SOUTH COAST AIR QUALITY MANAGEMENT DISTRICT 

METHOD 5.2 

DETERMINATION OF PARTICULATE MATTER EMISSIONS FROM 

STATIONARY SOURCES USING HEATED PROBE AND FILTER 

MONITORING & ANALYSIS 

MARCH 1989 
”¤Ãÿ—‹ ÎÚÓ 

‹¤Ã¤Œ”×“flÃ×—“ —⁄ –flŒÃ×›À‘flÃ¤ ”flÃÃ¤Œ ¤”×ÕÕ×—“Õ ⁄Œ—” 

ÕÃflÃ×—“flŒ« Õ—ÀŒ›¤Õ ÀÕ×“Ÿ ÿ¤flÃ¤‹ –Œ—fi¤ fl“‹ ⁄×‘Ã¤Œ 

Ãflfi‘¤ —⁄ ›—“Ã¤“ÃÕ 

Õa1⁄2 ̈·±2 

ÔÚ —TMaÆTM·a©

ÔÚÔ –Æ·21⁄2·°¥a 

ÔÚÓ ⁄·¥ ̈aÆ Ãa3°aÆø ̈ ́Æa 

ÔÚÌ fl°°¥·1⁄2øæ·¥· ̈ß 

ÓÚ ⁄·a¥o –Æ±1⁄2ao ́ÆaÓÚÔ Õø3°¥·21 fl°°øÆø ̈ ́­ 

ÓÚÓ Õø3°¥·21 Œaø1a2 ̈­ 

ÓÚÌ –Æa ̈a­ ̈ ‹a ̈aÆ3·2ø ̈·±2­ 

ÓÚÏ Ÿø­ ±¥ ́3a ”a ̈aÆ › ̧a1⁄2μÓÚÎ –Æa ̈a­ ̈ –Æa°øÆø ̈·±2 

ÓÚÍ ‘aøμ › ̧a1⁄2μÓÚÈ Õø3°¥·21 ÃÆø·2 —°aÆø ̈·±2 

ÓÚË ›ø¥1⁄2 ́¥ø ̈·±2 ±o –aÆ1⁄2a2 ̈ ×­±μ·2a ̈·1⁄2 

ÓÚÁ Õø3°¥a ÿø2o¥·21 

ÓÚÔð ›ø¥·æÆø ̈·±2­ 
ÌÚ ‘øæ±Æø ̈±Æß –Æ±1⁄2ao ́ÆaÌÚÔ fl°°øÆø ̈ ́­ 

ÌÚÓ Œaø1a2 ̈­ 

ÌÚÌ –Æa ̈a­ ̈ –Æa°øÆø ̈·±2 

ÌÚÏ –Æa°øÆø ̈·±2 ±o Õø3°¥a ›±¥¥a1⁄2 ̈·±2 ÃÆø·2 

ÌÚÎ ‘aøμ › ̧a1⁄2μ 

ÌÚÍ Õø3°¥a Œa1⁄2±TMaÆß 

ÌÚÈ fl2ø¥ß­·­ 

ÌÚË ›ø¥1⁄2 ́¥ø ̈·±2­ ø2o Œa°±Æ ̈·21 

ÌÚÁ ›ø¥·æÆø ̈·±2­ 

ÏÚ ¤21·2aaÆ·21 ›ø¥1⁄2 ́¥ø ̈·±2­ ø2o Œa°±Æ ̈·21 

ÏÚÔ ›ø¥1⁄2 ́¥ø ̈·±2­ 
ÎÚÓÛÔ

”¤Ãÿ—‹ ÎÚÓ 

‹¤Ã¤Œ”×“flÃ×—“ —⁄ –flŒÃ×›À‘flÃ¤ ”flÃÃ¤Œ ¤”×ÕÕ×—“Õ ⁄Œ—” ÕÃflÃ×—“flŒ« 

Õ—ÀŒ›¤Õ ÀÕ×“Ÿ ÿ¤flÃ¤‹ –Œ—fi¤ fl“‹ ⁄×‘Ã¤Œ 

