi OO NO CO o
CO + rf VONO t^.
NHft
do V* o
NiOtl
t^OO ON
O o O *o O jo
is r^ do do os "on
NO NO NO NO NO NO
O *o p jo O jo
b b hi hi s n
is ts ts ts ts ts
O *o O o O *o
co to "rj- tJ- vo io
is is ts ts c^ t^
O o p o O JO
no no t^ r^oo oo
r^ t-^ t^ r^ r- t
O JO p
On On O
l^ tsOO
183
TABLE VIII.
GRADIENTS.
After laying down the gradients on a working section, we have to
calculate the rise or fall chain by chain ; on a line of only 10 miles in
length this involves about 800 calculations, each of four or five figures,
and as accuracy is imperative in this matter, the whole of the work has
to be carefully checked. All those who have had to go through this
operation, know the amount of labour it involves. It will be seen by a
glance at Table VIII. that the work is there done ready to hand, and
that by the use of it, the operation of checking the figures will be quite
unnecessary. Every professional man knows also, that although the
matter of calculating gradients for parliamentary sections is very simple,
very serious mistakes often occur; probably from so much of this work
being often done late in the night, when men are more than tired. The
writer will just mention one case, which occurred not very long since. On
an important line of about 20 miles in length, a clerical error of this
description was carried through the section, and the consequence was
that no further step was taken than to deposit the plans, for it was only
afterwards, unfortunately, that the error was discovered. Not only
about 2,000 in cash was lost in this matter, but the line of railway
also. By a very simple use of this Table, and the application of a
horizontal and a vertical scale, even the possibility of error is entirely
avoided.
E
1
N
S
O t~- l-l Tf- M lO
O M VD COOO rj-
O VO ^ tJ- t}- to
p OO OO ON rj-
O NO CO b 00 VO
NO to to ^ -3-
n On O d CO to
t^ O n CO CO t-.
to to to On co r}-
00 co On >o co 11
d O is vow in
T 1 - tJ- CO CO CO CO
d- N O On 00
4 tsO vo S On
to >. O N w O
O On p p t* ?t-
OvNO to co w On
C N S CJ s >-<
1 N 1 to
N n tovo n M
r}- NO0 N M t4-
NO On S VD w co
K io rj- c" ii ON
43
O
O
O
OO
BRERS'?
O tJ-oo O w on
O M3 CO d M O
O t^ to CO M ON
00 m co On O vo
d tooo r+- O
tJ-nO 1*- On O NO
HI CJ Tj-VO O to
tsinmM b 00
O O O O O ON
00 tO O N M Tj-
tO CO O NftN
r^ co <o O to
N N NtOCMfl
vb io co S O On
On on On On Onoo
CO IO CO M COOO
tovo t1- n covo
CO to w CO
c ft r~. o co
00 vb io V*- to c
00 00 00 00 00 00
43
O +M tSM W
O M m~ l)-tN
O co d l>. r-~ d
p tJ- on t*- p t^
O 00 vo to ^ d
00 r-> t^ r^ t^ t-.
