worth something like 35s. a ton. I can-
not help thinking that may be all very
true up to a certain point, but at the
same time it is very evident that the
sewage varies in different towns enor-
mously, and that it would be difficult to
get a cement of a constant character;
and it is a very important thing, so far I
as I understand engineering work, that I
cement should be of a very constant
character.
Then, thirdly, there is the destructor,
and, to my mind, the destructor has
reached its highest state of perfection at
Ealing, from the great thought that Mr.
Jones, the surveyor of Ealing, has given
to it. His sludge there is mixed with
house refuse and burnt Mr. Jones's
view is that every town produces suffi-
cient house refuse to bum the sludge.
One has to notice the differences of
destructors. I have seen a good many
myself, and I should say the differences
are mainly two ; first, a certain escape of
offensive vapors from the shaft, and I
think those offensive vapors are mainly
due to partial burning — the destructive
distillation, as a matter of fact, of the
materials, instead of their complete
destruction ; secondly, the escape of fine
sand and such like from the shaft at
certain stages of the operation. I have
seen those two nuisances very well
marked, and I had occasion to advise on
them on more than one occasion. I can-
not help thinking myself that in Jones's
destructor, where he places a muffle
furnace or ** fume destroyer," as he calls
it, between the furnace and the main
shaft, he has, in a great measure, met
those two difficulties. I think, myself,
that Jones's destructor is a very credit-
able thing. .
I feel rather a difficulty in saying a
word on the subject of standards, and
yet I do not know that one can altogether
omit it. I can only say that Professor
Dewar and myself found out the ab-
surdity of comparing a sample of raw
sewage with a sample of effluent. People
go to a sewage works, and take a sample
of sewage and a sample of effluent and
compare them, which is of course mani-
festly nonsense. Tou can only compare
them by taking, say, half-hourly samples
of effluent and half-hourly samples of
sewage, mixing them all together and
comparing the average. You cannot
compare a sample of sewage with a
sample of effluent, for this reason. Say
they are both taken at twelve o'clook.
The twelve o'clock sewage, say, is strong
sewage, but the twelve o'clock effluent
probably is the effluent of the six o'clock
sewage, when it is at the weakest ; so that
you are comparing the effluent of a very
weak sewage with very strong sewage,
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THE TBEATMEJN^T OF SEWAGE.
15
or it may be the opposite. You cannot
compare one sample with one sample
taken at the same time, or compare them
in any way except by taking ayerages.
Of course, it is very important in talang
samples by which you are to come to
any conclusion that you should know the
weather, the average flow, and so forth.
Now one word on what may be called a
practical standard. We always hear
about standards, and they are not very
satisfactory. We had the Rivers Puri-
fication Bill, which I am very glad to say
the House of Ck)mmons in its wisdom
turned out. That was a very great point,
because it was a very bad bill, altogether
bad both in principle and in tiieory. We
want a bill, however, to keep sewage out
of rivers, and we ought to have it. We
must leave the manufacturers alone for
the present.' It is quite hard enough
in our days for people to get a living,
and we must not be interfering too much
with trade. I do not mean to say that
will not come, I think it will; but we
cannot do everything at once. But I
will tell you what we can do. We know
sufficient about sewage now; the Local
Government Board has taught us a good
deal, doubtless. At any rate, we do
know enough about it to know that we
can purify it, or clarify it, up to a certain
point And I think we ought to keep
our sewage out of our rivers, and it is
the duty of the local authority to do it.
But we cannot be having elaborate
chemical tests. Let us have some com-
mon sense standard. Something of this
sort I may throw out as a suggestion.
First, that your effluent shall be clear
and colorless when seen in a white pint
cylindrical bottle. Secondly, that it
should not be alkaline to test paper —
you can get that, and an alkaline effluent
is not a good effluent Thirdly, that on
the addition of a grain of sulphate of
alumina, or say, one grain of alum, dis-
solved in 100 grains of water, added to
the pint bottle, it shall not produce
appreciable turbidity after standing thirty
minutes — ^you can get that Fourthly,
that if you take that white cylindrical
bottle half filled with sewage, and shake
it up, it shall not leave foam or much
froth after standing ten minutes. These
are practical tests.
I do hope the day is not so far off
when we shall have some means by which
we can persuade local authorities to
purify and deal with their sewage. But
I say again that if we are to do it, we
must not act as the creators of a hobby,
we must be prepared to sink the hobby ;
we must not go as violent irrigationists,
because it is clear that that v^ not do ;
we must not go as violent precipita-
tionists, it is clear that will not do. We
must be prepared to consider what is
the best method to treat the sewage of
the place for which we are called upon to
advise.
