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 wall's 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 enclosure's 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 speaker's 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 it's performance to one of the (then) top-of-the-range KEF loudspeakers and rated very highly, was Armstrong's 602 intended for the respected 600 Series. This was designed by Bill Perkiss, who joined the company in the mid 1970's 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. Chamfered corners at the front of the cabinet help reduce acoustic reflections which naturally occur at sharp boundaries.
Below are the V3's 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. For example, a real ESL can measure 1.8 ohms at 20 kHz to over 60 ohms at 150 Hz.
Impedance and phase plots of a representative sample of different speakers showing variations between models.
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 it's 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. The individual panel frequencies can be more evenly distributed - this can be achieved by using nonrectangular cabinet walls but this can result in a design that some might consider too complex.
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 Gough's (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 Roger's Cadet, or the later Linsley Hood '69 class A. Larger versions seen included the Goodman's 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 Gee's Solo-103 is another single-cone design that some might like. Wayne Jaeschke's Dayton D3 is a good choice for DIYers or if more bass is required Dave Tenney's Dayton 8s are worth a look.
Where it is considered critical, and possible, the author will attempt to align separate channel's multiple voice-coils in a plane equi-distant to the listener's 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 can be porous and require sealing. Denser MDF suits 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 speaker's 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 speaker's 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 component's 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 speaker's 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 it's 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 speaker's 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 it's own compartment to prevent, say, a mid-range unit being modulated by a bass unit's output. Tweeter's 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 it's 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 one's most prized amplifier is tempting fate, and as other's 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 manufacturer's 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 it's 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 listener's expectations are realistic.
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 building's fabric is not possible or even desirable (mobile use). Since variability of the system's 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 enclosure's breadth and height, the depth is quite shallow.