Õa1⁄2 ̈·±2 Ô ±o Ï 

ÔÚ —TMaÆTM·a© 

ÔÚÔ –Æ·21⁄2·°¥a 

fl ­ø3°¥a ·­ ©· ̈ ̧oÆø©2 ·­±μ·2a ̈·1⁄2ø¥¥ß oÆ±3  ̈ ̧a 

­± ́Æ1⁄2a  ̈ ̧Æ± ́1 ̧ ø ­ø3°¥a  ̈Æø·2 æß ø 3a ̈aÆ·21 ­ß­ ̈a3Ú 

⁄·¥ ̈aÆøæ¥a °øÆ ̈·1⁄2 ́¥ø ̈a 3ø ̈ ̈aÆ ·­ 1⁄2±¥¥a1⁄2 ̈ao ±2 ø 

 ̧aø ̈ao 1¥ø­­ o·æaÆ o·¥ ̈aÆÚ ›±2oa2­øæ¥a­ ø2o 

°øÆ ̈·1⁄2 ́¥ø ̈a °ø­­·21  ̈ ̧Æ± ́1 ̧  ̈ ̧a o·¥ ̈aÆ øÆa 1⁄2±¥¥a1⁄2 ̈ao 

·2 ·3°·21aÆ­ 1⁄2±2 ̈ø·2·21 oa·±2·¶ao ©ø ̈aÆÚ Ã ̧a 

·3°·21aÆ­ øÆa 1⁄2±2 ̈ø·2ao ·2 ø2 ·1⁄2a æø ̈ ̧  ̈± 3ø·2 ̈ø·2 ø 

­ø3°¥ao 1ø­  ̈a3°aÆø ̈ ́Æa ±o ø°°Æ±®·3ø ̈a¥ß ÔÎ±› 

 ̄Íð±⁄ ̃Ú fl ­a°øÆø ̈a  ̈Æø·2 o±Æ ­ ́¥o ́Æ·1⁄2 ø1⁄2·o 3·­ ̈ 3øß 

æa ÆaØ ́·Æao  ̄­aa Õa1⁄2 ̈·±2 ÔÚÓ ̃Ú 

Ã ̧a  ̈± ̈ø¥ °øÆ ̈·1⁄2 ́¥ø ̈a 3ø­­Ù 3aø­ ́Æao 

1ÆøTM·3a ̈Æ·1⁄2ø¥¥ßÙ ·­ oao·2ao ø­  ̈ ̧a ­ ́3 ±o  ̈ ̧a 3ø­­ 

1⁄2±¥¥a1⁄2 ̈ao oÆ±3  ̈ ̧a °Æ±æaÙ o·¥ ̈aÆÙ ©ø­ ̧·21­Ù ø2o 
ÎÚÓÛÓ

·3°·21aÆ­ øo ̈aÆ Æa3±TMø¥ ±o  ́21⁄2±3æ·2ao ©ø ̈aÆÙ  ̈ ̧a 

±Æ1ø2·1⁄2 a® ̈Æø1⁄2 ̈·±2Ù ø2o  ̈ ̧a ­ ́¥o ́Æ·1⁄2 ø1⁄2·o 3·­ ̈ 

1⁄2±¥¥a1⁄2 ̈ao ·2 ø ­a°øÆø ̈a Õ—®  ̈Æø·2  ̄·o ÆaØ ́·Æao ̃Ú 

Ã ̧a ­±¥·o °øÆ ̈·1⁄2 ́¥ø ̈a 3ø ̈ ̈aÆ ·­ oao·2ao ø­  ̈± ̈ø¥ 

°øÆ ̈·1⁄2 ́¥ø ̈a 3ø ̈ ̈aÆ 3·2 ́­ a® ̈Æø1⁄2 ̈øæ¥a ±Æ1ø2·1⁄2 3ø ̈ ̈aÆ 

ø2o ­ ́¥o ́Æ·1⁄2 ø1⁄2·oÚ 

