B 479737
TA B L E OF
FR E S N E L IN T E G R A LS
* * * - * *.
t
a tº A2"
C. M. SPARRow
ROUSS PHYSICAL LABORATORY
UNIVERSITY OF VIRGINIA
1934
PHOTO-LITHO PRINT REPRODUCTION OF
AUTHoR’s MANUSCRIPT BY
EDWARDS BROTHERS, INC.
ANN ARBOR, MICHIGAN





T A B L E
of
F R E S N E L T N T E G R A L S
C. M. Sparrow
The greater part of the following table was made some years
ago in connection with a study of imperfect gratings; exist-
ing tables not being adequate by reason of their too large
interval. This manuscript, table was resurrected and slight-
ly extended to meet a teaching need, and is here reproduced
in the hope that it may prove of some use to others.
The table gives the values of the integrals
X 2.
C(x) - J cos "3 dx
O 2
IX 2.
S(x) = ſ sin Tº dx
O 2
for values of x (the arc length of the Cornu spiral) from
O to 8 at intervals of . 005. C and S are positive numbers
less than unity, so that a decimal point is to be placed be-
fore each tabulated entry.
For values of x greater than this C and S may be readily cal-
culated with sufficient accuracy by the formulae
c(x) = 0.5 + . . sin II (x - & : )
Tſ X 2 Tr” x
S(x) = 0.5 - – cos II (x" _ 2 )
Tſ X Tr”x 2.
ROUSS PHYSICAL LABORATORY
UNIVERSITY OF VIRGINIA
1 9 35 4.
F R E S N E L
I N T E G R A L S

x C S X C S X C S X C S
O. OOO OOOO OOOO ||O.25O 2498 OO82 |O. 500 4923 O647 |O. 750 69
. OC5 OO5O OOOO .255 2547 oo&7 .505 4969 O666 || .755 6963 2T28
... O |O Of OO OOOO .26O 2597 OO92 .5 to 50 15 O686 . 760 6999 2 167
... O 15 O15O OOOO .265 2647 OO97 . 515 5061 o'706 .765 7030 22O6
. O2O O2OO OOOO .27O 2697 of O3 .52O 5 loſſ O727 .770 7060 224.5
o.O25 oz.5o oooo ||o.275 2746 oiog |0.525 5 153 of 48 ||0.775. 7090-2285
. OBO O3OO OOOO .28o 2795 of 15 .530 B 198 oz.69 .780 - 7ſ 19-2327
. O35 O35O OOOO .285 2846 O 121 .535 5243 O'790 . 785 7 147 2368
. O4·O O4OO OOOO .29O 2895 O128 .54O 5288 O812 . 790 7175 24O9
. O45 0450 OOOO • 295 2945 0134 , 545 5355 O854 || . T95 72O3 2451
O. O50 0500 OOOO || 0.300 2994 of 41 ||o.550 5377 oë57 ||0.8oo 7230 2493
. OBE OB5o Oool . 305 3044 O 148 . 555 5422 oë8o . 805 7257 2556
. O60 O600 OOO! . 31 O 5093 of 55 . 560 5466 O904 .810 7283 2579
. Q65 O650 OOO! . 3 15 3143 of 65 .565 551 O O928 .815 73O8 2622
. O7 O O"ZOO OOO2 . 32O 31.92 O 171 .57O_5553 O952 .820 7333 2665
O. O75 O750 OOO3 || O. 325 324. 1 ol’9 |o. 575 5597 OS76 ||O. 825 Tºº? T27OS