VO t+- tovo vo 0O
OO to VOVO NO tO
M O 00 t^-VO to
>. t^vo vo VO VO
d 00 to On
(--oo 00 vo tj-
r*- to s w O On
vo VO NO NO VO to
to 00 O to d
,CO 11 S O0 to M
00 N NVD to tJ-
lO to to to to to
t-t
8
r-l
O t~- to00 O NO
O to m >o t~. CO
O 1 NO to COVO
p d t}- l^ O to
b Onoo i>- i>-vb
xj" CO to CO CO CO
CO r*. t-~ CO CO ON
TJ- t^ cJ 00 covo
m 00 00 ft COOO
t-^ tJ-oo to r-*
to io rj- CO CO d
CO CO CO CO to CO
no t4- d to
00 tJ- O ON O S
to t}- tovo O >o
tl Nfl N COOO
is "m i-i b b on
to CO to CO CO d
00 to rj- O NVD
w to w On t"- to
M 00 f-.NO N CO
t}- On to 11 NW
ONOO OO 00 Nts
c* d d H d d
43
1
O
O 0O OO ON IOOO
O "^ O t^00 M
O O covo m 00
O VO d 00 to M
b On OnOO 00 00
M ft + d NO rj-
NMH ONVO CO
>0 + tJ- rJ-VO ON
00 to c> ONVO CO
t- r-% t^vb no vb
CO S O VO to f)
ON S to tJ- O VO
C* ts f)0O to s
HH 00 VO CO M ON
vb to o io io Vf
B\NN VOOO 00
d to <*-oo tr--
ftoo 00 00 vo
>- TJ- c O 00 vp
"^ + + * to CO
1
8
O NO M NO f>- +
O M VO CO covo
O d + r-^ co
O ON00 t^. t^vp
t4" CO CO CO CO CO
tJ-oo cooo co r^
HI OO OO ON COOO
t^ rj-00 co r^
JO JO TJ- to to c<
CO CO CO CO CO CO
On tJ- O On to c
tO rj- lONO O "O
d N S N toco
M M O O ft
to to to to co d
H to m on Nvd
n 00 nvo t-~ co
<d- on to m t^ co
Onoo mm nn
H ct V c t Vl
O
B
a
1
n
O VO rJ-NO OO O
O ONOO C< NO
O N wrt tsO
NO to tONO t- O
VO CO H ON C-^VO
O O O On ON ON
t-NO U-l to O +
WM +H O S
co co co On to
cJ vo O rj- p to
+ H h ONOO vb
On On OnOO 00 OO
to to 00 O
M ON O O O NO
VO O O to O O
M 00 to N O 00
tO CO S it b 00
00 00 00 00 00 N
>> i>. m d cooo
NHOOVO COOO
rj- N rt VD CO d
VO to rj- to CO CO
i^vb io t}- co d
n n N r>. n N
i
CO
O d 00 ON CO O
O t- COVO CO
O ^J- to w CO O
d VO M J>- tO O
ON i>.vo rj- CO d
r-- r-~ N N C-- N
t~- tr^ On to O O
vo to 1000 O 0O
t tr~- t^ w no
VB + rt H p ft
b onoo i>.vb Vj-
t^NO NO NO VO vo
H M O 11 O "O
O N to CO t"-
t-^ to N d O
00000c ftp . M
co is i-i b b on
NO NO NO NO NO to
CO co vo vo
to 11 rl- O vo
MOVNNO rj"
d co to n p d
00 i>.vo io to V}-
to VO to to to vo
00
a
3
3
O OO d CO ON O
O ^-OVmOO O
O NO VO 1-1 O0 O
00 t-~ t->oo 00
OO *H b ON00 OO
to to to -4- rj- r*-
MOO tt NO N
t^. o N o 00
M M M tJ- r-.
M CO J-| t-. O d
Nvo >o "t}- "<^- co
^t- Ti- ^. ^ ^j. ^.
