Speaker design considerations

Again, this is such a vast and sometimes emotional subject to cover that a mere scratch of the surface is offered here. With speakers there are two important don'ts; never touch the cone assembly, even fleetingly, and never bring large speaker magnets together. The best audible results are usually obtained when there is no discernible cone movement.

Although it is easier to construct a perhaps boring rectangular box if resource is limited, it is what is done with the box that can produce the wow factor. One recalls a rather nice Bose system that mounted two speakers on the front of the cabinet and eight on the back. This acknowledged the fact that most perceived sound is reflected. To give arguably better sonic qualities, speakers could be set against the longest wall in a room to improve the bass response, usually at a distance of about a ¼ of the walls' length from the corner. These speakers sat at the same distance apart, but about a metre away from the wall, the eight rear speakers facing it.

The finish of a speaker is important if, say, sales are a consideration. To prevent warping, both sides of the wood used in a cabinet must be sealed or treated - when the construction of a box is finished a couple of coats of primer both inside and outside the box won't go amiss. This should be done after removing all debris and wood particles with a vacuum cleaner, since these can damage a speaker. Touring cabinets can be over-painted (usually matt-black) easily, although aluminium primer has been used. Those intended for outside use may have asphalt roofing felt and bitumen coverings (which not only waterproof but help reduce cabinet resonances), whereas an expensive hardwood (the dust from which can produce allergic reactions in some) may require oiling or waxing.

Some very striking, even dramatic, finishes have used the same techniques used for finishing guitar bodies, ie; spraying or graining to give a colour scheme or pattern, then spraying with some 20 coats of lacquer (allowing six weeks to cure) and then buffing to a glass finish. One subtle scheme, used on car bodies as well, used a black undercoat with alternating coats of silver and gold glitter loaded varnish which, when finished properly, gave a remarkable 'depth'. Such care and attention will then produce an object that is desirable to many for years to come. However, with a small 'production run', say for domestic use, such lengths may be considered too complex, or unnecessary, and impatience can then give rise to a regretable and unattractive appearance. Cut plywood panels can be easily made to produce curves, for large scoops for example, if steamed for half an hour before fitting, although some practice will be needed to get a first-rate fit first-time.

Most of the worst damage to speakers is caused by over-zealous/ignorant users, moisture and rodents. To help overcome the latter, fit metal grilles over all openings, diaphragms and ports.

For a beginner, ambitious projects are best avoided. A worthy bass-reflex design intended for inexpensive drive units is shown below, which can be used for surround-sound or multimedia.


The port exiting from the enclosures' top, the coil can be wound on a non-metallic former 28mm long by 28mm diameter. Wind 7 layers of 1.5mm dia enamelled copper wire. Use 100V caps and 10W resistors. Since exposed cones are finger magnets, grilles can be glued to speakers' rims. Offsetting the tweeter might improve.

A simple, effective, but larger, 2-way reflex design used a Soundlab 8" (20cm) bi-cone bass unit (8LUX, res 40Hz) in a 31 litre box (int dimens: 28cm wide x 49.5cm high x 24cm deep, 14mm teak veneered chipboard) with a port (5.5cm dia x 3.5cm long) below the woofer. A dome tweeter with a similar crossover was added and a piece of furniture foam helped to damp the box.

A 'serious party' 3-way speaker used 12" 300W Electrovoice bass units (30Hz) to replace 50W versions in 70 litre closed boxes (Q=0.7) which proved to be excellent for reggae and orchestral level classical music. These are still used today (30 years on) as a very acceptable reference.


Compact three-way speakers appear to offer much in the way of performance versus size for domestic circumstances. One notable example, likened in its' performance to one of the (then) top-of-the-range KEF loudspeakers and rated very highly, was Armstrongs' 602 intended for the respected 600 Series. This was designed by Bill Perkiss, who joined the company in the mid 1970s' after leaving Goodmans. The design was originally intended to be an infinite baffle design, but ended up as a well-damped three-way reflex which is easily reproduced.

    

A similar format was used in the design (below) from the early '80s whose cabinet employed butt-jointing, although reinforcement can be added. The dome mid-range unit did not require a separate enclosure within the cabinet. During construction, this was compared favourably with the Yamaha NS1000M, Gale GS401A, KEF 105 II and Popular Hi-fi Boxers, each of which had their particular strong points.