fl2 øo¶ ́­ ̈3a2 ̈  ̈±  ̈ ̧a ·3°·21aÆ 1⁄2ø ̈1⁄2 ̧ ·­ ø¥¥±©ao 

o±Æ ­ ́¥o ́Æ·1⁄2 ø1⁄2·o o±Æ3ao oÆ±3 Æaø1⁄2 ̈·±2­ æa ̈©aa2 Õ—Ó

ø2o Õ—Ì ©· ̈ ̧  ̈ ̧a ­ø3°¥a  ̈Æø·2 1⁄2±3°±2a2 ̈­Ú ... ̧a2 

ø33±2·ø ·­ ·2¶a1⁄2 ̈ao  ̈± a2 ̧ø21⁄2a  ̈ ̧a aoo·1⁄2·a21⁄2ß ±o ø 

1⁄2±2 ̈Æ±¥ oaTM·1⁄2aÙ ø ­a1⁄2±2o øo¶ ́­ ̈3a2 ̈  ̈±  ̈ ̧a ·3°·21aÆ 

1⁄2ø ̈1⁄2 ̧ ·­ ø¥¥±©ao o±Æ  ̈± ̈ø¥ ­ ́¥oø ̈aÚ Ã ̧·­ øo¶ ́­ ̈3a2 ̈ 

·­ ø¥¥±©ao o±Æ o¥ ́·o 1⁄2ø ̈ø¥ß ̈·1⁄2 1⁄2Æø1⁄2μ·21  ́2· ̈­ ±2¥ßÚ 

fia1⁄2ø ́­a ±o  ̈ ̧a 1⁄2±3°¥a®· ̈ß ±o  ̈ ̧·­ 3a ̈ ̧±o  ̈a­ ̈aÆ­ 

3 ́­ ̈ æa  ̈Æø·2ao ø2o a®°aÆ·a21⁄2ao ·2  ̈ ̧a  ̈a­ ̈ 

°Æ±1⁄2ao ́Æa­Ú 

ÔÚÓ –Æ±æa ø2o ⁄·¥ ̈aÆ Ãa3°aÆø ̈ ́Æa 

–øÆ ̈·1⁄2 ́¥ø ̈a 3ø ̈ ̈aÆ °ø­­·21  ̈ ̧Æ± ́1 ̧  ̈ ̧a °Æ±æa ø2o 

o·¥ ̈aÆ ·­ 1⁄2ø ́1 ̧ ̈ ·2  ̈ ̧a ·3°·21aÆ­Ú Õ±3a ±o  ̈ ̧a 

°øÆ ̈·1⁄2 ́¥ø ̈a °ø­­·21  ̈ ̧Æ± ́1 ̧  ̈ ̧a  ̧aø ̈ao °Æ±æa ø2o 

o·¥ ̈aÆ 3øß æa a· ̈ ̧aÆ ­ ́æ¥·3ao ±Æ ­ ́æ3·1⁄2Æ±2 ­±¥·o 
ÎÚÓÛÌ

°øÆ ̈·1⁄2 ́¥ø ̈a 3ø ̈ ̈aÆÙ ø2o  ̈ ̧aÆao±Æa  ̈ ̧a °øÆ ̈·1⁄2 ́¥ø ̈a 

1⁄2ø ́1 ̧ ̈ ·2  ̈ ̧a °Æ±æa ø2o o·¥ ̈aÆ o±a­ 2± ̈ 3aa ̈  ̈ ̧a 

oao·2· ̈·±2 ±o ­±¥·o °øÆ ̈·1⁄2 ́¥ø ̈a 3ø ̈ ̈aÆÚ 

×o  ̈ ̧a °Æ±æa ø2o o·¥ ̈aÆ øÆa μa° ̈ øæ±TMa ÁÌ±›  ̄Óðð±⁄ ̃ 

ø2o ­ ́¥o ́Æ·1⁄2 ø1⁄2·o ·­ °Æa­a2 ̈ ·2  ̈ ̧a ­ø3°¥ao 1ø­ ·2 

Ø ́ø2 ̈· ̈·a­ 1Æaø ̈aÆ  ̈ ̧ø2 Ôð °aÆ1⁄2a2 ̈ ±o  ̈ ̧a ­ ̈ø2oøÆo 

