Victorian Institute of Engineers.
(ESTABLISHED I 883.)
1924, APRIL 9th.
PROCEEDINGS
The Ordinary General Meeting of the Institute was held at the Rooms on Wednesday, April gth, at 8 p.m.
The PRESIDENT, Mr. J. N. REESON, M.Inst.C.E, occupied the chair.
The Minutes of the Annual General Meeting of March 12th were confirmed.
Apologies for absence were received from Messrs. A.
Casson Smith, J. Wilkins, D. O. Reeson and R. J. Bennie.
An invitation was received from the Institute of Surveyors to a lecture to be delivered on the following Friday evening by Mr. Connell upon "Instruments of Precision."
A lecture was delivered by Mr. J. Sarvaas upon "Storm Water Discharge in City Areas."
At the conclusion of the lecture the President moved a hearty vote of thanks to the author for his interesting paper, which was carried by acclamation.
After discussion by the President and Mr. J. T. N. Ander- son, Mr. Sarvaas replied, and the meeting closed at 9.35 p.m.
STORM WATER DISCHARGE IN CITY AREAS.
By Mr. J. Sarvaas (Member).
One of the most difficult problems which confront the civil engineer is the determination of the waterway that must be provided to carry off the maximum discharge from any catch- ment area. As far back as 1888 the late Professor Kernot contributed a paper on the "Waterways of Bridges and Cul- verts" to the transactions of this Institute.
The formula which he proposed has been largely resorted to since that time. It is an empirical formula, closely re- sembling that proposed by Colonel Dickens, and takes the form
A = CMS
Where A is the waterway to be provided in square feet, M
174 THE VICTORIAN INSTITUTE OF ' ENGINEERS.
the area drained in square miles, and C a co-efficient of th°
value 3o for flat, absorbent areas, 4.0 for undulating country part cultivated, and 8o for steep inabsorbent areas. Lis regards the application of the formula to fixing the watei • ways of bridges and culverts, my own experience is that it gives results well on the safe side.
One could name about a dozen formulae of an empirical character that have been proposed by American engineers.
Chief among these are the Burkli-Ziegler Q
=
.-ARC S and McMath Q=ARC d A and Colonel Dickens formula Q=825 ;/M3The Symbols signify in each case—
A. Drainage area in acres.
Q. Cubic feet per second reaching the sewers.
M. Area of. catchment in square miles.
R. The average rate of rainfall in inches per hour dur- ing the heaviest rainfall.
S. Is the general fall of the area per i,000, and. C is a constant, which may vary from .9 to .3 in the Burkli-Ziegler formula and that of McMath.
When one endeavours to apply these various empirical formu- he to a given area, the results are very discordant. Thus for a io-acre block, with a one per cent. fall, we get the following results:—Burkli-Ziegler, 27 cu. secs.; McMath, 2i cu. secs; Col. Dickens, 36 cu. secs. Such discrepancies create a feeling of uneasiness as to the reliability of such empirical formulae, and we cannot but regard as a conse- .quence our knowledge of how to provide for waterways as
unsatisfactory.
Another paper dealing with the subject is that contributed in 1898 by Mr. G. Charnier, of Sydney, and published in the Transactions of the Institute of Civil Engineers, vol. 134., page 313, entitled "Capacities Required for Culverts and Flood Openings."
The formula therein recommended is Q= ARC Mi
M
or substituting for A its value in square miles Q=64oXRXC 4I~
3
STORM WATER DISCHARGE IN CITY AREAS. 175 Where Q denotes the maximum discharge at the outlet in
cubic feet per second, R the average rate of greatest rain- fall in inches per hour for such duration as will allow the flood water flowing to the outlet from the farthest extremity of the catchment area, and C is a co-efficient of surface dis- charge, giving the proportion of rainfall that may be expected to flow -off the surface. M is the catchment area in square miles. It is claimed by the author for this formula that it takes special account of the duration of the rainfall, and that in applying it in January, 1897, in investigating the suffi-
,ciency of waterways on the Cootamundra-Gundagai Railway for the Government of New South Wales, he obtained reason- ably close results between computed discharges by the for- mula and actual measurements.