-1 O0 O rj- O O
O T+- to CO
00 to m O
to On d vo O t}-
fi m m b b 'on
+ * * ^J- -^ CO
to ft O m vo rj-
to O tJ- tovo tJ-
d no m 00 vo vo
OO d J>n M VO W
0000 n i>.vb vb
CO CO CO CO to CO
1
1
O -+vo VO + O
O d tJ- to * O
O 00 00 *4-
tJ-oo co on rj- p
vb "0 >o rj- "<J- *3-
d d d d d d
ON ONVO 00 O to
00 r--oo n on
to to IO N O 00
to M JsMOVO
to co In V< Vj it
d H H d
w tJ- O N O to
O f* tO N O M
ft to S O O O
d ONVO WON
m b b b b ft
c d d d d m
00 tJ- O to CO n
M O N >~ CO C*
n CO VO ft tooo
tJ- w 00 vnwp
ON ONOO 00 00 00
W n W M M M
no
1
S
to
O d tooo d O
O M d d d O
O ^OMArt O
d ONVO ^" j" p
co d d d d d
On On to rj- O tr-*
ONOO ONVO O *+-
t^ t-^ MX) O +
N>OMM O OO
M "h M M M O
O d 00 N
tovo d co O
ri- t-, l-l to to
vp rh to m 00
b b b b b on
ft d ooo vo hi
to vooo tovo d
O VO d ftvo tJ-
!>. to t*- c> M O
ft ft ft ft ft ft
8
O d tovo ** O
00 00 -4-
+OO to On t+- O
VO to VO t}- ^- TJ-
OnOO On CO O On
to -o to N O 0O
to w t^ CO O NO
CO CO c* cJ c w
O d tooo 11
ON to S O O O
c Onvo to r-~
H O O O O ft
d O N h to d
M tO IO ON tOOO
rj- 11 00 VO CO O
ft ftoo 00 00 00
d d d d d d
c) O H r) O O
e e< d c* d w
2
OHO covo O
O On t^- to to
O to r-^ r*- to
H p p jt y\ p
i-i K to On to d
m O O On On On
'(d ftO O n
M COOO CO tJ-
t^VO vo OO O (H
tO Cl O ON O M
00 to IS 00 NO CO
00 00 00 r- n t-^
vo m to ft
S ft O n O w
H M O VO O 1
tovo O TJ- O VO
b t^ to Is b i>s
rvvo vo vo vo to
M to M rJ-VO to
t+- to f- d vo N
ON rj- to COVO to
d O 00 t-vo no
io CO b 00 VO rj-
VO to to Ti- T+- tJ-
ct H d m
ouva
O "o yo p "o
\j~) iovb vb ir-- r-
S d d d d d d
O o p ;o JO
00 0*0 On On b b
N N d M to to
O to to to
h m r) f) m m
CO CO CO CO CO CO
p yo p to "o
tJ- tJ- io iovb vb
CO to CO CO CO CO
hi vo d m hi oo O tJ- o o m vo d O hi vo OnvO vo vo d vo co r> VO O O t$- d r.
OO VO covo t}- vo O mn VOOO t-< CO -q- ON t-^OO vO CO hi VO O CO rj- p* OO O hi vO hi
O VO VO ONVO VO O vo v 00 CO hi M mooooo m mM O h MN CO O O CO tJ> r--
hi vp p) 00 vo d P t^ vo CO d hi OpN ON00 K OS OnOhc<1>i}- vooop t$-oo +
to '<-, o ONOO ">- vb vb vo t1- co d m b O 00 i w
On On OnOO 0000 oooooooooooo oo oo oo t^ n n
O O & o o +
hi O N d co On
oo O +c< +
O O On On On On
h boo i>-vb vo
OO 00 tNtNh-tN
O hi t- m vo d
O <* O Onoo oo
o r- r^oo d oo
O O d tJ- VO
vo "<$ co d hi b
t-s t- t^ r^ t-~ r-.
rj- vooo r^ r^ o
t^ VO M VOVO t^.
VO VO OO H. NO CO
N <3NM ri-VO ON
onoo do i--vb vo
VO NO vo vo vo vo
H N SO\0 N
vovo On t^. O vo
HI HI N vo O vo
d jooo hi vooo
vo rj- CO CO d hi
VO VO VO vo VO vo
vo O vo COOO
tJ-VO CO n CO
d O O d On O
d vo p 00 vo vp
hi b O do "r^vb
vo vo vo vo vo vn
O covo O O On
rj- co ii OO d c<
VO CO CO TJ-OO CO
O covo On d vo
*+m'h N H b
vo vo vo vo vo vo
O t^ VOOO O 00
O t) O tl Onoo
O OO 00 ON hi vo
p co r^. hi vo o
b onoo oo r>. r-s
vo + tJ- tJ- T*- tJ-
VO O VOOO T$- CO
M tN + M T+-00
M t^ VO tJ- r|- vo
vo On + on tJ- On
vb vo vo "d- *d- co
-* + + ^> 4- +
t-^00 h MNm
vo O co voo r-~.