The midrange and tweeter are offset from the centre of the cabinet so that the pair are mirror imaged on the two speakers. This improves stereo imaging, mainly by reducing edge diffraction which is a major cause of poor stereo. The worst case for diffraction is when the tweeter is mounted equidistant from the three nearest cabinet edges. Re-radiation will then take place and this will cause a discontinuity in the frequency response. By offsetting the unit the diffraction is smeared and reduced to insignificant levels.

Below are the V3s' impedance, frequency and polar plots.

Note how the impedance of the speaker (upper trace) is frequency dependent and differs considerably from the previous example. Lively loads like isobariks, ESLs, ribbon types, etc, can easily dip below 1 ohm, then causing catastrophic output stage failures. In amplifier tests 'simulated loads' may be adopted, that for an ESL is shown below. These may not accurately reflect reality, or connecting media.


As a general rule, the power dissipation of an amplifier driving a 60° reactive load (usually considered to be a worst case loudspeaker load) will be roughly that of the same amplifier driving the resistive part of that load. For example, a loudspeaker may at some frequency have an impedance of 8R and a phase angle of 60°. The real part of this load will then be 4R, and the amplifier power dissipation will roughly follow the curve of power dissipation with a 4R load.

An important point to make is that care should be taken to seal and make airtight all joints, seams and gaps (with the obvious exception of ports) since these can make quite disconcerting and very unmusical noises. Corner joint battens (glued and screwed) stiffen a structure considerably and can help reduce the likelihood of leaky seams (these can be located with talcum powder or chalk). Since speakers, at some point, might have to be removed for replacement or testing, the use of, say, self-tapping screws to mount them is not recommended, especially if the enclosure material is chipboard, which can be quite porous to air if not sealed. Ideally, use bolts with T-nuts.

For larger sizes, a very solid box is a prequisite, so don't underestimate the need for bracing to reduce box resonances. After all, why waste wanted acoustic energy in rattling a box, and its' contents, to their later possible detriment? The panel around the speaker mounting hole can be doubled in thickness. However, front to back braces with additional lengths to increase strength and rigidity across long surfaces help as well. The normally wasted circular cut-outs made for speakers have been quartered and used for this. Don't neglect to include such items in the volume calculations. Effort made in these areas will definitely be repaid by improved performance, and having built a box remember that one might be reluctant to disassemble it. Bear this in mind when considering access for servicing. A sub-bass enclosure (closed box, driver 10"(25cm)+, Q=0.7) might look like this (face down).


Note the provision at the rear of the speaker for a separate power supply, amplifier and filter. This reduces extensive disassembly for repairs and can help balance a light structure if the speaker is heavy. If an enclosure or stand requires 'ballasting', loose sand or lead shot can burst seams and joints, especially when moving them. Fixed sheets of lead and even lead-loaded concrete can be used, but don't over-estimate the strength of the overall structure. Taking the time to find the optimum position for a small quantity of ballast will avoid the damage caused by indiscriminate assumptions.

Enclosure linings, often 2" fibre-glass insulation wadding, are intended to reduce reflections and standing waves. They do not decrease the effective volume of the enclosure and neither do they increase it. Polyester fibre (for sleeping bags and duvets) can be used, which does not break up as some types of fibre-glass can.

A number of good books are available, two whose designs have been built are given below.

"Designing, building and testing your own speaker system" by David B Weems, ISBN 0-8306-8372-7 (0-8306-3374-X pbk). A simple but effective approach, the larger scale tapered-pipe speaker is recommended (below). Larger units using 8" bass units with a 'presence' cone gave a good account, four or more of which and a LF bandpass enclosure make for a very respectable domestic arrangement.


Note how the central partition will stiffen the structure. Use corner joint battens as well (not shown).

"High power loudspeaker enclosure design and construction" (Eminence, ISBN 0-9518252-1-6) offers some excellent advice. All you'll need to know, scoops, w-bins and bandpass bass units are covered.