. O3O O8OO OOO3 . 330 3291 O 187 .58o 5640 Tool 555-735Taº-
. O85 O85O OOO5 .335 3340 O 196 .585 5683. 1026 . 835 7404 2797
. O90 O900 OOO4 . 54 O 3589 O2O5 .590 5726 1052 . 840 7426 2841
. O95 O95Q OOO4 . 545 3438 O2 14 .595 5769 to 78 .845 7448 2886
O.TOOTiOOOTOOOB || 0.35o 3487 oz24 ||o. 600 581 i 1105 ||o. 850 7469 295t
... iO5 iO5o oooé . 355 3536 oz.34 . 605 5853 Ti22 .855 7490 2.977
. 1 1 O 1 1 OO OOO7 . 360 3585 O244 .6 to 5895 ( 160 .86o 75 to 3023
. 1 15 1 150 OOO8 . 365 3634 O254 .615 5937 t 188 .865 7529 3069
. 120 12OO OOO9 . 37.0 3683 0264 .62O 5978 1216 . 870 7548 31 15
O. 125 1250 oolo, Ilo.375 373 TO275 |0.625 6019 1245 ||O.875 TV555T3T5 i
. 130 1300 OO 11 . 38o 5780 oz86 .63o 6060 1274 .88o 7584. 5208
. 135 1350 Oo 12 . 585 3829 O298 .635 61 oo 1305 .885 760 i 3255
. 14 O 14 OO OO 14 . 390 3878 O.309 . 64 O 6140 1333 . 890 7617 3303
. 145 1450 OO16 . 395 3925 O321 . 645 6180 1363 . 895 7633 3350
O. IBO IBOC Ooſtz ſo. 400 3975 Os34 ||o. 650 6220 1394 ||o. 500 7648-3398
. 155 155o oo 19 .405 4023 O347 .655 6259 1425 .905 7663 3445
. 16O 16OO OO21 .4 to 4.072 O259 .66O 6298 1456 .9 to 7677 3494
. 165 1650 OO23 . 415 4 120 0372 . 665 6536 1488 .9 15 7690 3542
. 17O 1700 OO26 . 42O 4 168 O386 .67O 6374 1520 . 920 7702 359 1
O. 175 1750 0028 || O. 425 42.15 O400 ||o. 675 64. 12 1552 ||o. 925 7714, 364
TSO T3CO Oo3ſ .43O 4264 C4 14. .68o 5450 1585 .93o 7725, 3689
. 185 1850 Oo34 .435 451 1 O428 .685. 6487 1618 .935 7735 3738
. 190 1899 OO36 .44 O 4359 O445 .690 6524 1652 .94o 7744 3787
• 195 1949 OO39 || .445 4407 O458 || .695 6561 1686 || .945 7753 3836
0.200-T399-0043 To. 450-4454-0474TO.755-6557 iſ:Tö.55öT776T =555
T.205 T204.9 OC45 .455 4502 O490 .705 T5535 1756 .955 7768 3954
. 21 O 2099 OO49 .46O 4549 O506 . 71 o 6668 1792 . 96.O 7774 3984
.2 15 2149 OO52 .465 4596 OB23 .715 67O3 1828 . 965 778o 4034
.22O 2199 OO56 .47O 4645 O539 .72O 6738 1864 .97O 7785 4083
0.225-2545-0555TO.475-4555 5555TO.735T6773TT500Tö.575 Tºgg AT33-
.23OT2299 OO64 .48o 4.737 OB74. .73O 6306 1937 .98o 7792 4. T8
.235 2348 OO68 . 485 4784 O392 .735 6839 1974 .985 7795 4233
. 24.O 2598 OO72 . 490 4850 O61 O . 74 O 6872 2012 . 990 7797 4283
.245 2448 OOT”7 . 495 4877 O628 .745 6904 2050 .995 7798 4535
o.25o 2498 ooS2 ſlo. 50o 4923 oë47 ||o.750 6936 2089 |! .oOo. 7799 4383
F R E S N E L
I N T E G R A L S