o±Æ ø°°¥·1⁄2øæ¥a Æ ́¥aÙ ø ­a°øÆø ̈a ø2o 1⁄2±21⁄2 ́ÆÆa2 ̈ 

3aø­ ́Æa3a2 ̈ ±o ­ ́¥o ́Æ·1⁄2 ø1⁄2·o ·­ ÆaØ ́·ÆaoÙ  ́­·21  ̈ ̧a 

°Æ±1⁄2a­­ oa­1⁄2Æ·æao ·2 ”a ̈ ̧±o ÍÚÔÚ ×o  ̈ ̧a °Æ±1⁄2a­­ ·­ 

­ ̈aøoß ­ ̈ø ̈a ø2o ­ ́¥o ́Æ·1⁄2 ø1⁄2·o ·­ ¥a­­  ̈ ̧ø2 Ôð 

°aÆ1⁄2a2 ̈ ±o  ̈ ̧a ­ ̈ø2oøÆo o±Æ  ̈ ̧a ø°°¥·1⁄2øæ¥a Æ ́¥aÙ 

1⁄2±21⁄2 ́ÆÆa2 ̈ ­ø3°¥·21 ·­ 2± ̈ ÆaØ ́·ÆaoÚ 

×o  ̈ ̧a  ̈a3°aÆø ̈ ́Æa ±o  ̈ ̧a °Æ±æa ø2o o·¥ ̈aÆ ·­ 

3ø·2 ̈ø·2ao ø ̈ ËÓÛÁÌ±›  ̄ÔËðÛÓðð±⁄ ̃Ù ø¥¥  ̈ ̧a ¥·Ø ́·o 

­ ́¥o ́Æ·1⁄2 ø1⁄2·o °Æa­a2 ̈ ·2  ̈ ̧a ­ø3°¥ao 1ø­ ©·¥¥ æa 

1⁄2ø ́1 ̧ ̈ æß  ̈ ̧a °Æ±æa ø2o o·¥ ̈aÆÚ 

ÔÚÌ fl°°¥·1⁄2øæ·¥· ̈ß 

Ã ̧·­ 3a ̈ ̧±o ·­  ́­ao  ̈± 3aø­ ́Æa °øÆ ̈·1⁄2 ́¥ø ̈a 

a3·­­·±2­ oÆ±3 ­ ̈ø ̈·±2øÆß ­± ́Æ1⁄2a­Ú ×o  ̈ ̧a °Æ±æa ø2o 

o·¥ ̈aÆ  ̈a3°aÆø ̈ ́Æa ·­ 3ø·2 ̈ø·2ao ø ̈ ÔÓð ı ÔÏ±›  ̄ÓÏË 

ı ÓÎ±⁄ ̃  ̈ ̧·­ 3a ̈ ̧±o 1⁄2ø2 æa o±¥¥±©ao o±Æ “Õ–Õ  ̈a­ ̈­Ú 
ÎÚÓÛÏ

 ̈a­ ̈­Ú —2¥ß  ̈ ̧a °øÆ ̈·1⁄2 ́¥ø ̈a 3ø ̈ ̈aÆ 1⁄2±¥¥a1⁄2 ̈ao ·2  ̈ ̧a 

°Æ±æa ø2o o·¥ ̈aÆ ·­  ́­ao 
ÎÚÓÛÎ

o±Æ “Õ–Õ 1⁄2±3°¥·ø21⁄2aÚ ⁄±Æ ‹·­ ̈Æ·1⁄2 ̈ Œ ́¥a­Ù  ̈ ̧a 

°øÆ ̈·1⁄2 ́¥ø ̈a 3ø ̈ ̈aÆ 1⁄2±¥¥a1⁄2 ̈ao ±2 æ± ̈ ̧  ̧ø¥TMa­ ±o  ̈ ̧a 

 ̈Æø·2 ·­  ́­aoÚ
ÎÚÓÛÍ

”¤Ãÿ—‹ ÎÚÓ 

‹¤Ã¤Œ”×“flÃ×—“ —⁄ –flŒÃ×›À‘flÃ¤ ”flÃÃ¤Œ ¤”×ÕÕ×—“Õ ⁄Œ—” 