A number of enthusiasts prefer single speaker designs driven directly. The proprietor of a local B&O dealer, Jabez Gough of Goughs' (no longer extant), came up with a design (1961 UK patent 912,430) using 8" drivers that generated much interest. This consisted of a cabinet with hinged lid to direct the sound (a perhaps crude precursor to acoustic lens technology?), with ports to either side of the speaker which was mounted on the top, under the lid. Importantly, perhaps acknowledging the variance in speaker spec, it was held that dimensions, including that of the seams was not critical, although the author acknowledged that a lighter cone and coil mass could improve. A suitable amplifier could be the Rogers' Cadet, or the later Linsley Hood '69 class A. Larger versions seen included the Goodmans' twin-axiom 10/12 speakers (bi-cone) and other 'exotics'. This author did not find the resulting sonic performance disagreeable. One critic suggested that the inclusion of a coil of 24 x 24 x 1" fibreglass below the speaker reduced a 'boxiness' quality.


Tony Gees' Solo-103 is another single-cone design that some might like. Wayne Jaeschkes' Dayton D3 is a good choice for DIYers or if more bass is required Dave Tenneys' Dayton 8s are worth a look.

Where it is considered critical, and possible, the author will attempt to align separate channels' multiple voice-coils in a plane equi-distant to the listeners' position, a method used by a small number of manufacturers' whether the speakers be mounted to radiate horizontally or vertically; see Beovox Uni-phase and 2 series, Beolab 5, Linkwitz PA applications, etc. A slanted or raked baffle is used in other designs. For example David Huckle retains this in a Troels Gravesen / Jesper Spohr design.

Although high-tech composites can appear in some enclosure designs (eg: B&W Nautilus), wood is considered to be best by many, some manufacturers emphasising the fact that their sub-bass units are made of this. Chipboard and denser MDF suit domestic circumstances, Marine Birch plywood suiting large PA touring cabinets. Concrete can be employed for LF designs, although thought should be given to the pattern before commiting to a cast, together with a pumice aggregate if movement is required. Innovative shapes can be made, but the need for a vibrating table, to expel air, might have to be considered.

Interesting sub-bass (20-80Hz) reinforcement can be achieved by mounting a bass unit at the end of a tube (transmission line) whose length represents a ¼ of the desired wavelength (smaller versions are sometimes seen in car audio). A relatively simple construction, the critical element is sourcing the tubes. Choose a fibrous, eg; thick cardboard, composition to reduce resonances. The rear of the speaker should be 'open' and, if placing upright, have a heavy base. Performance will vary with the type and size of driver (preferably large), and to the extent and amount of damping material (polyester, wool, fibreglass, etc) placed in the tube. Ideally, the inner diameter of the tube should match the diameter of the speakers' diaphragm. However, the general arrangement of a system using 18"/45cm (600W, 33Hz) speakers (tube = 24"/61cm dia, 12.6'/3.84m length - 22Hz) that performed well is shown below, although smaller designs using low-resonance 8"/203mm bass units and 6'/1.83m tubes (40Hz) can impress. Notwithstanding architectural resonances, if desired or if space is at a premium this type can be slung horizontally from a ceiling in which case a heavy base (lead-loaded concrete) can be dispensed with. If one is used, channels for core ventilation and wiring can be cast in this.


The larger scale approach is considered to give far better performance than smaller sub-woofer units. A 20 litre unit intended for a living room using two 6½"/165mm speakers can, with filtering and a 2"/50mm port, offer a 'wide' bandwidth of, say, 25-110Hz and a 'narrow' band of 18-65Hz (-6dB). However, even when driven by a 100W amplifier, the response peaking at between 25 and 35Hz will, for those who have heard better, result in a 'boominess' which will not do the justice that a larger arrangement will.

Significant improvements in existing closed box systems have been seen when a second box of half the existing speakers' internal volume is made to match the existing one, which it then sits beneath. Two ports are then calculated and fitted, one connecting the two cavities and an external one on the new box.

Power distribution varies across the spectrums covered by the various drivers used. 'Normal' play-back will give the following ratios;


In disco use, frequencies below 150Hz and above 5kHz may be subject to excessive equalisation thus requiring greater power handling capacity.