I cannot help feeling strongly on one
other subject I know we cannot alter
it ; we have this water-carried sewage to
deal with; but one cannot help asking
the question, if one were called upon to
advise for another London, or in another
planet, should we advise the water-
carriage system? I have thought this
subject over very earnestly lately. The
advocates of the water-closet system
urge that water, as a vehicle to carry the
refuse, commends itself to us on the
groimd of cleanliness and cheapness.
They would compare, and do compare,
the natural power of gravitation, such
as is made use of by the water-closets,
with an organization of men and carts such
as is required, for instance,' by the midden
system. I confess the advantages at
first sight are all on one side, but I must
say there are some facts which point in
the opposite direction. Diluting with
water is the very best known method of
rendering whatever is valuable in sewage
practically worthless, and sometimes an
ungovernable nuisance. The excreta of
animals are no doubt intended for the
food of plants, and, again, for us through
their intervention. Of course, do what
we like, do what we please, nature will
assert herself and assert her plans,
although it is certain we do pur very
best to embarass nature by meddlesome-
ness, but the nutritive food of the plant
we drown with water, and then our
ingenui^r fails to deal vnth the filthy
mixture. We cannot utilise it unless we
abandon all sanitary precautions. It
pollutes our air; it may render our
ground a simple stinking morass, and
defile our watercourses. Let me put it
to you; here in London 80 gallons of
water per head is brought horn pure
sources, let me say, at great cost, with
vast engineering skilly filtered, and per-
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18
VAN NOSTRAND'B £KGIN££BING magazhstk
haps refiltered with extraordinary care,
stored with sorupuloos anxiety, analysed
by one chemist after another, and what
fort About one-ninetieth part of the
water is used for drinking purposes, and
a large quantify is destined to be the
mere diluent of our sewage, to perplex
us by its uselessness, and to steal our
healUi with the perpetual nuisance it
creates.
EXAMINATION AND TESTING OF BERLIN WATER SUPPLY.
Ftom Abetraota of the Institatlon of CtwU. Boflrtneen.
The testings of the Berlin water dur-
ing the period from July 1, 1884, to
April 1, 1885, haye been regularly carried
out, in accordance with the plan agreed
upon between the Director of the Mu-
nicipal Waterworks, Mr. Oill, M. Inst
C. £., and the civic authorities. The
chemical analysis was arranged as fol-
lows:
1. Estimation of the residue from the
evaporation of 200 cubic centimetres of
water, dried for fiye hours at 110^ Centi-
grade.
2. Estimation of the yolatile portion
of the residue by calcination, moistening
the ash with carbonate of ammonia and
again ftalmning it at a low temperature.
3. Estimation of the chlorides by ti-
tration of 200 cubic centimetres with ^
normal silver solution, according to
Mohr*s system. >
4. Estimation of the ammonia (after
separation of the lime, magnesia, iron,
&c, by means of soda-lye and carbonate
of soda) by calorimetric tests of the
liquid decanted from the residue, with
Nessler's solution.
5. Estimation of the lime by tatraiion of
the amount of oxalic acid necessary for
the precipitation of the lime, by means
of chameleon solution, on Mohr*s sys-
tem.
6. Estimation of the oxidizabihty in a
solution of sulphuric acid, on boiling for
ten minutes, on Kubel*s system.
The inve^igations for nitro-organisms
were both microscopical, and by means
of pure cultivation on a solid medium
(10 per cent meat juioe>pepton-gelatine).
Few variatioais in the chemical compo-
sition of the water of the Sjunee and that
of Lake Tegel were obserred, but the
contents in micro-organisims ftuctuated
considen^ly. The Spree wattf is richer
in chlorides and in substances capable of
being reduced in an add solution by the
chameleon tests, also in fertile germs of
micro-organisms. An appreciable amount
of ammonia could only be found in the
Spree water, and this reached on one oc-
casion 0.23 milligram per litre. The
water of Lake Tegel only showed on
one day a measurable quantity of am-
monia, yiz. : 0.04 milligram per litre.
The efficacy of the sand filters is next
examined. On all occasions the contents
in organic matter, chlorides, the oxidisa-
bihty and micro-organisms were reduced
by filtration, but the dissolved lime was
slightly increased. The tests on March
2d showed that the filtration had only
reduced the fertile germs in each cubic
centimetre from 963 to 468, whereas in
the previous week the reduction had
been from 210 to 68, and in the previous
fortnight from 250 to 28. This led to
an exchange of correspondence with the
Engineer, and to the discovery that,
owing to the formation of a thick sheet
of ice over the uncovered filter- Ixasin, it
had been impossible to cleanse it.