ÕÃflÃ×—“flŒ« Õ—ÀŒ›¤Õ ÀÕ×“Ÿ ÿ¤flÃ¤‹ –Œ—fi¤ fl“‹ ⁄×‘Ã¤Œ 

Õa1⁄2 ̈·±2 Ó ±o Ï 

ÓÚ ⁄·a¥o –Æ±1⁄2ao ́ÆaÓÚÔ Õø3°¥·21 fl°°øÆø ̈ ́­ 

 ÓÚÔÚÔ Õø3°¥·21 ÃÆø·2 

fl ­1⁄2 ̧a3ø ̈·1⁄2 ±o  ̈ ̧a ­ø3°¥·21  ̈Æø·2  ́­ao ·2 

 ̈ ̧·­ 3a ̈ ̧±o ·­ ­ ̧±©2 ·2 ⁄·1 ́Æa ÎÚÓÛÔÚ Ã ̧a 

°Æ±1⁄2ao ́Æa o±Æ  ̈ ̧a °Æa°øÆø ̈·±2 ±o  ̈ ̧a ­ø3°¥a 

1⁄2±¥¥a1⁄2 ̈·±2  ̈Æø·2  ̄1⁄2±2­·­ ̈·21 ±o °Æ±æa ¥·2aÆÙ 

·3°·21aÆ  ̈Æø·2Ù ø2o o·¥ ̈aÆ  ̧±¥oaÆ ©· ̈ ̧ 

o·¥ ̈aÆ ̃ ·­ 1·TMa2 ·2 Õa1⁄2 ̈·±2 ÌÚÓÚÔÚ 

⁄·1 ́Æa ÎÚÓÛÔ ­ ̧±©­  ̈ ̧a ·3°·21aÆ  ̈Æø·2 øoo·®ao 

 ̈±  ̈ ̧a  ̧aø ̈ao o·¥ ̈aÆ æ±®Ú Ã ̧a ·3°·21aÆ­ 1⁄2ø2 

æa ­a°øÆø ̈a ø2o 1⁄2±22a1⁄2 ̈ao  ̈±  ̈ ̧a o·¥ ̈aÆ ©· ̈ ̧ 

·2aÆ ̈  ̈ ́æ·21  ̈ ̧ø ̈ ©·¥¥ ©· ̈ ̧­ ̈ø2o  ̈ ̧a o·¥ ̈aÆ 

± ́ ̈¥a ̈  ̈a3°aÆø ̈ ́ÆaÚ 
ÎÚÓÛÈ

Ã ̧a ­ø3°¥·21  ̈Æø·2 1⁄2±2­·­ ̈­ ±o  ̈ ̧a o±¥¥±©·21 

1⁄2±3°±2a2 ̈­Ê 

 øÚ –Æ±æa “±¶¶¥a 

Ã ̧a 2±¶¶¥a 3ø ̈aÆ·ø¥ ­ ̧± ́¥o æa ÌÔÍ 

­ ̈ø·2¥a­­ ­ ̈aa¥ ±Æ 1¥ø­­Ù ©· ̈ ̧ ­ ̧øÆ°Ù 

 ̈ø°aÆao ¥aøo·21 ao1aÚ Ã ̧a  ̈ø°aÆ ø21¥a 

­ ̧± ́¥o æa ‰ Ìð± ø2o ±2  ̈ ̧a ± ́ ̈­·oaÙ  ̈± 

°Æa­aÆTMa ø 1⁄2±2­ ̈ø2 ̈ ·2 ̈aÆ2ø¥ o·ø3a ̈aÆÚ 

Ã ̧a ­ ̈ø·2¥a­­ ­ ̈aa¥ 2±¶¶¥a ­ ̧± ́¥o æa 

