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Conductivity - corrected for temperature and pressure

Let us consider a conductivity sensor integrated on the RBRconcerto³ C.T.D. The conductivity reading from Channel-1 without corrections is given by a simple linear function:

<table class="latexmath-mathblock" style="width: 100%; margin-left: 0; margin-right: 0; border: none;">
        <tbody style="border: none;">
        <tr>
          <td nowrap class="latexmath-center" style="border: none; vertical-align: middle; text-align: center;">
            <img src="data:image/svg+xml,%3csvg xmlns:xlink='http://www.w3.org/1999/xlink' width='19.959ex' height='2.724ex' viewBox='0 -820.2 8593.4 1172.9' role='img' focusable='false' style='vertical-align: -0.819ex%3b' aria-hidden='true' xmlns='http://www.w3.org/2000/svg'%3e%3cdefs%3e%3cpath stroke-width='1' id='MJMATHI-43' d='M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMATHI-72' d='M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMATHI-61' d='M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMATHI-77' d='M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 -11 404 5T355 48Q354 47 352 44Q311 -11 252 -11Q226 -11 202 -5T155 14T118 53T104 116Q104 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Q21 293 29 315T52 366T96 418T161 441Q204 441 227 416T250 358Q250 340 217 250T184 111Q184 65 205 46T258 26Q301 26 334 87L339 96V119Q339 122 339 128T340 136T341 143T342 152T345 165T348 182T354 206T362 238T373 281Q402 395 406 404Q419 431 449 431Q468 431 475 421T483 402Q483 389 454 274T422 142Q420 131 420 107V100Q420 85 423 71T442 42T487 26Q558 26 600 148Q609 171 620 213T632 273Q632 306 619 325T593 357T580 385Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMAIN-3D' d='M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMATHI-63' d='M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMAIN-30' d='M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMAIN-2B' d='M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMAIN-31' d='M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMAIN-22C5' d='M78 250Q78 274 95 292T138 310Q162 310 180 294T199 251Q199 226 182 208T139 190T96 207T78 250Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMATHI-52' d='M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 351T538 338L545 333Q612 295 612 223Q612 212 607 162T602 80V71Q602 53 603 43T614 25T640 16Q668 16 686 38T712 85Q717 99 720 102T735 105Q755 105 755 93Q755 75 731 36Q693 -21 641 -21H632Q571 -21 531 4T487 82Q487 109 502 166T517 239Q517 290 474 313Q459 320 449 321T378 323H309L277 193Q244 61 244 59Q244 55 245 54T252 50T269 48T302 46H333Q339 38 339 37T336 19Q332 6 326 0H311Q275 2 180 2Q146 2 117 2T71 2T50 1Q33 1 33 10Q33 12 36 24Q41 43 46 45Q50 46 61 46H67Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628Q287 635 230 637ZM630 554Q630 586 609 608T523 636Q521 636 500 636T462 637H440Q393 637 386 627Q385 624 352 494T319 361Q319 360 388 360Q466 361 492 367Q556 377 592 426Q608 449 619 486T630 554Z'%3e%3c/path%3e%3c/defs%3e%3cg stroke='currentColor' fill='currentColor' stroke-width='0' transform='matrix(1 0 0 -1 0 0)'%3e%3cg transform='translate(167%2c0)'%3e%3cg transform='translate(-13%2c0)'%3e%3cg transform='translate(0%2c-50)'%3e%3cuse xlink:href='%23MJMATHI-43' x='0' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-72' x='760' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-61' x='1212' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-77' x='1741' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMAIN-3D' x='2735' y='0'%3e%3c/use%3e%3cg transform='translate(3792%2c0)'%3e%3cuse xlink:href='%23MJMATHI-63' x='0' y='0'%3e%3c/use%3e%3cuse transform='scale(0.707)' xlink:href='%23MJMAIN-30' x='613' y='-213'%3e%3c/use%3e%3c/g%3e%3cuse xlink:href='%23MJMAIN-2B' x='4901' y='0'%3e%3c/use%3e%3cg transform='translate(5902%2c0)'%3e%3cuse xlink:href='%23MJMATHI-63' x='0' y='0'%3e%3c/use%3e%3cuse transform='scale(0.707)' xlink:href='%23MJMAIN-31' x='613' y='-213'%3e%3c/use%3e%3c/g%3e%3cuse xlink:href='%23MJMAIN-22C5' x='7012' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-52' x='7512' y='0'%3e%3c/use%3e%3c/g%3e%3c/g%3e%3c/g%3e%3c/g%3e%3c/svg%3e" class="latexmath" style="width: 159.672px; height: 21.792px; vertical-align: -0.819ex;" alt="LaTeX Math" />
          </td>
        </tr>
        </tbody>
      </table>