t^ HI VN vo CO
?* 9 j r* *-? r*
co co d d hi 1<
-+ + * + - +
co O r^ vooo
vo <4- vo M VO
HI O O "I VO CO
00 * p d r)r ex
bob onoo irx
T^- TJ- tJ* CO CO CO
0*000 +
t^VO VO T$- HI VO
d VO hi r^ + hi
O VO CO CNVO CO
t^VO VO vo vo vo
O + N tJ- vo t$-
O hi O vo On ON
O On On On O d
O vo co p 00 vo
VO V}- "<4- rj- co CO
d d d d C d
oo vo co on c* N
VOOO Nh fl ON
VOOO Nt< N
N ONtsTJ- H ON
m'h il rt d m
c* H c< N H d
tJ- *J-vO VO COVO
00 vovo d cooo
CO t^ VO CO hi
Iswifl O 00 vo
M ' H M b b
d d d d d d
d 00 r* C\
00 d O t-. O t^
OOOO covo
rj- d O ^p d 00
O O O Os OnOO
d d d hi hi hi
CO ON O vo d
co co f- t^ O OO
HI CO VOOO d vo
VO CO hi Onoo vo
co co co d is d
O Nh OOO N
O VO VOOO T$- t|-
O tJ- On rt- O VO
vo co hi p On t^
V* CI S "d HI HI
On covo O hi vo
t~ tJ- covo h4 On
d OnVO CO hi OO
VO rj- to cJ ^ On
HI M HI H. hi b
d rsfoto ts m
On d 00 vo vo On
vo vo co d hi
00 c^vo vo tJ- CO
b b b b b
w O O On tJ-
tJ- 1 O CO VO TJ*
O O O O HI CO
d hi p 00 vp *J-
b O O On ON OS
t^vo vo + hi VO
d vo h. t-~ rt- hi
O vo CO ONVO CO
t^vo VO vo vo vo
O hi O vo O On
O ON ON On m p|
O vo CO O 00 vo
VO + tJ- rj- CO CO
*0 0\N(I (* ON
VOOO H NH N
d On f~> "4- M ON
CO d d S d hi
00 vo t^ co co On
co t* vo CO M
t^ vo d O 00 vo
HI HJ HI HI O O
00 d O 00 hi 00
OOOO covo
tJ- N O vo d 00
O O O On Onoo
C) (< (< O ()
t) rt H f<
d fS d H d d
d d d d d d
d d d hi hi m
co O t^ t}- co rj-
hi O co -. p> vo
VO O C~- t^ ON CO
CO tJ- tJ- VOVO 00
hi b Onoo t^vb
l~ t^vo vo vo vo
Of) H +M)
O vo O tJ- t^. t^
O 00 ON hi vo hi
O hi covp 00 hi
vb vo rj- co (S d
vo vo vo vo vo VO
covo O 00 VO On
vo On O vovo hi
ONOO O H vo n
covo O covo O
hi O O OnOO 00
VO VO VO vo vo vo
co d hi on O On
H +O0O O tl
ON N ts N O CO
MN vo O tJ-
i-vb vb vo vo Vj-
vo vo w-> vo vo vo
vo co I s * d co
NMO Tl- ON HI
t^ CO O VO VO HI
00 COOO t- JxOO
CO CO d HI b ON
vo vo vo vo vo tJ>
lO O COVO covo
CO O VOOO ONVO
M O O ft3
VOOO hi tJ- f- hi
co d d hi b b
VO VO VO VO VO VO
O 00 00 00 00 d
ooo n o noo
O OO On hi rJ-00
VOOO H Nm V)
onoo oo i>- i-^vb
+ + <* tJ- ^4- tJ-
vo p* O co O VO
vo r~- O "4- O vo
rj- m O On O hi
O jo p jir O vo
vb VO VO *<J- t+- CO
+ + + + TJ- T*-
t$- vo r-- hi vo
co r-^ tJ- >!-
rt-OO d 00 vo d
p VO HI vo d 00
co Is d <t HI b
+ + + + + +
d O O vo On vo
00 covo 00
OO O d t^ vo
rr- p vp 00 p co
O b OnOO 00 !>.