With crossovers, air-cored coils may be bulkier but have a better ability to pass transients than ferrite-cored coils, which can momentarily saturate on high power peaks. Keep them well-spaced to prevent any flux linkage between them. A 'Loudspeaker Passive Crossover Choke Coil Calculator' can be found here and a 'Guide to producing inductors and other wound electric components' here. To reduce losses, aim for a DC resistance of less than ½ ohm. A wire diameter of at least 1.5mm is recommended.


Those intimidated by the thought of winding half a kilo of copper wire on to a toroid might like to consider using the secondary windings of mains transformers (isolate primary connections) instead. Transformers with open-circuit primaries can thus be re-used.

Capacitors should have high voltage ratings to prevent possible failure under high power drive. 50V ratings are often seen, but 100V is obviously better. Useful types can be those intended for mains motors and flourescent lighting. Such components can reduce costs and give performance indistinguishable from 'audiophile' components, combined with high voltage ratings.

Choosing a speaker

Let's say a domestic system envisaged requires good bass drivers. Two ranges are considered; one intended for hi-fi and the other for high power use. Plotting some of the specs can help the selection process, eg;


The first graph shows how low frequency performance is proportional to size, as is efficiency, shown by the second graph. Taking the 8" units as an example it can be seen how output can vary in one size, but different models, by as much as 13dB and by 17dB across the whole range selected. Most speakers' frequency ranges are quoted at -6dB. Looking at the frequency responses, the two largest speakers tend to peak after about 1kHz, suggesting that their use be restricted to 500Hz and below.

Taking these considerations into account four choices are made;

6½"; low power, but a useful resonance for its' size. A good choice, perhaps, for the tapered-pipe speaker above.
8"; more economical than 225W version.
10"; good combination of power, resonance and cost, although lowest impedance must be noted.
15"; lowest resonance, ample rating, reasonable cost.

Limitations of cone travel will usually occur long before power ratings are exceeded. As a consequence, working maximum outputs of driving amplifiers can be a tenth of those stated, or even less.

Once mechanical and economic considerations have been made Thiele-Small parameters can then be used to determine an optimum enclosure. If aiming for an optimum bass performance when building a number of identical enclosures, design and build for the lowest resonance (largest volume) given by the speakers' specification tolerance, then reduce volume by adding polystyrene blocks or tiles and/or cut ports to length to suit the individual driver fitted. In a multi-way system where three or more units cover different parts of the spectrum, ensure each speaker has its' own compartment to prevent, say, a mid-range unit being modulated by a bass units' output. Tweeters' diaphragms are usually mechanically isolated and need not be so mounted.

Tolerances of ±10%, whether mechanical or electrical, are often considered acceptable (resonant frequencies can be quoted at some ±15-30%, the constructor can measure these but some might find the procedure too complicated for small production runs). Avoid mounting a speaker in the dead centre of a baffle since this will result in standing waves and pronounced peaks and troughs in the frequency response. Aim for an assymetrical baffle layout. The accepted ratio of height/width/depth is 2.3/1.6/1 although other shapes are permissible.

The speaker cone alignment of some even respectable makes of large bass drivers when supplied as new can be questionable to say the least. This can be checked, preferably as soon as possible after purchase, by driving the unit with a low frequency whilst listening for any 'scraping'.

Isobariks vs Linkwitz

The search for the greatest possible bass output from the smallest possible enclosure is frequently driven by the fact that, say in a three-way system, the bass unit will often consume twice the power of the other two channels put together. Both approaches have their limitations.

Given the aesthetic inelegance of the isobarik clam-shell approach and its' extreme vulnerability of exposed speaker assemblies (as with any design employing exposed baskets or cones, particularly from inquisitive fingers and other accidents), attempting to force two tightly coupled, but invariably unequal, speakers to act as a single unit with ones' most prized amplifier is tempting fate, and as others' experiences have shown, invariably does.


With fcs quoted at ±15-30%, attempts can be made to match units, but results can disappoint, unless one has access, say, to a manufacturers' entire production run. The load presented to the amplifier can be very lively especially with low-loss cables which can add capacitance. Ideally then, if only one unit blows (usually the front one), the pair should be replaced. Then there can be a power amplifier to repair... For this type of load (as with ESLs!), current-limited paralleled output pairs and heavy-duty diodes clamping the output to the power rails are recommended, ie: assume intermittent short-cicuits and/or back EMF, which quite a few amplifiers simply will not/cannot tolerate.