Daily examinations were made of the
water from each of the filter-beds, to
test their action with respect to yield,
endurance, rapidity of yield under press-
ure, and influence of temperature, and
these tests were made in comparison
with the unfiltered water. Comparative
investigations were also made respecting
the efficacy of open and covered filter-
beds, and the ftict was estabHshed that
the open filter>bed removes considerably
more fertile genus than the covered one.
Precauti<His were taken to test moet
carefully for the erfnothrix pofyspora,
both in the freshly-collected sampdee and
in those which had stood for twenty-four
hours, but on no occasion was the pre-
sence of this conferva detected by micro-
scopic examination of the water from the
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LOGARITHMIC AND RIBBED OBLIQUE AROHEB.
17
Spree. It was, however, often present
in the water of Lake Tegel. The inves-
tigations generally prove that the water-
supply is rendered more or less impure
after leaving the source, either by the
distribution through the pipes or by
storage in the high-pressure reservoir at
Charlottenberg. Nothing, has, however,
transpired to indicate, either chemically
or microscopically, the presence of in-
jurious agents of any description in
the water of Berlin.
LOGARITHMIC AND RIBBED OBLIQUE ARCHES.^
Bt JOHN L. CfULLEY.
Written for Vajv NoaTRA]n>*8 BHeniXKRiKa Magaxiks.
Chaptsb VIl.
LOOABITHMIO METHOD.
69. This method of constructing ob-
lique arches is so-called because naperian
lorarithms are used in their calculations.
The soffit coursing joints by this meth-
od are always normal to the plane of the
arch face, wherever they come in contact
with it, and hence it is these coursing
joints are normal to an^ plane parallel
with the arch faces at their points of con-
tact in the parallel plane. The soffit
heading joints are elliptical curves in
planes parallel with the arch faces, and
are, therefore, normal to the coursing
joints of the soffit at their intersections.
The heading and coursing joints of the
soffit being thus normal to one another,
they will also be normal to one another
in the developed soffit
70. Fig. 86 shows the plan and devel-
opment of the soffit of a semi-circular
oblique arch, whose elevation and right
section is shown at ABC and HI J.
The curve N X'K normal to the curve
S X'G at its middle joint X' is the de
veloped soffit coursing joint through that
point. Through the middle point B of
the spring line S O, draw the dotted line
B P partdlel to the curved ends of the
soffit SG and OQ. Divide BP thus
drawn in to any convenient number of
parts of equal length (Fig. 37) and
through the point of division, draw their
coursing Joints parallel to the curve
N X'B The widths of the courses are
thus determined on the middle curve
BP, in order to show the same order of
arraDgement and of size of the several
courses in the arch faces, but their dimen-
sions may be fixed on any other parallel
curve to B P. It will, however, be found
most convenient to take the middle curve
BP, and also to make the courses of one
width on this curve.
71. Having thus determined the posi-
tion of the coursing joints in develop-
ment, the heading joints are drawn
in the several courses at desired or
convenient points, and their elliptical
* Copyrii^t, 1888, by John L. Galley.
Vol. £XXV.— No. 1—2
curves are drawn parallel to B P, or to
the curves of the developed arch ends.
It should be borne in mind that the
heading and coursing joints in the devel-
opment are drawn paitdlel with B P and
with N X^'B on lines parallel to the spring
lines S O and G Q. Thus, if we cut out
a cardboard templet, one of whose edges
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18
VAN NOSTRAND'S ENGINEERING MAGAZINE.
will correspond with the curve NX'K
and its left-hand ^ edge is straight and
parallel to S O, and through the points
of division in RP we draw the several
coursing joints shown in Fig. 87, this
templet should be moved so that its left
hand straight edge shall always be par-
allel to the spring line S O. In like man-
ner the heading joints may be drawn with
BHg. 37
a templet of curvature S X'G, but in mov-
ing it over the development S O Q G, its
extremities S and G should always move
on the spring lines S O and G Q, whilst
the curved face of the templet moves
parallel to the end curves S G and O Q.
These precautions should always be ob-
served, otherwise the curved lines drawn
would not be correct or in accordance
with the requirement of article 69.
72 The equation of the normal curve
N XTK to S X'G at its middle point X'
will now be determined.