t}- t1- co co to co
t-~. O oo c*n hi f.
vo O vo vovO t-
t- O COOO tJ- HI
vp d c^ d oo tJ-
vo VO t*- r}- CO CO
CO CO CO CO CO CO
O vo d d vo oo
O d VO t-^oo oo
O On On O d vo
O vo hi OO rj- O
CO IS Cl hi HI HI
CO CO CO CO CO CO
t~-00 O ON CO rj-
t^ t4- O N CO O
On rh O VO CO hi
VO CO O VO CO O
O O O On On On
co co co d d d
VO O hi t}- O tJ-
vo r- vo On O vo
ONOO 00 00 O M
vo co O t^ vo d
do do do i>. i>. K
d d d d d d
OO NO t}-vO c^
00 vo d rj- vo
COVO O OO 00 O
Onvo tJ-oo co ON
vb vb vb io vo tJ-
d d d d d d
00 O tJ-oo O On
tsooo n cooo
co O vo rj- d O
OO VO CO hi On is
tstsi-s t^-vb vb
O covo vo CO t}-
O vo t^- to t}- On
O on On O hi d
vo d o On r^ vo
vb vb vb vo vo vo
oo tJ- o vo t- d
oo d O hi vo vo
+ 1^.0 covo
CO hi 00 vo vo
vo vo vo V}- rj- "<1-
00 vovo l^ O d
tNM H rj- O 00
"4" ON tJ- On vo O
CO hi p 00 t^vp
r}- *tl- tJ- CO CO CO
t}- co d cooo
o\wo " d t)
vo co O t}- On vo
t}- co d Onvo t}-
eo to co d d d
hi O OO t-^vo vo
ONOO VO vo *JT CO
OO 00 00 00 00 00
O
O HMOO m N
O oo oo hi r-. <*
VO tj- t}- VO VOVO
t) m o p^p r^
oo do do i>. t^ r-
t}- d O r^ covo
rj-vo O vo co d
r-^oo hi co vo
vo vo vo xj- co d
t>. t^ i> i>< i>- t^
OnOO CO ri- O hi
covo M h IflTj"
NCNH Ti-N O
hi O O OnOO OO
K t^ t-^vb vb vb
t}-vO O O VO VO
covo r- tJ- d
l vp vp r}- CO d
vb vo vo vb vb vo
OO O oo co co on
co O vo tJ- d O
OO vo co hi On t^
f- f* r~ r^vo vo
O vo OO tJ- tJ- on
O On On O m d
vo d O On r^ vo
VO VO VO vo vo vo
On d O "-, t^. vo
rj- t^ O covo O
CO HI 00 vo VO
vo vo vo tJ- + tJ-
OO tJ- CO VO O 00
rj- On tJ- On vo O
CO hi 00 r~~vo
rj- TJ- rj- CO CO CO
On co O hi pj co
VO CO O r}- ON vo
t}- co d ONVO ri-
co co co p) d d
r-. O + Onvo On
d O r- d <* O
O O ** t}-oo rx
t--oo On hi covo
d O OO tNUlM
T$- rj- CO CO CO CO
O tJ- vo On co co
O O O OO rt- vo
O t^oo rt h w
O MIS t^ Ct
H b do i> vo rj-
WM t) fl rt
NM O t^ CO ON
O On hi co co
On t^. O vo CO rj-
l- co vo CO O
d m b do t^vb
d d d hi m hi
VO tJ- co On O ON
d 00 O 00 O vo
OO r(- rj- vn O VO
r^ vo co hi 00
+ Mt) in O OO
H. W HI HI HI O
m vo O t}- vovo*
vovo O ONOO d
vovo O d co d
t -vo vo vo vovo
ir-^vo vo co ON
O O O O O ON
O vo O vo vo
t-. t^OO OO On On
CO CO CO CO CO CO