X C S X C S X 9–5– X -*—É
1 . OOO # 4383 || 1.25O 6801 6586 || 1.5oo. 4453. 6975 || 1.750 3219 4993
. OC5 7798 4433 .255 6762 6618 . 505 44O9 6955 .755 3224. 4943
... O 1 O 7798 4483 .26O 6722 6648 .5 to 4361 6935 .76O 3232 4894
..o 15 7796 4535 .265 6682 6678 .515 45 16 69 12 .765 524O 4845
• O2C 7793 4583 .27O_664 67O7 .52O 4272 6890 .77o #3 4796
1 - O25 7790 4632 || 1.27 66oo 6740 || 1.525 4228 6866 || T.775 3260 474
. O3O 7785 4682 280T6555T3765 .53o 4 185 684 i .78o 3273 4699
. O35 778o 4732 .285 65.15 6790 .535 4 142 6815 .785 3287 4650
. O4O 7774. 4782 .29C 6473 6815 . 540 4 too 6788 .790 3302 4605
• O45 7768 4832 .295 643o 6840 || .545 4058 6760 || .795 33 18 4555
1. C50 7760 4881 || 1.300 6586 6863 || T.E.50 4018675 TIT. 800 3356 450
. O55 7752 4930 .305 6342 6886 . 555 3978 67ot .805 3356 44.62
. O60 7742 4979 .5 to 62.97 6908 .56O 3939 6670 .81 o 3376 44 16
. O65 7732 5028 . 515 6252 6929 .565 390C 6638 .815 3397 437
. O70 772 t 5077 . 32O 62O6 6949 .57O 3862 6605 .82O 342O 4527
1.075 77 IC 5126 III.325 6T60 6968 II.575 L3825T657 ITT.825T3445-4284
.08o 7697 5174 .33d 6 t 13 6987 .58o 5789 6536 .83O 3470 424
. O85 768.4 5222 .335 6066 7004 .585 5754 6500 .835 3498 4 198
. O90 7669 527O . 540 6019 7O2 1 .590 572O 6464 .84o 3525 4 157
. O95 7654 53.18 . 345 5972 7036 .595 3688 6426 .845 3554. 41 16
1. TOOT7638 5365 III.350T59237050TT.600T3655-6385 ITT.850T3584. 4076.
... 105 7622. 54 12 . 355 5874 7062 . 605 3624 655o .855 5616 4038
. 1 1 O 7604 5459 . 360 5826 7075 .6 to 3593 63 to .86O 56.48 4 OOO
. 115 7586 5506 . 365 5778 7086 . 615 3564 6270 .865 368 1 3965
. 120 7567 5552 .37O 5729 7097 .62O 3555 6229 .87O 3716 5927
1. 125 7547 5598 || 1.375 5.680 / TO6 ||.625 35086186TT.&ſº 375T 3852
. 130 7526 5643 . 38o 563O 7114 . 650 3482 6144 .880 T3788 3858
. 135 7504 5688 . 385 5580 7121 .655 3457 6101 .885 3826 3826
. 14o 7482 5733 .390 553 7127 .640 3453 6057 .890 3864 3793
. 145 7459 5777 . 395 548 i 7 132 . 645 34 to 60 15 .895 3904 3763
1. 150 7435 582 T.400TB45T-7735 TT 650Tſſ 5555TT.366. Tā54AT5754T
, 155 74 to 5364 .405 538o 71.38 .655 3368 5922 .905 3986 3706
. 16o 7385 5908 .4 to 533o 7 140 .66O 3348 5876 .9 ſo 4028 3679
. 165 7559 5950 .4 15 5280 714 .665 335o 5830 . 915 4O70 3654
. 17O 7532 5992 .42O 5250 7140 .670 33 13 5782 .920 41 15 3629
1. 175 7.305 6.O34 || 1.425–5180 / 139 || 1.675 32.98 EZ34T1.925 4 159 B&O
. 180 7276 6O75 .430 B 151 7135 .680 3283 5687 . 950 42O4, 3584
. 185 7247 6116 .435 5081 7131 .685 327O 5638 .955 4249 3564
. 190 72.17 6156 || .440 5031 7126 || .690 3258 5590 || .940 4296 3545
. 195 71 86 6 196 .445 4981 712o .695 3248 354 1 .945. 4342 3528
1 - 200 7 154 6234 || 1.45C 4932 7112 || 1.700 3238 5492 || 1.950. 4390 3512
.2O5 7122 62.72 .455 4.883 ºf iO3 .705 3230 B443 ISB5TA435 #-
. 21 O 7089 63 l O .46O 4834 7.093 || . T 10 3224 5393 . 960 4486 5484
.215 7056 6347 .465 4786 7082 .715 3219 5343 . 965 4535 3472
.22O 7021 6383 .47 U 4737 7070 || .720 32 15 5293 .97O 4584, 3462
i.225 6986 64 19 || 1.475 4639 7.558 || 1.725 3212 5243 || 1.975 4634 3454
.25o 6950 6454. .48o 4641 7043 .750 32 11 B 193 .98o 4633 344.7
.255 6914 6488 .485 4594 7028 .735 321 1 51.43 . 985 4732 5441
.24O 6877 6522 . 490 4546 7.O 11 .74O 3212 5093 . 990 4782 3437
.245 6839 6554 . 495 4500 6994 . 745 32 14 3043 .995 4852 3434
1.25o 6801 6586 || 1.500 4453. 6975 TT.750 3275-4553 T3.000 4882 3434
F R E S N E L
I N T E G R A L S

g
X S 2× C S X C S X C S
2.oOo. 4882 3434 ||2.25o 64 of 5055||2.5oo. 457461.92 ||2.750. 42.55 4 39
. OC5 4932 3434 .255 6396 5103 .505 4528 6172 .755 4272 4 loë