Mr. Coane in his book on Australian Roads recommends this formula of Chamier's, and suggests the use of Professor Kernot's formula as a check. We might quote the follow- ing as an illustration of its. application:—Rainfall assumed at
12 inches in 24 hours, with a maximum of 3 inches for one hour. Co-efficient of discharge .66. Area of catch- ment 75 square miles, with 14 miles as the longest distance for flood water to traverse. The inclination of the valleys i >
taken to be such as will maintain for the main stream an average velocity of about 32 miles per hour.
It follows that the duration of the rainfall would have to be taken for a period of not less than 3 2 or 4 hours, and as the greatest downpour in that time could not be expected to exceed 6 inches, the average rate would be
4 or I?, inches per hour.
Then Q = 640 X i X .66 t 753 = 16384 Cu. Secs.
The use of the empirical formulae referred to is still quite general. However, in the United States the tendency is to abandon the use of empirical formulae and introduce in their stead what has been called a "rational method" of investiga- Lion for the run off of storm waters from city areas. It is
by way of illustration of the proceedure by this method that this paper has been prepared and brought under the notice of our members for discussion. -
The capacity of any waterway to carry the maximum dis- .charge from any catchment area depends upon
(I) The heaviest rainfall.
(2) The catchment area.
(3) The surface discharges.
Reliable information regarding the rainfall likely to be ex- perienced is a very important factor. To take it into account -we require to know the time of duration of the maximum rain-
fait
This we know from experience lasts only a few min-176 THE VICTORIAN. INSTITUTE OF ENGINEERS.
utes. The longer the period considered the lower is the maximum rate. Storms usually increase and decrease irre- gularly. What múnicipal and sanitary engineers require to possess are statistics of the maximum rates of rainfall to be experienced in a locality for intervals of not more than five.
or ten minutes.
Such records can only be made by employing pluvio- graphs or self-recording rain gauges which automatically graph on achronographic sheet a continuous record of the rainfall. Such instruments have not yet been regularly in- stalled in our larger towns. What is desirable to know is- not simply the maximum rate for say any five-minute period, but a record of a considerable number of consecutive five- minute periods both before and after the occurrence of the- maximum.
In Melbourne we are in possession of rainfall records giv- ing particulars of the heaviest falls recorded in brief intervals.
of time on certain dates' from a few minutes up to six hours.
A common method of utilising this information is to graph the several maximum rates recorded for periods of 5, Io, 15 minutes, etc., up to say 6 hours, with the rates as ordinates and lengths of periods as abscissae, and then to draw a curve through the ends of the ordinates, which will as nearly as possible pass through the maximum points. It may then be assumed that this curve will represent the maxi- mum intensity of rainfall as a guide in estimating the cap- acity of sewers.
RUN-OFF TO SEWERS.
If intense rainfalls continued at a uniform rate for con- siderable intervals of time, it would be an easy matter to fix the size of a sewer provided also that all the rain falling flowed direct to the sewer. However, neither of these con- ditions exist. Rainfalls at high rates usually vary from minuté to minute, and the maximum rate lasts for less than io minutes, and the area covered by this maximum rate is frequently quite limited in, extent, and changes in position continuously. Moreover, all the rain that falls in a city area does not reach the sewer directly or ultimately, 'and that which does reach them occupies a greater or less period- of time in doing so.
The causes are not difficult to enumerate. They are the- varying absorbtive capacities of the surfaces in the area.
The different kinds of roof material, and nature of construc- tion of the footpaths, yards, and roadways, for example, ex- hibit in each case different absorbtive capacities.
A considerable amount of research has been devoted tc this matter, and for the purpose of providing a working basis
STORM WATER DISCHARGE ÍN CITY AREAS. 177 for sewerage work the late E. Kinchling, of 'few York, tabu- lated values as follows for ratios of run off to rainfall:—
Roof surfaces, .7 to .95 Asphalt pavements, .85 to .9
Stone, brick and wood. pavements with cemented joints, .75 to .85
Same, with open uncemented joints, .5 to .7 Macadamised roads, .25 to .6
Gravelled roads and walks, .15 to .3
Parks and gardens (depending on nature of surface slope and subsoil), .oi to .2
For the sewerage of Cincinnati, 1912, the factors used were
—Roofs .g, asphalt, brick and road block pavements ,85, granite blocks .75, unpaved yards and lawns .25 to .15.
TIME OF REACHING SEWERS.
Time is occupied by the particles of water after reaching the surface of the roof, yard or street to find its way into the sewer. This is undoubtedly a difficult factor to deal with.