O vo O vo O vo
b b m I* ( m
+ * + t1- + t4-
O vo vo O vo
co co r}- r- io vo
+ Tl" Tj- + Tj- tJ-
O vo O vo O vo
vb vb i^ r--oo do
rt- rt- rt- rj- rj- ^
O vo O O O O
on'on'o '<-> d co
TT tJ- vo vo vo vo
! -+o
w c
rJ
t}-oo vo
N00 M
n
VO
_
vo
vo
O
M
oo
vo vO O covo
O
i
"* NOO
VO
vovo
VO
covo
c*
n
to
CO
n
t"
<d- rj- C
oo
N rt
N
r-
vo On
VO
t-. l-l
On O
CO
a
o
H
r^
vo
CO
vo On vo co
r^
<*-
O N **
11
On N
vo
vo vo r}-
VO VO
vo
r>-oo
CN
M
CO
vo
r>- O covo
ON
3
rh *
l-l
OM N
NO
vo tJ-
CO
r
_
ON00
fs
r^vo
.o
^- ^}- CO c<
HI
n r>. n nvo vo
VO VO NO
vo vo vo
vo
vo
<~r
VO
VO
VO
VO
vo vo vo
1/1
VO tJ- m VO
CO VO
o
CO M
O OO
vo
VO
CO
M
VO
h
On vo O
r^
o
4$
vo vo
<<*- N
C)
O NO\w
CO
tj-vo
Noo
r^
CO
143
vo O
CO
vo -sj-
r>
o
VO
vo
r^-
<o
vo
V.O
ON rt- O
r-.vo
o
vo vo vovo
Noo
o
W COVO
oo
11
"* N
N
rJ-00
M
VO
O vo O
ej- ON
vo t*-
co
N
n o
o
ON 00
t^vo vo
VO
^ *
CO
H
rJ
i_
M O O
ONOO
CO
VO VO VO VO VO VO
o * ^- <* 'J- <*
'd- "* <+ -* -+ -*
^" ^* ^J- <*-
CO
3
O VO
N
n
On CO
CO
On ii
Q
r5
NOO
VO
"+ o
OO
co O r~>00
o
$
N CO
*
tx
d oo
covo oo vo
ON
CO
o
VO
CN
1-^
r--. t^-vo
vo
^4-
covo
M
COOO VO
tJ- VOVO
O
vo
M
t>.vO
r>
ON N vo
l^-
o
O MNO
tJ-00
CO
N N
N
d
N
COOO
^" ON VO
"i
t^
co O vo
CO
On
NVO
vn
VO
^- CO
co rt c*
_
_
O
r>
ONOO OO 00
t^. i-^ r-vo vo
vo
CM
CO CO
CO
co
CO CO
CO
CO CO
ro
CO
CO
CO c*
H
C<
c4
N
d
d c<
d
IS
vooo
_
On >* d
N r*- O
O
vo
VO
rj- onoo
rsi
vo
ONVO vo CO
ON
VH
OO hi
N
co
M ON
vo
CO ON CO
vo
*
vo vo N
vo
*
oo
>0 CO CO t^.
t^
HI OO
VO rj-
VO
ON c*
t
r)
oo
vo rt
Onoo oo
oo
ON 11 CO VOOO
o
VO l-l
00
VO C ON
vo
CO 11
OO
VO
co
M
On r-
^"
rJ
oo
vo vo co
M
On
r-l
00 OO
to
N NVO
VO VO vo
vo
vo vo
VO
t}- rj- ** r}- r*-
CO
CO CO CO
CO
C<
co on vo on nvo
to
t^ vo vo VO
CO
h
N On t$- On
co
^1-
COOO t-^
On vo
1
ON O OO
O rj-
covo tJ-VO
rl
N
VO
p*
cs
VO
rt
N
rj-
ONVO VO
SO
CO
vo ON N
n
N r>.
CO
ONVO
CO
ON
r^vo
vo
<* ^
rj- -^1- vovo
t^ On
VO
d O
ON NVO tJ-
CO
M O
Onoo vo
VO
-t
CO
C<
w
O
ONOO t-^VO
vo rj-
ON ON00 00 OO 00
00 00 oo
r*.
t- tN.
t
l
N N
r-- r^
VO VO vo VO VO VO
ON N
r*.
z
hi On
N CO ON CO VO VO
M
vovo
covo
vo
On On t}- COOO
t^
i
M OO
VO
*- ^t-
vo
On N
N
H
M
VO
d
Onoo
X)
00
ON w CO VOOO
vo w 0O
VO
ON
vo
CO 11
SO VO
CO
ON N
?