In article 41 will be found the expres-
sion
y=r sin. a tang. 6 (32)
Now since x is dependent upon a for
its value this equation contains a ratio of
a; to y, and is therefore an equation of
the end curve S X'G, and might be used
for it in place of equation (17). Let b be
the complement of a, and we have
y=r COS. b tang. 6 (33)
Again a is usually expressed as so
many degrees, or as W. 180°. It is in
fact the length of an arc of n 180° to
radius unity. Thus, the expression tang.
36° means the tangent to an arc of 36°
to radius unity, but not the tangent of
36°. a therefore equals n ;r,
but x=n7rr,
but a=-^— d.
a5=r a
(34)
25=
TTC
~-rb{SS)
Differentiating equations (33) and (35)
and dividing we have :
r tan. 6 sin. b db , i^ . ,
= — tan. u sm. b
dy
dx
rdb
(36)
Now, let y (Pig. 36) be the ordinate to any
point in N X'K that y is for the correspond-
ing point in S X'G for the ordinate x. At
an infinitesimal distance from the point
of contact X' the curves N X' K and
S X'G are straight lines. Thus, in Fig.
38, let X' be the origin of co-ordinates
X'Y the axis of y, and X'X that of x.
Now, if on X X' we lay off an infinitesi-
mal distance X'B, and through B draw
A C parallel to X'Y, the curves AX' and
C X' are exactly at right angles to one
another within these lunits, and the ordi-
nates to A will be :
—dx and dy* and the ordinates to C will
be
—dy and —dx. The triangles AX'B and
BX'C are similar, whence
— dy : —dx : : —dx : dy\
dy __^
dx "" dy'
or
(37)
but ^=— tang. Q sin. b (see eq. 36)
da,
" dy
or rfy'=
,=tan. 6 sin. ^(38). But dx=— rdb
rdb
^ r__ db
tan. 6 sin. 6"~ tan. 6 ' sin. b
r db
tan. d 2 sin. ^ b cos. ^ b
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LOGARITHMIC AND RIBBED OBLIQXTE ABOHES.
19
__ r db COB.* ^ b
~ tan. d ' cot. -J ^
=^^^log.oot.ift (39)
.-. 3^=r cot log. cot. J d + C (40)
or, snbBtitating (90°— a) for b we have:
y'=r cot d log. cot ^ (90**-a) + C (41)
as the eqtiation of the curve N X'K in
which if
a=0, a;=0, and log. cot i (90°— a)=0
or 0=0,
whence the equation of NX'K becomes
y'=r cot e log. cot i (90— a) (42)
wherein, if a and x=0, y=0
7CT
if a=90% x=z— and y = — «
TtT
if a=— 90°,aj = — ^andy=a
By the aid of Eqs. (42) and (32) the
soffit coursing and heading joints in the
development may be determined with
great precision.
73. T?ie coursing beds of oblique arches
by the logarithmic method are generated
by a radial line normal tOy and moving
along the axis of the arch as one direc-
trix, and on a cylindrical curve as the
other directrixj which at aU points is nor-
mal to planes parallel to the arch faces.
This second directrix is usually taken
in the soffit, and we will so treat it here,
but should be in cylindrical surface,
midway between the intrados and the ex-
trados.
74. The great similarity in the genera-
tion of the coursing bed surfaces by the
helicoidal and by the logarithmic meth-
ods. It should be noted both are gener-
ated by a radial line normal to, and mov-
ing along the axis of the arch. Their
difference is in the fact that, in one case
the second directrix is a helix, and in the
other, a normal curve to the arch faces.
It matters little what this second direc-
trix is so long as its curvature is known.
But it is of tbe greatest importance that
we keep in mind that the first directrix is
radial in the logarithmic just the same as
it is in the helicoidal meUiod ; nor should
this idea, in the treatment of oblique
arches by either of these methods, be
ever lost sight of. It is the fundamental
principle and renders these two methods
quite similar in construction, and for this
reason the treatment of logarithmic
arches is readily understood when the
problems connected with helicoidal arches
have been^once mastered.
75. Agam, it should be noted the only
straight Hne elements in the coursing
beds by either methods are radial ; that
is, they are in lines normal to the axis of
the arch, and consequently, are always
normal to the coursing joints, both intra-
dosal and extradosal. The only straight
lines in the soffit, by either methods, are
lines parallel with either the axis or the
spring lines of the arch, nor should this
fact be lost sight of.
76. Now, if NX'K (Fig. 36) is the in-
tradosal joint and MXX the extradosal
joint of a coursing bed passing through
X' in the devel^ment, and if through
any point 1 in Na K we draw 1 2 in di-
rection perpendicular to s^o continued, the
point 2 in MX'L is the intersection of
the radial element through 1 in NX'K.