... O 10 4982. 3437 .26O 6388 5152 .51 o 4483 6150 .76O 4513 4079
. O15 5032 5441 .265 6379 52O1 . 515 4459 6126 .765 4354 4052
. O2O 5082 344.7 .27O 6368 5250 || .52O 4396 6 1 ol .77o 4398 4026
2.025 5132 3454 ||2.275 6356 5298][2.525–4354–5074T2.775TAAAZTAOCZ
. Ojo 5181 3463 .28o 634 TB346 .55o 4313 6.d45 .78o 4487 3981
.ož5 5239 3473 .285 6324 5394 .535 4274 6o 15 . 785 4532 3962
O4O 5278 3485 .29O 6307 5440 || .540 4235 5985 . 790 4579 3044
. O45 5326 3498 .295 6287 5486 || .545 4 198 5950 . 795 4626 3929
2. O50 5374-35 13 ||2.3oo 6266 553 IT2.550. 4.162-5915 T2 .800. 4.675 3515
.055 5422 B530 .305 6244 5576 || .555 4 128 5879 .805 4724 .3904
. O60 5468 3547 .5i O 62.19 5619 || .56O 4094 5842 . 31 O 4775 3894
. O65 55 14 3566 .515 61.92 5662 .565 4O63 58O3 .815 4822 3887
. O70 5559 3587 . 32d 6 165 5704 .57O_4,O_53 5763 .820 4872 3882
2. O75 56O4, 36 TO ||2.325 636 574.4 || 2.575 4 OO4. Fºllº. 825. 4922 3880
. O80 5648 3633 .330 61 of 5784 .580 3978 5679 .83o 4972 5679
. O85 569 O 5658 .335 6074 5822 .585 3953 B636 .835 5022 3880
. O90 57.33 3685 . 340 604 t 5860 .590 3950 559t .84O 5072 3885
. O95 5775 3714 . 345 6006 590? .595 3909 5546 .845 5122 3892
2. TOO 58.15 3745 ||2.550 j97O 593 l II 2.6CO 589C 55JO ||2.85C 517 39CO
...tos 5854 3774 . 355 5932 5964 . 605 3875 5454 .855 522O 391 O
. 1 1 O 5893 3806 . 560 5894 5996 || . 61 O 3857 54.06 .86O 5268 3923
. 1 15 5950 38.59 . 365 5854 6O28 . 615 3844 5358 .865 53t 6 3938
• 120 5967 3873 || .370 5814 6056 || . 62o 3832 5309 || .870 5363 3955
3. 125 6.OO2 3908 ||2.375 T5772–6084 || 2.625–3822–5.260TIE.87.5 T5409 3974
. 13o 6036 5945 . 38o 5729 61 to || .650 3815 52 to .88o 5454 3996
. 135 6068 3983 . 385 5686 6 134 . 655 38 to 516o . 885 5498 402O
. 14 O 6 1 OO 4022 . 290 564 6157 . 640 3806 51 1 O .890 554t 4045
. 145 615O 4062 . 395 5596 6 178 . 645 3805 5060 . 895 5584 4O72
2. 15OT6159-4 loº TE2.4COT355GT6 is "TI 2.650 38.05 polio ||2.900 5624 4 loi
; 155 6.186 4.146 .405 5504 6214 .655 38o3 4960 .905 5664 4132
. 16O 6212 4.188 .4 to 5456 6230 . 660 3813 49 1 .91 o 5701 41.65
. 165 6236 4232 .415 5408 6244 .665 3820 486t . 915 5737 41.99
• 17O 6259 4276 .42O 5359 6256 . 670 3829 4812 .92O 5772 4235 |
2. Tº T628OT432TE2.425 T53 to 6266 TI3.675 3840-4763_TIE.925 5805 4272
. 180 65oo 4367 .450 5261 6275 .68o 5853 4715 .93o 5836 4312
. 185 65 18 44 14 .435 52 12 6281 .685 5868 4668 .935 5866 4352
. 190 6555 4461 .44C 5162 6286 .690 5885 462O .94 O 5895 4594
. 195 635C 4508 .445 51 12 6289 .695 3904 4574 .945 59 18, 4457
3.250T5353-4557T2 .455-5062 3285 T2 .700 3.925 4529 ||2.950 5942 448t
.205 6374. 4606 || .455 5o 12 6288 .705 3948 4484 .955 5963 4526
21 O 6384 4655 .46O 4962 6285 .71 o 3973 444 1 .96o 5983 4572
.215 6592 4704 .465 4912 628O .715 4OOO 4398 . 965 6.OOO 462O
.22O 6399 4754 .47O 4862 6275 .720 4028 4357 •97o 6015 4667
2.225 64.04 4804 ||2.475 482 6264 || 2.725. 4058 4317 ||2. 6028 471
.23O 6407 4853 .48O 4764 6255 .73O 4O90 4279 .98o 6O39 4764
.235 6468 4903 . 485 4716 624O .735 4 123 4242 . 985 6048 4815
.24O 64 O8 4955 .490 4668 6226 .74o 4 158 42O6 .990 6052 486.5
.245 6406 5oo3 || .495 462o 6210 || 745 4 194 4172 || .995 6056 4912
2.356T64OTBö53T3.550T457AT5T53T3.750T 4235-4 139 I-3. Ooo 6058 4963
F R E S N E L
I N T E G R A L S

X C S X C S X C S X C S
3. Ooo 6058 4963 || 3.250-4264 B642||5.5oCT5526T4 lºſa T3.750–4536T5844
. OO5 6056 5o 13 .255 42.54 5602 .505 5372 4 173 .755 4886 5838
. Oi O 6053 BO65 .26O 42O5 5561 .5 to 5416 4 196 .76O 4837 5828
... O 15 6048 51 t 3 .265 4 179 55t 8 .515 5459 422 .765 4789 58 16
. O2O 6O39 5 162 .270 4 154 5475 .520 550 4248 .77O 4741 580 !