where R is the normalized voltage ratio from Channel-1 monitoring conductivity,  c0,c1  are the core coefficients of the linear equation, and Craw is the uncorrected conductivity output, reported in mS/cm for RBR marine instruments.

The equation which corrects the output for the effects of both temperature and pressure on the conductivity cell is:

<table class="latexmath-mathblock" style="width: 100%; margin-left: 0; margin-right: 0; border: none;">
        <tbody style="border: none;">
        <tr>
          <td nowrap class="latexmath-center" style="border: none; vertical-align: middle; text-align: center;">
            <img src="data:image/svg+xml,%3csvg xmlns:xlink='http://www.w3.org/1999/xlink' width='54.282ex' height='6.118ex' viewBox='0 -1580 23371.2 2634.1' role='img' focusable='false' style='vertical-align: -2.295ex%3b margin-bottom: -0.153ex%3b' aria-hidden='true' xmlns='http://www.w3.org/2000/svg'%3e%3cdefs%3e%3cpath stroke-width='1' id='MJMATHI-43' d='M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMATHI-6F' d='M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMATHI-72' d='M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMAIN-3D' d='M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMATHI-61' d='M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMATHI-77' d='M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 -11 404 5T355 48Q354 47 352 44Q311 -11 252 -11Q226 -11 202 -5T155 14T118 53T104 116Q104 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Q21 293 29 315T52 366T96 418T161 441Q204 441 227 416T250 358Q250 340 217 250T184 111Q184 65 205 46T258 26Q301 26 334 87L339 96V119Q339 122 339 128T340 136T341 143T342 152T345 165T348 182T354 206T362 238T373 281Q402 395 406 404Q419 431 449 431Q468 431 475 421T483 402Q483 389 454 274T422 142Q420 131 420 107V100Q420 85 423 71T442 42T487 26Q558 26 600 148Q609 171 620 213T632 273Q632 306 619 325T593 357T580 385Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMAIN-2212' d='M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMATHI-4B' d='M285 628Q285 635 228 637Q205 637 198 638T191 647Q191 649 193 661Q199 681 203 682Q205 683 214 683H219Q260 681 355 681Q389 681 418 681T463 682T483 682Q500 682 500 674Q500 669 497 660Q496 658 496 654T495 648T493 644T490 641T486 639T479 638T470 637T456 637Q416 636 405 634T387 623L306 305Q307 305 490 449T678 597Q692 611 692 620Q692 635 667 637Q651 637 651 648Q651 650 654 662T659 677Q662 682 676 682Q680 682 711 681T791 680Q814 680 839 681T869 682Q889 682 889 672Q889 650 881 642Q878 637 862 637Q787 632 726 586Q710 576 656 534T556 455L509 418L518 396Q527 374 546 329T581 244Q656 67 661 61Q663 59 666 57Q680 47 717 46H738Q744 38 744 37T741 19Q737 6 731 0H720Q680 3 625 3Q503 3 488 0H478Q472 6 472 9T474 27Q478 40 480 43T491 46H494Q544 46 544 71Q544 75 517 141T485 216L427 354L359 301L291 248L268 155Q245 63 245 58Q245 51 253 49T303 46H334Q340 37 340 35Q340 19 333 5Q328 0 317 0Q314 0 280 1T180 2Q118 2 85 2T49 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q147 65 216 339T285 628Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMATHI-63' d='M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMAIN-31' d='M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMAIN-22C5' d='M78 250Q78 274 95 292T138 310Q162 310 180 294T199 251Q199 226 182 208T139 190T96 207T78 250Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMAIN-28' d='M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMATHI-54' d='M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMATHI-6C' d='M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMAIN-29' d='M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMAIN-2B' d='M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMAIN-32' d='M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMAIN-33' d='M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMATHI-50' d='M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z'%3e%3c/path%3e%3c/defs%3e%3cg stroke='currentColor' fill='currentColor' stroke-width='0' transform='matrix(1 0 0 -1 0 0)'%3e%3cg transform='translate(167%2c0)'%3e%3cg transform='translate(-13%2c0)'%3e%3cuse