The Linkwitz correction, applying a bass boost between a low-pass filter and power amplifier, does not rely on the uncertainties involved in mechanical interactions and their possible consequences at high energy levels. Some constructors, however, can be tempted to opt for a smaller driver which consequently wears out sooner (electrical power handling conflicting with mechanical specs / optimism conflicting with the real world).

It is considered best to manipulate signals on a low-level scale rather than at high power using expensive hardware, a handful of small components and perhaps larger enclosure being cheaper and, more importantly, safer. Whilst appreciating that each 'school' has its' adherents, and with good reason, personal preference and economics will dictate, when required, an approach utilising Linkwitz correction.

Crucially, it should be determined before embarking on a bass reinforcement project whether the listening area itself will sustain the desired wavelengths and/or the listeners' expectations are realistic.

Bessel arrays

Since it would appear that the more specialist and expensive equipment, proportionately speaking, has fewer listeners, thought has been given to experimentation with small Bessel arrays for youth or community projects. Budgeting for such users then applies interesting constraints, especially if 'hard-fixing' to the buildings' fabric is not possible or even desirable (mobile use). Since variability of the systems' sound is considered useful for differing locations, the means to make simple adjustments merits inclusion. A single-point stereo version could be used to determine the need and parameters for possible HF and omni-directional LF (<500Hz) reinforcement.


Co-axial automotive speakers can be employed, although access to the tweeter wiring may be required for some designs. This can be considered when choosing, as can any optimistic power ratings and resistance to corrosion. Stacked arrays give a particularly horizontal radiation pattern which can help reduce drive requirements and architectural resonances. Two or more rows, one above the other, would be set near the middle of the longest length of wall of the listening, or dance, area. Separate chambers (5 in this case) in a common enclosure will prevent problems with pressure differentials, the inner walls helping to stiffen the structure. In comparison with the enclosures' breadth and height, the depth is quite shallow.


Each speaker, ideally, is fed by its' own cable run from a common amplifier output connection point rather than interconnecting between speakers. Tedious perhaps, but this can ease identification of faulty units by reducing disassembly, if service access via the rear panel will not be possible. Alternatively, use bolts and tee-nuts to mount speakers. Although this particular model assumes a continuous rms rating of 10W per speaker, all can be upgraded considerably if desired (x10 max to retain original size). As mentioned above, some automotive speakers employ dual voice coils and stacked magnets.

Mobility being considered important, the drive can be low-voltage (classes C or D), only two amplifiers being required to power the whole array.

Feed for the bass reinforcement (considered mandatory), which can sit nearby, should be taken from the input (L+R via resistors). The filter can be adjustable in frequency (150-500Hz), phase and amplitude and be mounted in the bass units' case together with the bass amp and its' power supply. The bass enclosure can be ported and match the arrays' enclosure in external appearance and form if desired. A common PA design giving an output of 30Wrms (continuous) can meet all three speaker functions, given an array speaker rating of 10W each.


For best and most efficient results with a large body count, fly sound sources, including the bass, radiating down and across the dance area, although reflections from surfaces like rock faces can enhance.

Other arrays

An interesting paper ('Conventional and distributed mode loudspeaker arrays for the application of wave-field synthesis to videoconference' by Jose J. Lopez, Basilio Pueo and Maximo Cobos) covers DML and WFS techniques. In general, DML uses a number of drivers to vibrate a sheet fixed at each edge giving a reasonably even sound field. Since the vibration cannot be seen, an image can be projected on to the sheet. WFS uses two arrays above and below a '3D' TV. Using multiple microphones for the speakers a virtual 3D soundfield can be conveyed, again, over a wider field adding realism. 'The Research of the DML Loudspeakers Properties' by A. Dumčius and L. Bernatavičius gives further modelling.


Accommodating a speakers' environment into its' design will increase longevity. Robust construction, and protection for the cones, may figure largely, given that in a youth club say, the system might have to withstand repeated heavy impacts from a football and even heavy rainfall. Grilles and speaker cloth will protect from fingers and splashes but for worst case situations speakers can be shielded by separate cages or rafted on foam in ceilings, notwithstanding fire risks.