3.025 6028–32 ITT3.275-4132 B43TT 3.535–554 TAZ78TX.775–4594 BT33
.03o 6015 5259 || .280 41 12 5385 || .530 5579 43 to .750 4645 Bºſé5
. O35 6.OOO 5306 .285 4095 5338 .535 5615 4344 .785 4605 5740
. O4O 5982 5355 .290 4080 529O .54o 5650 438? .790 4562 57 14
• O45 5962 5399 .295 4 O68 5242 - 545 5683 44 19 .795 4521 5686
3. O50 594 i 5444 || 3.300 40585.192 || 3.550 T5713-4.459 TE2800.T.448 T5656
.055 59 tº 5488 .305 4:05.1 5 143 .555 574 t 4500 .805 4445 5625
. O60 5891 5551 . 31 O 4O46 5093 .56O 3767 45.45 .81 o 4408 5587
. O65 5865 5572 . 3 15 4O44 5045 .565 5790 4587 815 4575 5549
. O70 5833 5612 . 32O_4044. 4995 .57O 38.1 ! 4652 .82O 434.4 55 1 O
3. OTE 58OO 5659 || 5.325 4.047. 4945 || 3.575 3829 4678 || 3.825 43 1554.69.
.080 5767 5688 . 330 4053 4893 .580 5845 4726 .83o 4289 5427
. O85 5732 5723 . 355 406 1 4844 .585 5858 4775 .835 4266 5385
. O90 5695 5757 . 340 4072 4795 .590 5868 4824 .84O 4245 55.57
• O95_5656 5788 . 345_4085 4748 .595_5875 4873 .845 4227 529O
3. 100 5616 5818 || 3.350 4 to 1470c lºº. 6oo 588o 4923 || 3.850. 42 tº 524.3
. 105 5575 5845 . 355 4 1 19 4654 . 605 5830 4973 .855 4 199 5 195
. 1 1 O 5532 5871 . 360 4 14 O 4608 . 6 1 O 5880 5022 .86O 4190 5 146
. 15 5488 5895 . 565 4 163 4564 . 615 5876 5072 . 865 4 184. 5096
. 120 5443 59 16 . 370 4 189 4521 .62O 5870 5122 .87O 4 18O 5046
3. 125 T5396.5936 Iº. 375-4212-448&TE.625 T5850-517 UT 3.875-4 lºg 4997
. 130 5349 B952 .38o 4246 4439 . 650 5848 52 19 . 880 4 182 4947
. 135 53ol. 5966 || .385 4278 4400 . 635 5833 B266 . 885 4 188 4897
. 140 52.55 5979 . 390 43.12 4364 . 646 3815 5313 .890 4197 4848
• 145_52O5 5.988 . 395 4348 43529 . 645 5795 5359 . 895 4209 4800
3. 150 5 155 5996 || 3.4CO 4385 42.96 || 3.650 57725403 || 3.9 oo 4223 4752
. 155 5 to:5 6000 .405 44.24 4265 .655 5746 54.46 . 905 4:24.1 4705
. 16O 5055 6.OO3 .4 10 4465 4237 .66o 5718 5488 . 91 O 4262 4660
. 165 5005 6.OO3 .4 15 4508 42 lo . 665 5688 5527 . 915 4285 4616
. 17O 4955 6.OOO .42O 4552 4 186 . 67 O_5655 5565 , 920 45 tº 4573
3. 175 4905 5994 || 3.425.4595.4164 IB. 675 562o 560 TT 5.925 4555-452
. 180 4856 5987 .430 4645 4 145 .680 5584. 5635 . 950 4370 44.92
. 185 4807 5977 .435 4690 4 128 .685 5545 5667 .935 44O3 4455
. 190 4758 5965 .440 4738 41 14 .690 5505 5697 . 940 4439 442O
. 195 47 1 O 5950 .445 4786 4 1 O3 , 695 5463 3725 .945. 4477 4387
3.20C 4564 Bg33T3.450 4836 4094 || 3.700–5420 B750 || 3.350. 451& 4357
.205 4618 59 14 .455 4885 4088 .705 5575 577 .955 4558 4329
. 21 O 4573 B892 .46O 4935 4084 .7 to 5529 5790 . 960 4601 43O4
.215 4524 5868 .465 4985 4085 . 715 5282 5806 . 965 4645 428
• 22O 4486 584 1 .47O 5035 4085 .72O 5234 582O •97O 469 1 426 l
5.225 4445. 5812 || 3.475 2085 4O90 || 5.725 5185585 || 5.975 47.584244
.23O 4405 5782 .480 5 134 4097 .73o 5 136 5840 .98o 4736 42.5o
.255 4368 5750 .485 5183 41 of .735 5086 5846 .985 4835 42.19