xlink:href='%23MJMATHI-43' x='0' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-6F' x='760' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-72' x='1246' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-72' x='1697' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMAIN-3D' x='2426' y='0'%3e%3c/use%3e%3cg transform='translate(3483%2c0)'%3e%3cg transform='translate(120%2c0)'%3e%3crect stroke='none' width='19326' height='60' x='0' y='220'%3e%3c/rect%3e%3cg transform='translate(4236%2c737)'%3e%3cuse xlink:href='%23MJMATHI-43' x='0' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-72' x='760' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-61' x='1212' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-77' x='1741' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMAIN-2212' x='2680' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-4B' x='3680' y='0'%3e%3c/use%3e%3cg transform='translate(4570%2c0)'%3e%3cuse xlink:href='%23MJMATHI-63' x='0' y='0'%3e%3c/use%3e%3cuse transform='scale(0.707)' xlink:href='%23MJMAIN-31' x='613' y='-213'%3e%3c/use%3e%3c/g%3e%3cuse xlink:href='%23MJMAIN-22C5' x='5680' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMAIN-28' x='6180' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-54' x='6570' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMAIN-2212' x='7497' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-54' x='8497' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-63' x='9202' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-61' x='9635' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-6C' x='10165' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMAIN-29' x='10463' y='0'%3e%3c/use%3e%3c/g%3e%3cg transform='translate(60%2c-738)'%3e%3cuse xlink:href='%23MJMAIN-31' x='0' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMAIN-2B' x='722' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-4B' x='1723' y='0'%3e%3c/use%3e%3cg transform='translate(2612%2c0)'%3e%3cuse xlink:href='%23MJMATHI-63' x='0' y='0'%3e%3c/use%3e%3cuse transform='scale(0.707)' xlink:href='%23MJMAIN-32' x='613' y='-213'%3e%3c/use%3e%3c/g%3e%3cuse xlink:href='%23MJMAIN-22C5' x='3722' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMAIN-28' x='4223' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-54' x='4612' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMAIN-2212' x='5539' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-54' x='6540' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-63' x='7244' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-61' x='7678' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-6C' x='8207' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMAIN-29' x='8506' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMAIN-2B' x='9117' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-4B' x='10118' y='0'%3e%3c/use%3e%3cg transform='translate(11008%2c0)'%3e%3cuse xlink:href='%23MJMATHI-63' x='0' y='0'%3e%3c/use%3e%3cuse transform='scale(0.707)' xlink:href='%23MJMAIN-33' x='613' y='-213'%3e%3c/use%3e%3c/g%3e%3cuse xlink:href='%23MJMAIN-22C5' x='12117' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMAIN-28' x='12618' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-50' x='13008' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-63' x='13759' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-6F' x='14193' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-72' x='14678' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-72' x='15130' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMAIN-2212' x='15803' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-50' x='16804' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-63' x='17555' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-61' x='17989' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMATHI-6C' x='18518' y='0'%3e%3c/use%3e%3cuse xlink:href='%23MJMAIN-29' x='18817' y='0'%3e%3c/use%3e%3c/g%3e%3c/g%3e%3c/g%3e%3c/g%3e%3c/g%3e%3c/g%3e%3c/svg%3e" class="latexmath" style="width: 434.256px; height: 48.944px; vertical-align: -2.295ex;" alt="LaTeX Math" />
          </td>
        </tr>
        </tbody>
      </table>