CJ
OO vo vo CO
ON
E
00 OO
t- fv.
nvo
VO VO vo
VO
vo vo
VO
tH .-*
^ ?r
CO
CO CO CO
co
N
On o Onoo c* oo
m O >onvo
OO O + w M *
00 O HI CO vo t^
oo oo r^vb vo rh
-+ * tJ- rJ- J- rl-
O t-vVO NO *
O oo O <* O vo
O 1--00 O vo hi
O M vo On c* vo
OOvo cow N*NO0O N
O cocom tJ-co VO rj-voOVO vo
OOOVOmOO vovOt^.O COOO
O tJ-OO Nr>.Hi vonivoNt^.N
vo O vo co co vo
vo O co N hi vo
O O vovo vo vo
o on vooo r~- hi
O vo co c* covo
O * On t$- On rj-
W tl M M b b
CO CO CO CO CO CO
O rj-vo NSM
O N r-^ vo vo c--
O Nw Onoo oo
O vo hi VO M 00
b On onoo oo t.
co N H M N
O COOO O vo CO
O covo O c* >*
O c< vo O vo m
VO HI NtJ-O N
K f>.vb vb vb >o
N d N c CJ H
"4" O <* ONVO ON
<d- O m o-OO M
"* O N vo vo r-.
rj* O vo m nm
rJ- '<+ co co p k
O co co t^- o N
O ON O P vo N
O co ON vo N O
pvO fl ONVO CO
m m b b b
M r. H M tl H
O ONOO tJ-mVO C0p00 0r}-ON
O +h O Nm M H N O W fl
O M hi CO vo ON COOO CO O VO rj-
p h- ^ H OO V) COOOOVOCOhi
b on on onoo oo oooo Ntsp-ts
c* O N O co t^-
rJ O vo On Onvo
d O oo N r-.oo
d O t> vo co hi
O N r d vo ON
O ON vovo C* CO
O M +NM Ifl
O oo vo rj- co hi
li b b 6 b b
OVOONHVOOO Nh 0\0 tl *
O N vo voOO vo NO hi OO O tJ- hi
OvoOVOdON ) ^m ooo N
p oo n vo + s r"P P* ? ^P Y^
O On On On On On On OnOO 00 00 oo
hi O ON vo t-. p
HI O pj ON CN CO
HI O ONOO OO ON
m poo r-^vo vo
vb vb vo vo vo vo
O 00 VO HI CO ON
O ON c* OO vo VO
O O d co vo l-^
VO ^f CO d HI O
vo vo vo vo vo vo
O t> ONVO COON MIOVOO H N
OOOddrht^. coOONOrJvo
O d VOOO hi t^ 00 N vo O tJ-OO
O ONOO N Nvo vo vo Ti- tJ- co N
VO ^- ^- ^- ^ ^ ^- V*- '-* Vj- "<* **
d O vo ON Onvo O On vovo CO rj- O l~-vO vo Onvo N hi On O + hi
d O OO N f-00 O M rl-NM >o OvoOVOcJONVOrJ-HiOOOt~.