In the empirical formulae previously referred to this is evi- dently made to vary as A
I M
3, whether the catchment be long and narrow or short and broad in other words, no matter what its shape may be..
One of the strongest arguments in favour of the rational method is that it abandons this arbitrary way of dealing with the area. The method may be tedious and absorb a lot of time, and in no way overcome all uncertainty and difficulty in fixing the time of in off, but it is much more .intructive and reliable than the use of an empirical formula.
It is impossible with absolute accuracy to estimate the time of run off from, a particular part of the catchment, even by the method of drawing contour lines, dividing the catchment into minute areas. We can appreciate the difficulty when we observe that the water from the roof of a building must flow down to the spouting (more or less obstructed by debris), then to the leaders or down pipes, then to a drain communi- cating with the street channels, and finally by these channels to the sewer inlet. The water falling on the footpaths and roadway has the least distance to travel. The time re- quired for a particle of water to reach the sewer depends on the distance it must travel over each kind of surface, and its rate of flow over such surface. Practically no data have collected for estimating the velocity of flow of rainfall over various surfaces, and the difficulty of doing so is great. The velocity obviously is affected by the slope and nature of the 'surface.
178 THE VICTORIAN INSTITUTE OF ENGINEERS.
But notwithstanding the difficulty in fixing velocities of run off for different parts of the catchment, and the division into contour areas, it is a far more- rational attempt than merely disposing of the difficulty by making the run off vary as simply 1! Ni3
In order to illustrate the procedure of the rational method,.
I have assumed a town area or block io chains by io chains, footpaths 12 feet wide, kerb to crown of roadway 21 feet.
The assumed velocities for the street channels are figured on the plarf We will also assume that the slopes of the footpaths and road surfaces ,are such that it takes a particle of water 12 seconds to run from building line to gutter, and
21 seconds from centre of road to gutter. The assumed rates of run off across the yard areas are also figured on the plan.
The ratio of absorption or run off factor will be taken as .g for the footpaths and roadway, and for the yard areas .4, and io seconds is allotted for the time of flow from A to B the inlet of the sewer.
The whole of the data are, of course, fictitious, and are merely quoted as a basis for illustrating how the minute areas may be plotted from such data, which forms the funda-
mental feature of the rational method.
The velocities specified for the street channels would de- pend upon the nature of the construction as regards materials
used and shape of the channels and their gradients. After giving consideration to these matters, the next step to be taken is to draw minute contour areas in the following way:—
The one-minute contour hannel crosses the gutter say at the southern street (6o io) x I = 5o feet from A, and that the eastern street, which runs north and south, (6o -- to) x 1.5 = 75 feet from A. It crosses the centre line of the eastern roadway (6o - to — 21) x 1.5 = 43i feet from A, and the building line of the southern street (6o — io — 12) x I = 38 feet from A, and the eastern building line (6o — 10 — I2) x 1.5 = 57 feet from A, and the centre line of the southern roadway 2g feet from A.
The second or two-minute contour line crosses the gutter of the eastern street 6o x 1.5 = go feet beyond the one- minute contour. The part of the contour line crossing the road and footpath will be parallel to the corresponding por- tion of the first contour line. So also with regard to the southern street, the portion of the second contour line cross- ing it is everywhere distant 6o x 1 = 6o feet from the first contour. Now from the point where the first contour crosses the building lines measure off 6o x 1 = 6o feet, which will give a point on the two-minute contour line in the yard area, and from the building line points of this. second contour, and'
STORM WATER DISCHARGE Ix CITY AREAS. 179
from this third point the contour lines across the yards may be approximately drawn. We next fix the three-minute contour line where it cuts the southern and eastern streets precisely in the same way as the preceding one, and measure off 6o feet at right angles to the building line to get a point on the third contour line within the yard area, and then the three- minute contour line may be approximately drawn. It is hardly necessary to further detail the drawing in of the re- maining contour lines up to the seventh for the eastern street and the eleventh for the southern. The eight-minute con- tour line, where it cuts the northern street gutter, will be fixed as follows:--The distance of the seventh contour of the eastern street where it crosses the gutter is 69 feet from the point of intersection of the northern and eastern gutters.