.24o 4331 57 16 .490 5232 4 19 .74O 5036 5848 . 990 4885 42 12
.245 4296 568O .495 5280 4 155 .745. 4986 5848 .995 4954 42O7
3.250 4264 5642 || 3.500 5326-4TEZT3.750-4956-584ATH.OCOT455ATA204
F R E S N E L
I N T E G R A L 5

X C S X C S X C S X C S
4. OOO 4984 42O4 || 4.25C 494O 374.7 || 4.5Co 5261 4342 || 4.750 4488 5433
.o.o.B 5054, 42O5 .255 4890 574o .505 5306 4363 .755 4457 5395
... O I O 5084 421 O .26O 484 || 5750 .5 to 535o 4587 .76o 4430 535i
... O 15 5133 4218 .265 4795 57 17 .515 5592 4414 .765 4406 5307
. O2O 5182 4229 .27O 4745 57 of .52O 5432 4444 .77o 4386 5261
4. O25 523o 4243 || 4.275 4699 5632 .525 547O 4477 || 4.775 4369 52.14
. O3O 5277 4260 .28o 4654 5659 .53o 5505 4512 .78O 355 51
. O35 5525 428O .285 461 I B635 .535 5538 454O . 785 4545 5117
. O4O 5568 43O3 .29O 4570 5605 .54O 5568 4589 .790 4339 5068
. O45 541 4329 .295 453 i 5574 .545 5596 463 i .795 4337 50 18
4. OBO 5452 4.357 || 4.3OO 4494 5540 .55o 562o 4675 || 4.8OO 4338 4968
. O55 549 tº 4388 .305 4459 5504 . 555 564 t 472? .805 4343 4918
. O60 5529 4421 . 25 to 4427 5466 .56o 5658 4768 .8 to 455 1 486.9
. O65 5564 4456 . 3 15 4398 5426 .565 5672 4816 .815 4364 482
• O7O_5597 4494 . 32O 43.71 E384 .57O 5683 4864 .82O 4580 4773
4.075 5627 4534 T 4.325 4347–534 OT 4.575 E.630-4514 || 4.325-4400-4727
. O8o 5655 4576 .33OT 4326 5294 || .58o 5694 4964 . 83C 4423 4685
. O85 5680 4619 .335 43O8 5247 .585 5694 5014 . 835 4449 464O
. O9C 5702 4664 . 540 4294 5 199 .590 5691 5064 .84O 4478 4599
. CŞ5 5722 47 1 O . 345 4283 5 150 . 595 5.684. 5 i 12 . 845 451 O 4561
4. 1 OC 5738 4758 || 4.550 4275 5 101 || 4.6CO 5675 5162 || 4.85o 4546 4526
... 105 575 T 4806 || .355 4271 505 .605 5659 52 to || .855 4584 4493
. 1 to 5761 4855 . 36O 427O 500 .61O 5641 5257 . 860 46.24 4463
. 1 15 5768 4904 . 365 4272 495t . 615 562O 53O2 .865 4666 4437
. 12O 5771 4954 . 57 O 4278 4902 . 620 5596 5346 .87O 47 1 1 4414
4. 125 5771 BC)O4 || 4.575 4287 4855 || 4.625 5568 5388 || 4.875 4757 4594
. 15o 5769 5054 . 580 4500 4804 . 630 5538 5428 .880 4804 4378
. 135 5763 5 104 . 585 43 tº 4756 .635 5505 5465 .885 4853 4565
. 14 O 5754 5-153 . 390 4335 47 lo . 64 O 547 O 55OO .890 4902 4556
. 145 5766 52O1 . 395 4358 4665 • 645 54.32 5532 .895 4952 455 1
4. 15O 5726 5249 || 4.400 4383 4622 || 4.650 5391 5562 || 4.900 5002 4350
. 155 57 O'7 5296 .405 44 11 4581 . 655 5548 5589 . 905 5052 4355
. 160 5685 534 . 4 1 O 4442 4542 .66O 53O4 561.2 .9 1 O 5 to 1 4360
. 165 566O 5384 .4 15 4476 4505 . 665 5258 5632 .9 15 515o 437 o
. 17O 5633 5426 .42O 4512 4470 .670 52 11 3648 .92O 5 198 4384
4. 175 5603 5466 || 4.425. 4550 4438 || 4.675 5163 p661 || 4.925 5245 44C2
. 180 5571 5504 . 450 4591 44O9 . 680 5 t 14 567 ? .93O 529O 4423
. 185 5536 554O . 435 46.34 4383 . 685 5064. 5677 . 935 55.34 4448
. 190 5498 5574 .44 O 4678 4359 . 690 50 14 5679 .94O 5375 4476