A huge range of speaker builder web-sites are available. A quick search, other than manufacturers' sites, included "Useful Conversions and Formulas" (WinISD, by Juha Hartikainen, a freeware design program that includes an oscillator can be downloaded from here too), "Car Audio: Woofer Enclosures" and "Ishtek", which are all worth a look. Pass Laboratories' Kleinhorn, J-Low and El Pipe-O designs offer interesting solutions.

For those daunted by math, the liberty has been taken to create a zipped Excel file that includes parts of "Useful Conversions and Formulas", which can be found here. Any functional errors are entirely mine.

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‫⸧潧杯敬愭慮祬楴獣挮浯术⹡獪㬧 瘠牡猠㴠搠捯浵湥⹴敧䕴敬敭瑮䉳呹条慎敭✨捳楲瑰⤧せ㭝猠瀮牡湥乴摯⹥湩敳瑲敂潦敲木ⱡ猠㬩紊⠩㬩ਊ⼯⼯⼯䰠捹獯䤠楮楴污穩瑡潩⼯⼯⼯⼯⼯⼯⼯⼯⼯⼯ਯ慶⁲祬潣彳摡㴠䄠牲祡⤨਻慶⁲祬潣彳敳牡档煟敵祲㴠∠㬢瘊牡氠捹獯潟汮慯彤楴敭㭲ਊ慶⁲浣牟汯⁥‽氢癩≥਻慶⁲浣桟獯⁴‽愢杮汥楦敲氮捹獯挮浯㬢瘊牡挠彭慴楸⁤‽⼢敭扭牥浥敢摤摥㬢瘊牡愠杮汥楦敲浟浥敢彲慮敭㴠∠摳瀯畡歬浥汢≥਻慶⁲湡敧晬物彥敭扭牥灟条⁥‽猢⽤慰汵敫扭敬猯畯摮执栮浴≬਻慶⁲湡敧晬物彥慲楴杮彳慨桳㴠∠㌱㠹㤰ㄳ㈸㔺ㄲ㝢昲挹㐹愸㑦㌹㥦ㄳ㈸ㅤ㈲攷っ∹਻瘊牡氠捹獯慟彤慣整潧祲㴠笠搢潭≺∺敨污桴⽜摡楤瑣潩獮Ⱒ漢瑮牡敧≴∺䌦呁栽慥瑬♨㉌䅃㵔楤敳獡獥㈥愰摮㈥挰湯楤楴湯♳㍌䅃㵔畳獢慴据╥〲扡獵≥∬楦摮睟慨≴