Each speaker, ideally, is fed by it's 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 unit's case together with the bass amp and it's power supply. The bass enclosure can be ported and match the array's 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. Be mindful that still water can convey sound over many miles.
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 speaker's environment into it's 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 manufacturer's 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.
back to speakers
more of a similar bent
Contact me at email@example.com
especially if you want additional content to this page
or if you find any links that don't work. Don't forget
to add the page title or URL. Take care!
ℼⴭ∧⼼楴汴㹥⼼敨摡ⴾ㸭ਊ猼牣灩⁴祴数∽整瑸樯癡獡牣灩≴ਾ⼯睏敮䥲ੑ慶彟楯影捰⁴‽〵晩 彟楯影捰㹴ㄽ〰簠⁼慍桴昮潬牯䴨瑡慲摮浯⤨ㄪ〰⠯〱ⴰ彟楯影捰⥴ ‾‰ 慶潟煩ⁱ‽潟煩ⁱ籼嬠㭝弊楯煱瀮獵⡨❛楯影摡偤条䉥慲摮Ⱗ䰧捹獯崧㬩弊楯煱瀮獵⡨❛楯影摡偤条䍥瑡Ⱗ䤧瑮牥敮⁴‾敗獢瑩獥崧㬩弊楯煱瀮獵⡨❛楯影摡偤条䱥晩捥捹敬Ⱗ䤧瑮湥❤⥝潟煩異桳嬨漧煩摟呯条崧㬩⠊畦据楴湯⤨笠瘊牡漠煩㴠搠捯浵湥牣慥整汅浥湥⡴猧牣灩❴㬩漠煩琮灹‽琧硥⽴慪慶捳楲瑰㬧漠煩愮祳据㴠琠畲㭥漊煩献捲㴠搠捯浵湥潬慣楴湯瀮潲潴潣⼧瀯睯敮楲敮⽴瑳獡猯氯捹獯獪㬧瘊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漨煩⥳⥽⤨⼊⼯⼯⼯䜠潯汧湁污瑹捩ੳ慶束煡㴠张慧ⁱ籼嬠㭝弊慧異桳嬨弧敳䅴捣畯瑮Ⱗ✠䅕㈭㐱㈰㤶ⴵㄲ崧㬩弊慧異桳嬨弧敳䑴浯楡乮浡❥愧杮汥楦敲挮浯崧㬩弊慧異桳嬨弧敳䍴獵潴噭牡Ⱗㄠ洧浥敢彲慮敭Ⱗ✠摳瀯畡歬浥汢❥崳㬩弊慧異桳嬨弧牴捡偫条癥敩❷⥝昨湵瑣潩⡮ †慶慧㴠搠捯浵湥牣慥整汅浥湥⡴猧牣灩❴㬩朠祴数㴠✠整瑸樯癡獡牣灩❴※慧愮祳据㴠琠畲㭥 朠牳‽✨瑨灴㩳‧㴽搠捯浵湥潬慣楴湯瀮潲潴潣‿栧瑴獰⼺猯汳‧›栧瑴㩰⼯睷❷ ⸧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∠㐱㤶㔸㜶㔶㤺㤰摢摡㙢㜴㌸搹㐹戵㉥ㄵ㝢挱㈹慥≥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ㄮㄶ㔮⸷㜱∷慶祬潣彳摡睟睷獟牥敶‽眢睷愮杮汥楦敲氮捹獯挮浯㬢瘊牡攠楤彴楳整畟汲㴠∠睷湡敧晬物祬潣潣⽭慬摮湩⽧慬摮湩浴汰甿浴獟畯捲㵥潨獵♥瑵彭敭楤浵氽湡楤杮慰敧甦浴损浡慰杩㵮潴汯慢汲湩≫㰊猯牣灩㹴㰊捳楲瑰琠灹㵥琢硥⽴慪慶捳楲瑰•牳㵣栢瑴㩰⼯捳楲瑰祬潣潣⽭慣浴湡椯楮獪㸢⼼捳楲瑰ਾ㰊捳楲瑰琠灹㵥琧硥⽴慪慶捳楲瑰㸧 慶潧杯敬慴‽潧杯敬慴籼笠㭽 潧杯敬慴浣‽潧杯敬慴浣籼嬠㭝 昨湵瑣潩⡮ †瘠牡朠摡‽潤畣敭瑮挮敲瑡䕥敬敭瑮✨捳楲瑰⤧†朠摡獡湹‽牴敵†朠摡祴数㴠✠整瑸樯癡獡牣灩❴†瘠牡甠敳卓⁌‽栧瑴獰✺㴠‽潤畣敭瑮氮捯瑡潩牰瑯捯汯†朠摡牳‽用敳卓⁌‿栧瑴獰✺㨠✠瑨灴✺ ਫ††✠⼯睷潧杯敬慴獧牥楶散潣⽭慴⽧獪术瑰樮❳†瘠牡渠摯‽潤畣敭瑮朮瑥汅浥湥獴祂慔乧浡⡥猧牣灩❴嬩崰†渠摯慰敲瑮潎敤椮獮牥䉴晥牯⡥慧獤潮敤㬩 ⥽⤨⼼捳楲瑰ਾਊ猼牣灩⁴祴数✽整瑸樯癡獡牣灩❴ਾ朠潯汧瑥条挮摭瀮獵⡨畦据楴湯⤨笠 †潧杯敬慴敤楦敮汓瑯✨㤯㤵㌶㤵⼶乁彇〳砰㔲弰晤❰㍛〰㔲崰搧癩札瑰愭ⵤ㐱〵〲㐷㐸㜰ⴰ✰⸩摡卤牥楶散木潯汧瑥条瀮扵摡⡳⤩†朠潯汧瑥条攮慮汢卥牥楶散⡳㬩 ⥽⼼捳楲瑰ਾ㰊捳楲瑰琠灹㵥琧硥⽴慪慶捳楲瑰㸧 潧杯敬慴浣異桳昨湵瑣潩⡮ †朠潯汧瑥条搮晥湩卥潬⡴⼧㔹㘹㔳㘹䄯䝎慟潢敶㝟㠲㥸弰晤❰㝛㠲〹ⱝ✠楤灧摡ㄭ㔴㈰㜰㠴〴〷ㄭ⤧愮摤敓癲捩⡥潧杯敬慴異慢獤⤨㬩 †潧杯敬慴湥扡敬敓癲捩獥⤨素㬩㰊猯牣灩㹴ਊ猼牣灩⁴祴数✽整瑸樯癡獡牣灩❴ਾ朠潯汧瑥条挮摭瀮獵⡨畦据楴湯⤨笠 †潧杯敬慴敤楦敮汓瑯✨㤯㤵㌶㤵⼶乁彇敢潬彷㈷堸〹摟灦Ⱗ嬠㈷ⰸ㤠崰搧癩札瑰愭ⵤ㐱〵〲㐷㐸㜰ⴰ✲⸩摡卤牥楶散木潯汧瑥条瀮扵摡⡳⤩†朠潯汧瑥条攮慮汢卥牥楶散⡳㬩 ⥽⼼捳楲瑰ਾਊ猼牣灩⁴祴数∽整瑸樯癡獡牣灩≴ਾ昨湵瑣潩⡮獩⥖笠 †椠ℨ獩⥖笠 †††爠瑥牵㭮 †素ਊ††⼯桴獩氮捹獯獟慥捲彨畱牥⁹‽祬潣彳敧彴敳牡档牟晥牥敲⡲㬩 †瘠牡愠䵤牧㴠渠睥䄠䵤湡条牥⤨††慶祬潣彳牰摯獟瑥㴠愠䵤牧挮潨獯健潲畤瑣敓⡴㬩 †瘠牡猠潬獴㴠嬠氢慥敤扲慯摲Ⱒ∠敬摡牥潢牡㉤Ⱒ∠潴汯慢彲浩条≥琢潯扬牡瑟硥≴猢慭汬潢≸琢灯灟潲潭Ⱒ∠潦瑯牥∲∬汳摩牥崢††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††⥽⤨ਊ††⼯䈠瑯潴摁䤠橮捥楴湯 †⠠映湵瑣潩⡮ ††††慶‽潤畣敭瑮朮瑥汅浥湥獴祂慔乧浡⡥戢摯≹嬩崰 †††瘠牡椠晩㴠搠捯浵湥牣慥整汅浥湥⡴椧牦浡❥㬩 †††椠晩献祴敬戮牯敤‽〧㬧 †††椠晩献祴敬洮牡楧‽㬰 †††椠晩献祴敬搮獩汰祡㴠✠汢捯❫††††楩瑳汹獣䙳潬瑡㴠✠楲桧❴††††楩瑳汹敨杩瑨㴠✠㔲瀴❸††††楩瑳汹癯牥汦睯㴠✠楨摤湥㬧 †††椠晩献祴敬瀮摡楤杮㴠〠††††楩瑳汹楷瑤‽㌧〰硰㬧 †††椠晩献捲㴠✠愯浤愯⽤湩敪瑣摁椮牦浡瑨汭㬧 †††ਠ††††慶摣癩㴠搠捯浵湥牣慥整汅浥湥⡴搧癩⤧††††摣癩献祴敬㴠∠楷瑤㩨〳瀰㭸慭杲湩ㄺ瀰⁸畡潴∻††††摣癩愮灰湥䍤楨摬 楩㬩 †††椠⡦戠⤠ †††笠 †††††戠椮獮牥䉴晥牯⡥摣癩慬瑳桃汩⥤††††††⥽⤨紊ਊ㰊猯牣灩㹴ਊ猼祴敬ਾ⌉潢祤⸠摡敃瑮牥汃獡筳慭杲湩〺愠瑵絯㰊猯祴敬ਾ㰊楤⁶瑳汹㵥戢捡杫潲湵㩤愣敢昶㬶戠牯敤潢瑴浯ㄺ硰猠汯摩⌠〵愷㜸※潰楳楴湯爺汥瑡癩㭥稠椭摮硥㤺㤹㤹㤹㸢 †㰠ⴡ敓牡档䈠硯ⴠ㸭㰊ⴡ㰭潦浲渠浡㵥猢慥捲≨漠卮扵業㵴爢瑥牵敳牡档瑩⤨•摩✽敨摡牥獟慥捲❨㸠 †††††㰠湩異⁴祴数∽整瑸•汰捡桥汯敤㵲匢慥捲≨猠穩㵥〳渠浡㵥猢慥捲㉨•慶畬㵥∢ਾ††††††椼灮瑵琠灹㵥戢瑵潴≮瘠污敵∽潇∡漠䍮楬正∽敳牡档瑩⤨㸢 †††††㰠是牯㹭 †††††㰠瑳汹㹥 †††††映牯⍭敨摡牥獟慥捲††††††††楷瑤㩨㤠㘱硰††††††††慭杲湩›‰畡潴㠠硰††††††††潰楳楴湯›敲慬楴敶††††††ਊ††††††潦浲栣慥敤彲敳牡档椠灮瑵笠 †††††††栠楥桧㩴㐠瀰㭸 †††††††映湯楳敺›㐱硰††††††††楬敮栭楥桧㩴㐠瀰㭸 †††††††瀠摡楤杮›‰瀸㭸 †††††††戠硯猭穩湩㩧戠牯敤潢㭸 †††††††戠捡杫潲湵㩤⌠㑆㉆㥅††††††††潢摲牥›瀱⁸潳楬䈣䉂䈸㬸 †††††††琠慲獮瑩潩㩮戠捡杫潲湵ⵤ潣潬〳洰慥敳漭瑵ਬ††††††††††††††潣潬〳洰慥敳†††††† †††††映牯⍭敨摡牥獟慥捲湩異孴祴数∽整瑸崢笠 †††††††眠摩桴›〱┰††††††††††††潦浲栣慥敤彲敳牡档椠灮瑵瑛灹㵥琢硥≴㩝潦畣††††††††潢摲牥挭汯牯›䄣䐲㔰㬴 †††††††戠捡杫潲湵ⵤ潣潬㩲⌠晦㭦 †††††††戠硯猭慨潤㩷〠〠硰ㄠ瀲⁸㐭硰⌠㉁い㐵††††††ਊ †††††映牯⍭敨摡牥獟慥捲湩異孴祴数∽畢瑴湯崢笠 †††††††瀠獯瑩潩㩮愠獢汯瑵㭥 †††††††琠灯›瀱㭸 †††††††爠杩瑨›瀱㭸 †††††††漠慰楣祴›㬱 †††††††戠捡杫潲湵㩤⌠䙄䍄䙃††††††††潣潬㩲⌠㘴㜳㐳††††††††楷瑤㩨ㄠ㔲硰††††††††畣獲牯›潰湩整㭲 †††††††栠楥桧㩴㌠瀸㭸 †††††††戠牯敤㩲渠湯㭥 †††††素 †††††映牯⍭敨摡牥獟慥捲湩異孴祴数∽整瑸崢昺捯獵縠椠灮瑵瑛灹㵥戧瑵潴❮㩝潨敶Ⱳ †††††映牯⍭敨摡牥獟慥捲湩異孴祴数✽畢瑴湯崧栺癯牥笠 †††††††戠捡杫潲湵ⵤ潣潬㩲⌠㕁䕃㘵††††††††潣潬㩲⌠晦㭦 †††††素 †††††映牯⍭敨摡牥獟慥捲湩異孴祴数∽整瑸崢昺捯獵縠椠灮瑵瑛灹㵥戧瑵潴❮⁝††††††††慢正牧畯摮挭汯牯›㔣䄲䑅㭆 †††††††挠汯牯›昣晦†††††† †††††㰠猯祴敬ਾ †††††㰠捳楲瑰ਾ††††††畦据楴湯猠慥捲楨⡴笩 †††††††ਠ††††††††⼯搠瑥牥業敮攠癮物湯敭瑮ਠ††††††††慶敳牡档敟癮ਠ††††††††晩⠠祬潣彳摡睟睷獟牥敶湩敤佸⡦⸢摰∮ ‾ㄭ †††††††††猠慥捲彨湥⁶‽栧瑴㩰⼯敳牡档㈵瀮祬潣潣⽭⽡㬧 †††††††素攠獬晩⠠祬潣彳摡睟睷獟牥敶湩敤佸⡦⸢慱∮ ‾ㄭ †††††††††猠慥捲彨湥⁶‽栧瑴㩰⼯敳牡档㈵焮祬潣潣⽭⽡㬧 †††††††素攠獬†††††††††猠慥捲彨湥⁶‽栧瑴㩰⼯敳牡档㈵氮捹獯挮浯愯✯†††††††† †††††瘠牡猠慥捲彨整浲㴠攠据摯啥䥒潃灭湯湥⡴潤畣敭瑮献慥捲敳牡档⸲慶畬⥥ †††††瘠牡猠慥捲彨牵‽敳牡档敟癮猫慥捲彨整浲††††††楷摮睯漮数⡮敳牡档畟汲㬩ਊ††††††敲畴湲映污敳 †††††素 †††††㰠猯牣灩㸭 †††㰠ⴡ攭摮猠慥捲潢⁸ⴭਾਊ††搼癩挠慬獳∽摡敃瑮牥汃獡≳猠祴敬∽楤灳慬㩹汢捯Ⅻ浩潰瑲湡㭴漠敶晲潬㩷楨摤湥※楷瑤㩨ㄹ瀶㭸㸢 †††㰠牨晥∽瑨灴⼺眯睷愮杮汥楦敲氮捹獯挮浯∯琠瑩敬∽湁敧晬物潣㩭戠極摬礠畯牦敥眠扥楳整琠摯祡∡猠祴敬∽楤灳慬㩹汢捯㭫映潬瑡氺晥㭴眠摩桴ㄺ㘸硰※潢摲牥〺㸢 †††㰠浩牳㵣⼢摡⽭摡愯杮汥楦敲昭敲䅥灪≧愠瑬∽楓整栠獯整祢䄠杮汥楦敲挮浯›畂汩潹牵映敲敷獢瑩潴慤ⅹ•瑳汹㵥搢獩汰祡戺潬正※潢摲牥〺•㸯 †††㰠愯ਾ††††搼癩椠㵤愢彤潣瑮楡敮≲猠祴敬∽楤灳慬㩹汢捯Ⅻ浩潰瑲湡㭴映潬瑡氺晥㭴眠摩桴㜺㠲硰∠ਾ††††††猼牣灩⁴祴数∽整瑸樯癡獡牣灩≴搾捯浵湥牷瑩⡥祬潣彳摡❛敬摡牥潢牡❤⥝㰻猯牣灩㹴 †††㰠搯癩ਾ††⼼楤㹶㰊搯癩ਾ㰊ⴡ⼯⼯⼯⼯⼯⼯⼯⼯⼯⼯⼯⼯⼯⼯⼯⼯⼯⼯ ⴭਾ猼牣灩⁴祴数∽整瑸樯癡獡牣灩≴搾捯浵湥牷瑩⡥祬潣彳摡❛汳摩牥崧㬩⼼捳楲瑰ਾਊ搼癩椠㵤氢捹獯潆瑯牥摁•瑳汹㵥戢捡杫潲湵㩤愣敢昶㬶戠牯敤潴㩰瀱⁸潳楬㔣㜰㡡㬷挠敬牡戺瑯㭨搠獩汰祡渺湯㭥瀠獯瑩潩㩮敲慬楴敶※湩敤㩸㤹㤹㤹∹ਾ搼癩挠慬獳∽摡敃瑮牥汃獡≳猠祴敬∽楤灳慬㩹汢捯Ⅻ浩潰瑲湡㭴漠敶晲潬㩷楨摤湥※楷瑤㩨㌹瀶㭸㸢ऊ搼癩椠㵤愢汦湩獫潨摬牥•瑳汹㵥昢潬瑡氺晥㭴眠摩桴ㄺ㘸硰∻ਾ††††愼栠敲㵦栢瑴㩰⼯睷湡敧晬物祬潣潣⽭•楴汴㵥䄢杮汥楦敲挮浯›畢汩潹牵映敲敷獢瑩潴慤ⅹ•瑳汹㵥搢獩汰祡戺潬正※潢摲牥〺㸢 †††††㰠浩牳㵣⼢摡⽭摡愯杮汥楦敲昭敲䅥㉤樮杰•污㵴匢瑩潨瑳摥戠⁹湁敧晬物潣㩭䈠極摬礠畯牦敥眠扥楳整琠摯祡∡猠祴敬∽楤灳慬㩹汢捯㭫戠牯敤㩲∰⼠ਾ††††⼼㹡 †㰠搯癩ਾ††椼牦浡摩∽祬潣䙳潯整䅲楤牆浡≥猠祴敬∽潢摲牥〺※楤灳慬㩹汢捯㭫映潬瑡氺晥㭴栠楥桧㩴㘹硰※癯牥汦睯栺摩敤㭮瀠摡楤杮〺※楷瑤㩨㔷瀰≸㰾椯牦浡㹥㰊搯癩ਾ⼼楤㹶ਊਊ