We have already determined the ordinate
of 1 to be
y-r cot. d log. cot i (90-a) (42)
but y' is also ordinate of the point 2,.
and £q. (42) is therefore the equation of
MXX when
aj'=r'a (43>
Chapter VDI.
method of woreino the v0ds80ib.
77. Reduce the face of the stone to be
worked to a true cylindrical surface by
aid of the soffit templet, Fig. 25, in the
manner as described in article 57. This
reduction may be accomplished in a va-
riety of ways, but the method there de-
scribed is believed to be the simplest and
best.
Let A B C D, Fig. 39, be the soffit thus
reduced, and let A'B'O'D' be the devel-
oped soffit of the voussoir to be worked.
Through B with the straight blade of the
soffit templet draw the element B £, and
through B' in the development draw cor-
responding line B'E' parallel to the
spring lines, or to the axis of the arch,
and through D' draw D'F' parallel to
B'E', and through A' and C draw A'Q'
and O'F' perpendicular to B'E' and to
D'F', respectively. Lay off on B E, B Q
and QE equal to B'Q' and to G'E'.
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20
VAN nostband's engineebixg magazine.
Then with the curved blade of the soffit
templet through G and E draw the cir-
cular arcs G A and E C, whose respective
lengths shall be equal to A'G' and E'C
in the development.
and D of the voussoir soffit are now de-
termined.
78. The heading and coursing joints
of this soffit are reduced in a simple man-
ner. Thus let a flexible rule of card-
Produce the arc E C to F and make
E F equal to E'F' in the development,
and with the straight blade of the soffit
templet draw the element F D parallel to
BE, and make FD equal to F'D' in the
development. The four comers A, B, C
board, thin hard wood, or other suitable
material be cut, vnth one edge of the
exact length and curvature of the devel-
oped joint A'B', and apply its extreme
points A' and B/ at A and B, press the
rule against the cylindrical soffit, and
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LOGABITHMIO AND RIBBED OBLIQUE ARCHES.
21
canse it to thoroughly conform to this
surface, and whilst so applied, work on
the soffit between A and B the line of
the curved edge of the rule, and the
joint A B will be determined. The joints
BG, CD and DA may be thus deter-
mined by rules cut to their developed
curves, and then applied to the worked
soffit of the voussoir in like manner as
A B was determined.
79. Another way of determining the
voussoir comers and joints in the worked
cylindrical soffit is : Let any comer B,
Fig. 39, be selected as before, and
through it draw the element B E. Then
cut a templet of cardboard, or of other
flexible material, to the exact size of the
cated upon the worked soffit of a vous-
soir.
81. The surfaces below the joints A D
and B 0, Fig. 39, are therefore worked to
the radial edge of this templet. When
so worked, radial lines are drawn with
this radial edge on the coursing beds
through the comers A, B, and D, thus
determining the lines of intersections of
the heading and of the coursing beds of
the voussoir. The heading surfaces are
then worked to these radial lines so
drawn, causing the surfaces to be normal
to the soffit, and therefore normal to the
coursing beds.
82. Much has been said as to what
should be the character of the heading
mig. 40
PL
AN
developed soffit A'B'C'D', and draw
across it the line B'E' parallel to the
spring lines of the arch, and apply this
templet with its corner B' at B and its
line B'E' on B E, and cause the templet
to conform throughout to the worked
cylindrical soffit surfaces, and when so
applied, work all the edges of the temp-
let on the stone, and thus determine all
the joints of the soffit at one operation.
BEDUOTION OF THE COUBSINa BEDS.
80. When it is remembered that the
coursing beds by this method (logarith-
mic) are generated by a radial line, it will
at once appear that the coursing bed
templet, Fig. 28, is as applicable to log-
arithmic arches as to helicoidal arches
for the reduction of the coursing beds,
when the coursing joints have been lo-
coursing surfaces, both by the helicoidal
and by this method. It has been main-
tained that these surfaces, by the loga-
rithmic method, should be planes parallel
to the arch faces ; that the strength and
stability of the arch demanded it, &c. It
in fact matters little, whether these sur-
faces are parallel to the arch faces or are
warped surfaces, normal to the coursing
beds. It is, however, the author's opinion
that the latter construction is the more
stable. It has the advantage, also, of
simpler construction.
83. The arch face stones are to be
worked precisely in the same manner as
described in Articles 63 and 64 for heli-
coidal arches. In the one the coursing