1⁄2±2­ ̈Æ ́1⁄2 ̈ao oÆ±3 ­aø3¥a­­  ̈ ́æ·21Ú — ̈ ̧aÆ 

3ø ̈aÆ·ø¥­ © ̧·1⁄2 ̧ ©·¥¥ 2± ̈ æa 1⁄2±ÆÆ±oao æß 

 ̈ ̧a ­ø3°¥ao 1ø­a­ ±Æ ·2 ̈aÆoaÆa ©· ̈ ̧ 

­ø3°¥a Æa1⁄2±TMaÆß 3øß æa  ́­aoÚ 

fl Æø21a ±o 2±¶¶¥a ­·¶a­ ­ ́· ̈øæ¥a o±Æ 

·­±μ·2a ̈·1⁄2 ­ø3°¥·21 ­ ̧± ́¥o æa øTMø·¥øæ¥a 

·2 ·21⁄2Æa3a2 ̈­ ±o ðÚÔÍ 1⁄23  ̄ÔÒÔÍ ·2Ú ̃Ù aÚ1Ú 

ðÚÌÓ  ̈± ÔÚÓÈ 1⁄23  ̄ÔÒË  ̈± ÔÒÓ ·2Ú ̃ ±Æ 

¥øÆ1aÆ ·o  ̧·1 ̧aÆ TM±¥ ́3a ­ø3°¥·21  ̈Æø·2­ 

øÆa  ́­aoÚ 
ÎÚÓÛË

¤ø1⁄2 ̧ 2±¶¶¥a 3 ́­ ̈ æa 1⁄2ø¥·æÆø ̈ao ø1⁄21⁄2±Æo·21 

 ̈±  ̈ ̧a °Æ±1⁄2ao ́Æa ± ́ ̈¥·2ao ·2 ”a ̈ ̧±o ÎÚÔÙ 

Õa1⁄2 ̈·±2 ÓÚÔÚ 

 æÚ –Æ±æa ‘·2aÆ 

À­a æ±Æ±­·¥·1⁄2ø ̈a ±Æ Ø ́øÆ ̈¶ 1¥ø­­  ̈ ́æ·21 

©· ̈ ̧ ø  ̧aø ̈·21 ­ß­ ̈a3 1⁄2ø°øæ¥a ±o 

3ø·2 ̈ø·2·21 ø 1ø­  ̈a3°aÆø ̈ ́Æa øæ±TMa  ̈ ̧a 

oa© °±·2 ̈ ø ̈  ̈ ̧a a®· ̈ a2o o ́Æ·21 ­ø3°¥·21 

ø­ oa­1⁄2Æ·æao ·2 Õa1⁄2 ̈·±2 ÔÚÓÚ 

¤· ̈ ̧aÆ æ±Æ±­·¥·1⁄2ø ̈a ±Æ Ø ́øÆ ̈¶ 1¥ø­­ °Æ±æa 

¥·2aÆ­ 3øß æa  ́­ao o±Æ ­ ̈ø1⁄2μ  ̈a3°aÆø ̈ ́Æa­ 

 ́°  ̈± øæ± ́ ̈ ÏËð±›  ̄Áðð±⁄ ̃Â  ́­a Ø ́øÆ ̈¶ 

¥·2aÆ­ o±Æ  ̈a3°aÆø ̈ ́Æa­ æa ̈©aa2 ÏËð±› ø2o 

Áðð±›  ̄Áðð±⁄ ø2o ÔÍÎð±⁄ ̃Ú ×o  ̧·1 ̧ 

 ̈a3°aÆø ̈ ́Æa­ øÆa a21⁄2± ́2 ̈aÆao ­aa › ̧ø° ̈aÆ 

» ­a1⁄2 ̈·±2 ±2 Õø3°¥·21 ÿ·1 ̧ Ãa3°aÆø ̈ ́Æa 