∺浥楡扡獵≥㭽ਊ慶⁲祬潣彳摡牟浥瑯彥摡牤㴠∠㐵㠮⸱㈱⸹㤸㬢瘊牡氠捹獯慟彤睷彷敳癲牥㴠∠睷⹷湡敧晬物⹥祬潣⹳潣≭਻慶⁲摥瑩獟瑩彥牵‽眢睷愮杮汥楦敲氮捹獯挮浯氯湡楤杮氯湡楤杮琮灭㽬瑵彭潳牵散栽畯敳甦浴浟摥畩㵭慬摮湩灧条♥瑵彭慣灭楡湧琽潯扬牡楬歮㬢ਊ⼯⼯⼯䌠楲整⼯⼯⼯⼯⼯⼯⼯⼯⼯⼯ਯ慶⁲瑣彯潣普㴠笠愠琺畲ⱥ椠›㈢㐹Ⱒ挠∺浩≧‬睫›∢素㬠⠊畦据楴湯⠠笩 †瘠牡挠㴠搠捯浵湥⹴牣慥整汅浥湥⡴猢牣灩≴㬩挠琮灹⁥‽琢硥⽴慪慶捳楲瑰㬢挠愮祳据㴠琠畲㭥 †挠献捲㴠∠瑨灴⼺眯睷愮杮汥楦敲挮浯愯浤樯⽳慰瑲敮⽲牣瑩潥江彤睫樮≳਻††慶⁲⁳‽潤畣敭瑮朮瑥汅浥湥獴祂慔乧浡⡥戢摯≹嬩崰※⹳灡数摮桃汩⡤⥣਻⥽⤨※ਊ⼼捳楲瑰ਾ猼牣灩⁴祴数∽整瑸樯癡獡牣灩≴猠捲∽瑨灴⼺猯牣灩獴氮捹獯挮浯振瑡慭⽮湩瑩樮≳㰾猯牣灩㹴㰊捳楲瑰琠灹㵥琢硥⽴慪慶捳楲瑰㸢⠊畦据楴湯椨噳
੻††晩⠠椡噳
੻††††敲畴湲਻††੽ †⼠琯楨⹳祬潣彳敳牡档煟敵祲㴠氠捹獯束瑥獟慥捲彨敲敦牲牥⤨਻††慶⁲摡杍⁲‽敮⁷摁慍慮敧⡲㬩 †瘠牡氠捹獯灟潲彤敳⁴‽摡杍⹲档潯敳牐摯捵却瑥⤨਻††慶⁲汳瑯⁳‽≛敬摡牥潢牡≤‬氢慥敤扲慯摲∲‬琢潯扬牡楟慭敧Ⱒ∠潴汯慢彲整瑸Ⱒ∠浳污扬硯Ⱒ∠潴彰牰浯≯‬昢潯整㉲崢਻††慶⁲摡慃⁴‽桴獩氮捹獯慟彤慣整潧祲਻††摡杍⹲敳䙴牯散偤牡浡✨慰敧Ⱗ⠠摡慃⁴☦愠䍤瑡搮潭⥺㼠愠䍤瑡搮潭⁺›洧浥敢❲㬩ਊ††晩⠠桴獩氮捹獯獟慥捲彨畱牥⥹笠 †††愠䵤牧献瑥潆捲摥慐慲⡭欢祥潷摲Ⱒ琠楨⹳祬潣彳敳牡档煟敵祲㬩 †素ਠ††汥敳椠⁦愨䍤瑡☠…摡慃⹴楦摮睟慨⥴笠 †††愠䵤牧献瑥潆捲摥慐慲⡭欧祥潷摲Ⱗ愠䍤瑡昮湩彤桷瑡㬩 †素ਊ††潦⁲瘨牡猠椠汳瑯⥳笠 †††瘠牡猠潬⁴‽汳瑯孳嵳਻††††晩⠠摡杍⹲獩汓瑯癁楡慬汢⡥汳瑯⤩笠 †††††琠楨⹳祬潣彳摡獛潬嵴㴠愠䵤牧朮瑥汓瑯猨潬⥴਻††††੽††੽ਊ††摡杍⹲敲摮牥效摡牥⤨਻††摡杍⹲敲摮牥潆瑯牥⤨਻⡽昨湵瑣潩⡮
੻††慶⁲⁷‽ⰰ栠㴠〠‬業楮畭呭牨獥潨摬㴠㌠〰਻††晩⠠潴⁰㴽猠汥⥦笠 †††爠瑥牵牴敵਻††੽ †椠⁦琨灹潥⡦楷摮睯椮湮牥楗瑤⥨㴠‽渧浵敢❲⤠笠 †††眠㴠眠湩潤⹷湩敮坲摩桴਻††††⁨‽楷摮睯椮湮牥效杩瑨਻††੽††汥敳椠⁦搨捯浵湥⹴潤畣敭瑮汅浥湥⁴☦⠠潤畣敭瑮搮捯浵湥䕴敬敭瑮挮楬湥坴摩桴簠⁼潤畣敭瑮搮捯浵湥䕴敬敭瑮挮楬湥䡴楥桧⥴
੻††††⁷‽潤畣敭瑮搮捯浵湥䕴敬敭瑮挮楬湥坴摩桴਻††††⁨‽潤畣敭瑮搮捯浵湥䕴敬敭瑮挮楬湥䡴楥桧㭴 †素 †攠獬⁥晩⠠潤畣敭瑮戮摯⁹☦⠠潤畣敭瑮戮摯⹹汣敩瑮楗瑤⁨籼搠捯浵湥⹴潢祤挮楬湥䡴楥桧⥴