CJOt^-vocOHi OOOVOtJ-COhi OOO Nui^-cl M O ONOO vo vo
rl rt m m h m hi p OOOO OOnOnOnOnOn On Onoo 00 oo oo
m m m m m m mmmmmhi li b b b b b b b b b b b
00 O C~- vo vo vo
NO VO HI Tj- HI
NO0O CO CO ON
N O d vo O <*-
O ^ CO VO o oo
o n hi on o o
O vovo O O co
O vo hi OO vo pj
O O O d vo N cooo co O tJ-
OvONdOOVO coOnhjOcoh
O O +t<0OvO cocJvoONN
O 0O VO vo ^ CO COCOCOTJ-rJ-VO
O 00 NVO VO '+ CON M b ONOO
00Nt-->-NN t-Nt-. NVO VO
g
O
o o
O
o
o
o
O
o
o
O
o
O
O O
O
O
o
o
o
O O O
O
oixya
<>
t}- vovo
N0O
ON
o
M
n
CO
-4- vo
VO
soo
On O
M
M
co
rl- vovo
r-s
a
o
vo
vo vo
VO
o
vo
VO
vo vo
vo vo
vo
VO VO vo VO
N
N
h
N
N N N
n
o
on o
tN
OO
O
OO vo
O
vo On
I
O
d
M
r)
CO
vo
_
M
O
o
t>-
T
N
rl
In
rt"
11
VO
M
<>
<o
'O
vo
r^vo
* o
CO
* ri-
o
CO
'/)
o
>o
4
o
t^
io
()
VO
ro
o
o
n
ro
N
VO
O
to
On rl- On
on
*> O
1/
vo
c oo
rt- O vo
rl M
-f
o
r>.
f>
M
(1
ONOO
OO
IN
r-^vo
vo
'O
$
*
CO
rl
_
M
%
OV^ 5
WM^Vl^-^^.
rj- r- rj- r}- rj-
*
rj- r*- r}- rj- rf
+
*t
*
*
CO
CO
CO
CO
CO
C-
CO
"4- 1--. O
rJ-VO
*1
N
rl
oo
oo
<*
CO
O vo
00
as
O
8
M
rl
o
h-. n
* o
-1-
O
r}- o
vo
*
"<* rj-
N
VO
cr
In
r^oo
rf-00
l^
rl
CO
o
CO
SO
VO
'1
?.
vo
r^
+
oo
'<r
On t^
o
M
covo
o
>r
in
vo r*
n
o
"to\wo
>o
*
t^ d
OO
r*- O
N
CO
OSVO
CM
ON U-)
H
ONVO
ro
o
r-
-t-
oo
"
r^
o
oo
(>.
r^
r-vo vo
VO
>n
rl- rj-
Ti-
CO
co d
rl
n
IH
_i
_,
O
o
0\
W
ro
CO
CO
co
CO
ro CO
CO
CO
CO
CO
CO
CO
CO
CO
CO
CO
CO
rl
H
n
OO vo
cl d
O VO
rt
+
O
r- d
*
,,"
+
M
VO
CO
On
rt
rh rJ-VO VO
covo
rl
O
O
O
tr>
o
o vo
o
O vo
On On
o
oo
t~-vo
d 00
SO
vovo
N
o
rl
O
*
O
0>
ON On
O
N
VOOO
d
IN
in
CO
O
r-.
vo
ro
q
O
o
o
n
ro
tJ-vo
VO
CO
O vo
co
OO
K)
d
On In r$-
rt
ONOH
O
OO
vo
+
rl
O oo
vo
Th Pi
O OO
vO
vo
vo vo r}- r}- rl-
1*1
ro
ro
d
rl
rl
rl
_,
h
M
M
i-i
O
o
o
OS
rl
d
Cl
d
d
d
rt
rt
d
rt
rt
rt
rt
rt
d
N
M
M
d
cl
M
rl
w
H
~
~
m
d
o
t
M
d
In
(N
_,
d
VO
vo
hi
o
rl
r--
ro
ro
IN
CO
N
o
O oo
O 00
o
vo
vooo
*
<+
vo
tj- rooo
p-i
ON On cl 0O VO
vo
ON &
n
cooo
"O
CO
+
vo
d
o
rl- On r}-
O
vo
rl
OnvO
CO
VO
v/~i
CO
rl
o
o
Q
Q
O
O
rl
ro
<*
M
VO
vo
co
N
O
On Invo
*
CO
d
hi
ONOO
C^VO
vo
^
ro
rl
o
On
OO
r-~vo
/-
*
CO
rt
rl
d d
O oo
rt
d
o
o
o
O
O
O
O
O
o
o