It will therefore take a particle of water 6o — 46 = 14 minutes to traverse the distance of the eighth contour line from the intersection point, and as the velocity for the northern gutter is 1.2 feet per second, 14 X 1.2 = 16 feet 8 inches gives us the distance, The other contour lines along the northern street gutter will be 72 feet apart, and the intervals between them in the yard area measured normal to the top boundary line 6o • x .4 = 24 feet apart. All the contour lines in each area of uniform slope are parallel. The contour lines for the western street are located in the same manner, and the diagram gives a plan showing the whole of the 25 minute area.
The whole of these minute areas must next be worked out for area either by computation or the use of a planimeter.
Then all the yard area between contour No. I represents the area of such surface from which the run off reaches the sewer in one minute. This area is 625 square feet for the yards and 3,891 for the street areas. The s .m of all he areas between the No. I and No. 2 contour lines, compriking 5,32 5 square feet of yard and 4,95o square feet of street area, will represent the total area from which the storm waters falling upon it reach the inlet at A in two minutes and so on.
From the Igth to the 24th contour there are two yard areas to give the run off. For the remainder (8 to 19) there are two yard and two street areas to combine in each case, and from (I to 8) one yard and two street areas.
The yard areas are now multiplied by .4, the assumed ratio of run-off for the yards, and each street area by .g.
A schedule is now prepared, as shown on the following page, in which the A column gives the areas for the streets and yards for each minute area, and the AI columns which give the values in the A columns multiplied by the ratio of run off. The results in the two AI columns are then summed for each minute area, and inserted in the total AI column.
180 THE \ICTORIAN INSTITUTE OF ENGINEERS.
Area of Street Area of Yards
Minute I=.9 I=.4
Area. A AI A AI
7 otal
AI R ' AIR
y
I 3891 3502 625 250 3752 .026 8.13
2 4950 4.455 532 5 2130 6585 .027 14.81 3 4950 4455 11,360 4544 8999 O23 1 7•25 4 -4950 4455 16,125 6450 10,905 029< 26.35 5 4950 4455 21,525 86ío 13,065 .030 32.58 6 4950 J455 26,925 15,225 19,680 .031 50.84 7 4950 4455 32,225 12,890 17,345 • 033 47.69 8 5143 4629 41,940 16,776 21,405 .041 73.13 9 4356 3920 31,388 12,555 16,475 .060 82.37
10 4356 3920 22,285 8914 12,834 .040 42.78 II 4356 3920 12,875. 5150 ,9070 .031 23.43
12 5152 4637 6477 2591 7228 .029 17..{6
13 5544 4990 9068 3627 8617 .028 20.IQ 14 5544 4990 12,205 4882 9872 027 zz.21
15 5544 4990 17,128 6851 11,841 .026 25.65 16 5544 499019,937 7975 12,965 .025 27.01 17 5544 4990 23,930 9572 14 562 .024 29.12 18 6794 6115 27,310 10,924 17,039 .023 32.65 19 — — 30,145 12,058 12,058 .021 21.10
20 ' — 23,811 9524 9524 .020 15.87
z1 1 7,663 7065 7065 .019 11.19
22 — 13,407 5363 5363 .018 8.04
~3 — 8268 3307 3307 .017 4.69
24 — 3335 1334 1334 .016 1.78
~5 — — 318 127 127 .015 0.16
91,468 82,321 435,600 174,240 256,561 .684 656.39
Average rainfall .0271 equivalent to 1.62 in.. ner hour, giving mean run off of 579.4 c. ft. per min. Max. run off depends on time when peak rate of fall took place in relation to area of run off. Thus if it took place 17 min. after start of storm run off would be increased to 656.39 c.f. per min.
G i
STORM WATER DISCHARGE IN CITY AREAS. 181 We next turn our attention to the available rainfall sta- tistics. As it takes 25 minutes for a particle of water to reach the sewer from the farthest minute area, we would 'select a storm of 25 minutes duration. Since the maximum AI is that of the eighth minute area and the centre of the peak about the 9th, we must arrange for the maximum rate of rainfall to occur 25 — 9 = 16 minutes from the beginning of the storm, because this will result in the maximum total run off.
Assuming a storm whose maximum rate gives 3.6 inches per hour or .o6 inches per minute, and five minutes earlier .027 inches from a rainfall graph, and five minutes later .029 inches, we can interpolate between these two values and the peak value .o6, and enter these values in the R column opposite the minute areas from 4 to 14 inclusive, and fill in the remaining R values either from further records .along the graph or by continuing the interpolation up from
4 to I and down from 14 to 25.