. 195 5459 5605 .445 4724. 4339 , 695 4964 5677 . 945 54. 14. 4507
4.2OO 54 18 5633 || 4.450 4771 4322 || 4.700 4914 5672 || 4.950 B450 454
.205 5375 5658 .455 4819 4309 . 705 4865 5663 .955 5484. 4577
.21 O 5550 568O .46O 4868 4299 .7 to 48 17 5651 .96O 55 15 46.17
.215 5284 56.99 .465 49 17 4292 .715 477o 5635 . 965 5545 4659
. 22O 5256 57 16 .47O 4967 4289 .72O 4724 56.15 .97o 5567 4705
4.225 5.188 5730 || 4.475 50.174289 || 4.725–4679 5592 || 4.975 5588 4748
.23o 5139 5740 .48o 5067 4293 .73o 4656 B566 .98o 5606 4795
.235 5090 5747 .485 51 17 43Oo .735 4595 5537 . 985 5619 4845
. 24 O 504O 5750 . 490 5 166 43 it .74o 4557 5505 .990 5629 4892
. 245 499C 5750 . 495 52 14. 4325 . 745 4521 547 O .995 56.55 4952
4.25o 494O 3747 || 4.5oo TB261 4342 || 4.750 4488 5453 || 5. Ooo 5637 4992
F R E S N E L
I N T E G R A L S
C S x C S X C S x C S
5657 4992 || 5.250 46 to 4556 || 5.500 4784. 5537 || 5.750 555 1 5049
.oO5 56.35 5042 .255 465o 4506 || .505 T 4759 5516 .755 5544 5058
... O to 5629 5091 .260 4692 4479 .5 ! O 4696 5491 .760 5533 5147
... O 15 5619 5 140 .265 4737 4456 .515 4655 54.62 .765 55.17 5.194
• O2O 5605 5 189 .27O 4783 4437 .52O 46.16 5450 .77O 5497 5240
5.025 5588 52.36 E.275–483 THAZZTE. 525–4580-5355TE.775T5473TB284
. O30 5567 5281 .28o 4879 44 to .53o 4548 B357 .78o 5444 B525
. O35 5543 5324 .285 4928 44O2 .535 451 9 5516 .785 54 12 5564
. O40 55 15 5366 .290 4978 4399 .540 4494 5275 .790 5377 54 oo
• Q45 5484 54O5 .295 5028 44OO .545 4473 5228 .795 5339 54.52
5.opo 54.5o 54.42 || 5.300–5078-4405 ICE.550 44.56-5TSTTE.800TB258 5457
. O55, 54 tº 5476 .305 5 t 27 4414 . 555 4443 5132 .805 5255 5486
. O60 5573 5506 . 3 to 5 175 4427 .56O 4434 5083 .81 o 521 O 5506
. O65 5331 B534 . 3 15 5222 4444 . 565 4429 5054 .8 15 5165 5523
.07.0 3288 5558 . 32O 5267 44.65 .570 4429 4984 || .820 5.1 14 5525
5. O75 5242 5579 || 5.325 55 1 1 4490 || 5.575 44.55 4934 || 5.825 5065 5543
. O80 5 195 5596 . 330 5352 4518 .58o 44.41 4885 .830 T5015 5546
. O85 5147 5609 . 355 5591 4549 . 585 4454 4837 . 835 4965 5544
. O90 5098 5618 , 34 O 5427 4584 .590 447 1 4789 .84O 4915 5538
. O95 5.048 B623 . 545 54.6C 4622 . 595 4492 4743 . 845 4866 5528
5. too 4998 5624 || 5.350 B450 466: Tºº. 600–45 tº 4700-Is. 850 48l.9 551.3
, 105. 4948 5621 , 555 5516 4705 . 605 4546 4659 .855 4775 54.94
. 1 1 O 4898 56.15 , 56O 55.59 4749 . 61 O 4578 4621 . 860 4728 5470
. 1 15 4849 5604 . 365 5558 4795 . 615 4613 4586 . 865 4686 5443
. 12O 4802 5589 . 370 5572 4843 . 62o 4651 45.54 .87O 4647 54 12
T; , T25T4755-557TT5.375 5583 4892 || 5.625 4692 4525 || 5.875 461 1 5377
. 150 A.7 to 5549 . 380 B589 4942 .63O 4735 4500 .88o 4578 5539
, 135 4.668 5524 . 585 559 1 4992 . 635 4781 4479 .885 4549 5298
. 14 O 4627 54.94 . 59C 5539 5042 . 64 O 4828 44.62 .890 4524 5255
. 145 4589 54.62 . 595 5583 509 1 . 645 4877 4449 . 895 4503 52 10