Õ± ́Æ1⁄2a­Ú 

... ̧a2aTMaÆ °Æø1⁄2 ̈·1⁄2ø¥Ù  ́­a æ±Æ±­·¥·1⁄2ø ̈a ±Æ 

Ø ́øÆ ̈¶ 1¥ø­­ °Æ±æa ¥·2aÆ­Ú — ̈ ̧aÆ©·­a  ́­a 

3a ̈ø¥ ¥·2aÆ­ 3øoa ±o ­aø3¥a­­  ̈ ́æ·21 

 ̄aÚ1Ú ÌÔÍ ­ ̈ø·2¥a­­ ­ ̈aa¥Ù ×21⁄2±2a¥Ù 
ÎÚÓÛÁ

×21⁄2±¥±ß ËÓÎÙ ±Æ ± ̈ ̧aÆ 1⁄2±ÆÆ±­·±2 Æa­·­ ̈ø2 ̈ 

3a ̈ø¥­ ̃ © ̧a2 ø1⁄2·o °øÆ ̈·1⁄2 ́¥ø ̈a­ øÆa 

°Æa­a2 ̈ ·2 1⁄2±21⁄2a2 ̈Æø ̈·±2­ ¥a­­  ̈ ̧ø2 Ô 

31Ò3Ì ø ̈ °Æ±æa 1⁄2±2o· ̈·±2­ ±Æ Õ—Ó ·­ ¥a­­ 

 ̈ ̧ø2 Óð °°3Ú 

... ̧a2 ø­­a3æ¥·21  ̈ ̧a °Æ±æa ø2o 2±¶¶¥aÙ 

TMaÆ·oß  ̈ ̧ø ̈ ø¥¥ 1⁄2±3°±2a2 ̈­Ù ·21⁄2¥ ́o·21 

oaÆÆ ́¥a­ ø2o ± ̈ ̧aÆ 1⁄2±22a1⁄2 ̈±Æ­Ù øÆa  ̧aø ̈Û

Æa­·­ ̈ø2 ̈Ù ¥aøμÛoÆaaÙ ø2o 2±2Û

1⁄2±2 ̈ø3·2ø ̈·21 o±Æ  ̈ ̧a ­ø3°¥aÚ 

 1⁄2Ú –· ̈± ̈ Ã ́æa 

À­a ø2 ÕÛ ̈ß°a –· ̈± ̈  ̈ ́æaÙ ø­ oa­1⁄2Æ·æao ·2 

Õa1⁄2 ̈·±2 ÔÚÔ ±o ”a ̈ ̧±o ÓÚÔÙ ±Æ ± ̈ ̧aÆ 

oaTM·1⁄2a ø°°Æ±TMao æß  ̈ ̧a ¤®a1⁄2 ́ ̈·TMa —oo·1⁄2aÆÚ 

fl ̈ ̈ø1⁄2 ̧  ̈ ̧a –· ̈± ̈  ̈ ́æa  ̈±  ̈ ̧a °Æ±æaÙ ø­ 

­ ̧±©2 ·2 ⁄·1 ́Æa ÎÚÓÛÔÙ  ̈± ø¥¥±© 1⁄2±2­ ̈ø2 ̈ 

3±2· ̈±Æ·21 ±o  ̈ ̧a ­ ̈ø1⁄2μ 1ø­ TMa¥±1⁄2· ̈ßÚ ×o 

 ̈ ̧·­ ·­ 2± ̈ °Æø1⁄2 ̈·1⁄2ø¥ ­aa › ̧ø° ̈aÆ » 

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