All that now remains to be done is to multiply the total _AI values by the corresponding R values, and divide by 12
to give cubic feet per minute values in the AIR column.
The sum of all the values- in the AIR column will give
-the maximum discharge that enters the sewer 656.39 cubic 'feet per minute, or 10.9 cubic feet per second.
The average rainfall for the period is .0271 inches per minute, equivalent to 1.62 inches per hour, which gives the mean run off as 579.4 cubic feet per minute.
The last schedule prepared is in no way essential for the purposes of design. It is very laborious to compile, but it is very instructive, for it gives the volume of water arriving at the inlet at the end of each minute of time from the begin- ning of the storm, and makes it very clear that the maximum amount of water arriving at the inlet depends upon the time of occurrence of the peak fall after the beginning of the storm, and the relation of the peak fall to the maximum minute area.
The advantages of the rational method over the usual empirical method of determining the discharge of storm water are that more detailed application can be made of rain- fall statistics. In empirical formulae only a single factor of ratio of run off can be used, whereas in the rational method account can be taken of the different kinds of surfaces in the area and their different absorbtive capacities. The ra- tional method by the system of contouring affords _a much better means of taking the shape of the catchment ' into ac- count, and consequently the time of run off, and generally affords a much better idea of the manner in which storm waters gather at the inlet from minute to minute. Greater
-precision can be claimed for the method, and this must have an important bearing upon economic construction of sewers.
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STORM WATER DISCHARGE IN CITY AREAS. I83
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IN HOURS 184. THE VICTORIAN INSTITUTE OF ENGINEERS.
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DISCUSSION. 185
DISCUSSION.
The PRESIDENT, in opening the discussion, said he had listened with considerable interest to Mr. Sarvaas's paper,.
and particularly to his application of the formulae which he- had given, in endeavouring to arrive at a rational basis for computing the discharge of surface waters and deciding on the size of storm water drains. As Mr. Sarvaas had so ably shown, the question was fraught with difficulties, and per- haps Mr. Sarvaas would allow •him, to mention one or two additional difficulties, in that in a comparatively undeveloped country like Australia, where the towns were -extending and developing very rapidly, an area which might be a rural area to-day, with natural means of absorbing water not only through the soil, but by its natural water courses, to-morrow might be an urban district where the absorption of the soil had almost ceased, and the natural water courses been turned into storm water drains, thereby very much curtailing their powers of discharge. He thought that was one of the reasons why very rapidly developing towns were sometimes subject to inconvenient floods. Another point was the sedimentation of the drains. A drain might be made sufficiently barge to carry away the computed water, and in a few years the area of the drain might be considerably lessened, thereby render- ing it inefficient. Mr. Sarvaas deserved great credit for having dealt with a very difficult subject. The paper was full of interest, and the tables would be of very great value to municipal engineers.
Mr. J. T. N. ANDERSON said he was present at a very memorable discussion in the history of the Institute, when the late Professor Kernot enunciated his formula, which Mr.
Sarvaas had quoted. The Professor made a bold stroke in taking the area of the bridge instead of the capacity under it. He was attacked by another member—Mr. G. J. Burke
—and a very heated discussion ensued. A generation has.
passed since them, and both leaders of that discussion had gone.
Stewart Murray had found that for wide areas a better formula than the 4 power was the 3 power. At the time of the great floods of 1891 the index used in the work of dram- mg the Yarra was 2 power in Col. Dickens's formula. Mr.
Burke claimed that Professor Kernot was unscientific in tak- ing the area instead of the discharge, and having no regard to the site of the catchment. Professor Kernot replied that he made no attempt to make a thing scientific that could not be done scientifically. He supported his empirical formula by hundreds of examples. He had collaborated with Professor Warren, of Sydney, in exhaustively investigating a large number of railway bridges th^t had been washed away by
1$6 THE VICTORIAN INSTITUTE OF ENGINEERS.
great floods in 1871-2 and 1886. When the engineer was faced with definite problems he had to do something like Mr.