Casting the equation into the style used by the logger would give:

<table class="latexmath-mathblock" style="width: 100%; margin-left: 0; margin-right: 0; border: none;">
        <tbody style="border: none;">
        <tr>
          <td nowrap class="latexmath-center" style="border: none; vertical-align: middle; text-align: center;">
            <img src="data:image/svg+xml,%3csvg xmlns:xlink='http://www.w3.org/1999/xlink' width='58.153ex' height='6.118ex' viewBox='0 -1580 25037.8 2634.1' role='img' focusable='false' style='vertical-align: -2.295ex%3b margin-bottom: -0.153ex%3b' aria-hidden='true' xmlns='http://www.w3.org/2000/svg'%3e%3cdefs%3e%3cpath stroke-width='1' id='MJMATHI-43' d='M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMATHI-6F' d='M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMATHI-72' d='M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMAIN-3D' d='M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z'%3e%3c/path%3e%3cpath 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418T161 441Q204 441 227 416T250 358Q250 340 217 250T184 111Q184 65 205 46T258 26Q301 26 334 87L339 96V119Q339 122 339 128T340 136T341 143T342 152T345 165T348 182T354 206T362 238T373 281Q402 395 406 404Q419 431 449 431Q468 431 475 421T483 402Q483 389 454 274T422 142Q420 131 420 107V100Q420 85 423 71T442 42T487 26Q558 26 600 148Q609 171 620 213T632 273Q632 306 619 325T593 357T580 385Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMAIN-2212' d='M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMATHI-78' d='M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMAIN-30' d='M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMAIN-22C5' d='M78 250Q78 274 95 292T138 310Q162 310 180 294T199 251Q199 226 182 208T139 190T96 207T78 250Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMAIN-28' d='M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMATHI-76' d='M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMATHI-6C' d='M117 59Q117 26 142 26Q179 26 205 131Q211 151 215 152Q217 153 225 153H229Q238 153 241 153T246 151T248 144Q247 138 245 128T234 90T214 43T183 6T137 -11Q101 -11 70 11T38 85Q38 97 39 102L104 360Q167 615 167 623Q167 626 166 628T162 632T157 634T149 635T141 636T132 637T122 637Q112 637 109 637T101 638T95 641T94 647Q94 649 96 661Q101 680 107 682T179 688Q194 689 213 690T243 693T254 694Q266 694 266 686Q266 675 193 386T118 83Q118 81 118 75T117 65V59Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMATHI-75' d='M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMATHI-65' d='M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMATHI-6E' d='M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMAIN-29' d='M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 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663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMAIN-2B' d='M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMAIN-32' d='M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z'%3e%3c/path%3e%3cpath stroke-width='1' id='MJMAIN-34' d='M462 0Q444 3 333 3Q217 3 199 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          </td>
        </tr>
        </tbody>
      </table>

where

  • Craw is the uncorrected conductivity,  c0    +    c1  ×  R

  • x0 x1 x2 correspond directly to the constants "Kc1", "Kc2" and "Kc3"

  • x3   is the calibration temperature "Tcal" in °C

  • x4 is the calibration pressure "Pcal" in dbar

  • n0   is the index of the temperature channel, in this example 2

  • value( n0 ) is the final output value of the temperature channel in °C

  • n1    is the index of the pressure channel, in this example 3
    value( n1 ) is the final output value of the pressure channel in dbar

  • Ccorr is the corrected output in mS/cm

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