੻††††⁷‽潤畣敭瑮戮摯⹹汣敩瑮楗瑤㭨 †††栠㴠搠捯浵湥⹴潢祤挮楬湥䡴楥桧㭴 †素ਊ††敲畴湲⠠眨㸠洠湩浩浵桔敲桳汯⥤☠…栨㸠洠湩浩浵桔敲桳汯⥤㬩紊⤨⤩㬩ਊਊ楷摮睯漮汮慯⁤‽畦据楴湯⤨笠 †瘠牡映㴠搠捯浵湥⹴敧䕴敬敭瑮祂摉∨祬潣䙳潯整䅲≤㬩 †瘠牡戠㴠搠捯浵湥⹴敧䕴敬敭瑮䉳呹条慎敭∨潢祤⤢せ㭝 †戠愮灰湥䍤楨摬昨㬩 †映献祴敬搮獩汰祡㴠∠汢捯≫਻††潤畣敭瑮朮瑥汅浥湥䉴䥹⡤氧捹獯潆瑯牥摁䙩慲敭⤧献捲㴠✠愯浤愯⽤潦瑯牥摁椮牦浡⹥瑨汭㬧ਊ††⼯匠楬敤⁲湉敪瑣潩੮††昨湵瑣潩⡮
੻††††慶⁲⁥‽潤畣敭瑮挮敲瑡䕥敬敭瑮✨晩慲敭⤧਻††††⹥瑳汹⹥潢摲牥㴠✠✰਻††††⹥瑳汹⹥慭杲湩㴠〠਻††††⹥瑳汹⹥楤灳慬⁹‽戧潬正㬧 †††攠献祴敬挮獳汆慯⁴‽爧杩瑨㬧 †††攠献祴敬栮楥桧⁴‽㈧㐵硰㬧 †††攠献祴敬漮敶晲潬⁷‽栧摩敤❮਻††††⹥瑳汹⹥慰摤湩⁧‽㬰 †††攠献祴敬眮摩桴㴠✠〳瀰❸਻††††⹥牳⁣‽⼧摡⽭摡猯楬敤䅲⹤晩慲敭栮浴❬਻††††慶⁲汳摩牥求捯‽潤畣敭瑮朮瑥汅浥湥䉴䥹⡤氧獹楬敤⵲摡汢捯⵫牷灡数❲㬩 †††瘠牡猠楬敤䡲汯敤⁲‽潤畣敭瑮朮瑥汅浥湥䉴䥹⡤氧獹楬敤⵲摡汢捯⵫潨摬牥⤧਻††††慶⁲汳摩牥汃獯⁥‽潤畣敭瑮朮瑥汅浥湥䉴䥹⡤氧獹楬敤⵲摡汢捯⵫汣獯❥㬩 †††猠楬敤䉲潬正献祴敬搮獩汰祡㴠✠汢捯❫਻ †††猠楬敤䍲潬敳漮据楬正㴠映湵瑣潩⡮
੻††††††汳摩牥求捯⹫慰敲瑮潎敤爮浥癯䍥楨摬猨楬敤䉲潬正㬩 †††††爠瑥牵慦獬㭥 †††素ਊ††††慶⁲晩慲敭湏潬摡㴠映湵瑣潩⡮
੻††††††敳呴浩潥瑵⠨畦据楴湯猠楬楩敤⤨笠 †††††††瘠牡猠㴠⠠楷摮睯朮瑥潃灭瑵摥瑓汹⥥㼠瀠牡敳湉⡴敧䍴浯異整卤祴敬猨楬敤䡲汯敤⥲爮杩瑨
›慰獲䥥瑮猨楬敤䡲汯敤⹲畣牲湥却祴敬爮杩瑨㬩 †††††††椠⁦猨㰠‽⤰笠 †††††††††猠楬敤䡲汯敤⹲瑳汹⹥楲桧⁴‽猨⬠㘠
‫瀧❸਻††††††††††敳呴浩潥瑵猨楬楩敤‬〱㬩 †††††††素 †††††††攠獬⁥੻††††††††††汳摩牥潈摬牥献祴敬爮杩瑨㴠✠瀰❸਻††††††††††汳摩牥汃獯⹥瑳汹⹥楤灳慬⁹‽戧潬正㬧 †††††††素 †††††素Ⱙㄠ〰⤰਻††††੽ †††椠⁦攨愮瑴捡䕨敶瑮
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