Sarvaas had suggested, and go into detail and adopt a ra- tional method. Where there was close population there was more rapid run off. In water supply the peak load occurred every 24 hours, but in drainage they had simply to judge from records of the past what the load would be. In sub-tropical country there was not much difficulty. If they designed for two inches in an hour, and took a rough rule of thumb idea that one-half of that actually got into the sewer, they had to provide for one inch per hour or one cubic foot per second over every acre to be drained.
The most important point was not the size of the drain, but the means of getting the water into it. In nine cases out of ten where the drains were inefficient it was duè to the fact that they were never running full. The inlets were not sufficient to fill the drains. Most drains were designed for .a maximum velocity of six feet per second. Those drains could easily be made to discharge double the quantity pro- vided the water could be got into them. If, however, the inlets were made so that they would admit a large volume of water to the drain, the s'courings of the street got right into the sewer. So that they were faced with the necessity ofmaking the inlets insufficient, or else getting the scourings of the streets into the sewer and having to remove them by some other method. Therefore they must hit the happy me- dium in every case. Established practice was very good practice, and they had the mistakes of their predecessors to benefit by.
As to the quantity of water running off art area, he was much interested by the statement quoted by Mr. Sarvaas that go per cent. of the rainfall on roofs found its way into the sewer. That always seemed to him to be a mistake. If they placed a rain gauge about a foot above the ground they would get one result; if it were placed five feet above the ground it would register less rainfall, and as they went higher the rainfall was reduced. How then could go per cent. of the rainfall on the roofs 'find its way into the drains. In the case of the catchment area of the Shannon, it had been shown that more water ran off than actually fell on the area. The explanation was that the catchment area consisted of a soil somewhat resembling peat, which held the water, and even though no rain should fall for months the water issuing from the peat-like catchment area would still keep the Shannon a big river. But in the case of,a non-absorbent thing like a corrugated iron roof it was absurd to think of more running doff than fell on it. They had to use their own discretion in 'every case, and it was their own judgment more than any .complicated calculation that would carry them through
DISCUSSION. I87 Mr.
J.
SARVAAS, in reply, said the matter they were dis- cussing was the result of his studies and reading on the sub- ject. The whole system was first proposed in America, andthe first engineer to suggest dealing with it on the lines he had referred to was the late Mr. Kirkling, of New York.
He was the first to advocate the supplanting of the empirical formulae. It had taken such hold, at any rate on the Iarger centres of population in the United St ,tes, that they were .actually dispensing with the empirical formulae and working things out on the rational basis. Very careful and elaborate statistics were required if the system was to be of any value.
At the present time they had not sufficient data to work out the records. Rainfall records should be taken with a great deal more minuteness for municipal and sanitary engineers.
They should know the maximum rainfall for five minutes or half an hour, and therefore must have rain gauges which would graph the records for them. It would take a consider- able time before sufficient statistics were available to get to work properly on the matter, and perhaps fruitful results would not soon be attained.
The system seemed to be " hardly applicable to country .areas. In a town they could work out sufficient individual areas and blocks, but in the country it would be a rather difficult matter. The method seemed to be more applicable to city areas than the draining of the basin of the Yarra or the Saltwater River. They would have to rely on empirical formulae for some time to come.
Professor Kernot's formulae had always given satisfactory results in the case of waterways and bridges. He had never known a failure, or that any of the bridges were showing signs of being deficient in waterway where that formula had been applied. But the unsatisfactory feature was that it took no notice câf the rainfall.
He had been interested in the subject ever since, as a student, he had heard Professor Kernot enunciate his for- mula. The formula had certainly encountered very consider- able criticism. About the year 1889 tremendous floods oc- curred in the Castlemaine district, which offered a very good opportunity of testing the accuracy of a formula like Col.
Dickens's, the height of the water over the baink being known, and the catchment area of the reservoir being about 3,600 acres. The bank fortunately escaped serious damage, and it gave a sort of weir measurement which made it pos- sible to gauge the quantity of water that flowed over at the time, and the rate of flow. It also gave an opportunity óf
-measuring the probable fall in the catchment. The byewash was certainly too small, but when they came to work it out
I88 THE VICTORIAN INSTITUTE OF ENGINEERS.
they had found the value of Q, the area M was known, and all they had to do was to equate the value of Q, leave the co- efficient out and find the value of C, and it came out different altogether from Dickens's result. It did not apply in that p:.rticula.r instance.
The Institute is not responsible for the opinions advanced or the accuracy of the statements made by the several authors and con- tributors.