5. 15O 4553 5427 || 5.4 oo 5573 5 140 || 5.650 4926 444 || || 5.90o 4486 51.63
. 155 452O 5389 . 405 5558 518 . 655 4975 4437 .905 4472 5i 15
. 16O 449 1 5348 . 4 1 O 5540 5235 .66O 5025 4458 .910 4465 5066
. 165 4465 5305 . 415 55.18 528O .665 5076 4445 . 915 4462 50 16
. 17O 4442. 5261 .42O 3492 5322 . 670 ± 125 4.453 .92O 4465. 4966
5.175. 4423 52 15 || 5.425 5462 5362 || 5.675 51754.466 || 5.925 4469 49 17
. 18O 44O9 5 167 .45O 5429 54 OO .68o 52 19 4484 .950 T448o 4868
. 185 4398 5 t 18 . 435 5393 5435 .685 5264 4506 .935 4495 482
. 190 4591 5069 .44O 5.554 54.66 .690 5307 4.552 .94O 4515 4774
#; #### # #3 # ### # # H:#; #3 #
. 2CO 9 4959 || 5 - 450 5269 55 19 •700, 52 95 • 950
.2O5 4394 49 19 .455 5223 B54O . 705 54 19 4652 .955 4597 4649
. 2 to 44O3 487O .46O 51.76 5556 .7 to 5450 467 .96O 4652 4.6 t 5
.215 44 16 4822 .465 5127 5569 .715 5477 47 13 .965 467O 4581
• 220 4433 4775 || .470 5078 5577 || .720 550 l 4757 || -970 47 1 1 4.552
5.225. 4454 4750 || 5.475 5028 558 1 || 5.725 5520 4805 || 5.975 4744. 4527
.25o 4479 46.86 .430 4978 558t .73o 5535 485.1 .980 4800 4507
.235 4507 4644 .485 4928 5576 .735 5546 4900 .985 4847 449 |
.24O 4538 4605 .490 4879 5567 .74O 5552 4949 .990 4896 4479
.245 4572 4569 .495 485.1 5554 .745 5554 49.99 .995 4945 4472
5.250 46 to 4556 || 5.5oo 4784. 5557 || 5.750 555 t 5049 |6. ooo 4995 4470



F R E S N E L
I N T E G R A L S
X C S X C S X C S X
6. OOOT 4.995 44.70 ||6.250 4493 4954 ||6.5oo 4816 5454 || 6.750
OO5 5045 4472 . 255 450 1 4905 . 505 4771 54.32 .755
O 1 O 5095 4479 . 26O 4513 4856 .510 4728 54.06 . 760
O 15 5144 449 . 265 4530 4809 || .515 4.638 5576 || . 765
O2O 3 19 1 4507 . 27O 455 1 4764 . 52O 4652 5342 . 770
6.025 T5237 4527 T5.275 T4576-472 TT6.525_4619 53.05 || 6.775
ojo 5280 4.552 .28O 4606 468 t .53O 4590 5264 . 780
. O35 532O 458 . 235 464 O 4644 .535 4566 522O . 785 4977 5469
O4. Q 3553 4.614 . 29C, 4677 461 . 54 O 4546 5174 . 790 4927 5465
O45 5: 93 465 () || .235 47 17 453 1 || .345 455 1 ºf 127 || . T95 4.878 34.52
6. O50 54.24 4639 || 6.3OO 476O 4555 || 6.550 4520 5078 || 6. 300 4851 54.36
. O35 5453 iº . 505 43 O5 45.34 . 555 45 15 5028 305 4785 54.15
O6O 5475 ºzº . 31 O 4852 4518 . 560 45 15 4978 31 O 4742 5390
O65 54.94 48". " . 3 15 4901 4506 . 565 452 4928 . 3 15 47.02 5360
Q7O 5508 4369 || 32O 4950 4499 || .570 453 1 4879 || . 820 4666 5326
6. O75 551& 49 13 || 6.525 FOoo 4497 || 6.575 4546 4332 @.325 4.633 3233
O3o 5525 4968 . 33O 5050 44.99 . 580 4566 4.786 . 83O 4605 5247
, O3.5 5523 50 18 . 335 5099 4507 . 585 4591 47.43 . 835 4581 52O3
ogo 55 13 5063 . 54 O 51.48 4520 . 590 462O 47O2 .84 O 4562 5 157
2–22 2222 217 | . .243 2135 4338 || .395 4653 4665 || .345 4548 5109
6 : 100 54.95 5165 ||6.350–5240 4560 || 6.500 #655-463TT5.355TA555 5566
ºs 3477-53ſ. . 355 5282 4555 . 605 4730-450 .855 4536 50 To
to 5454 5256 . 36O 5322 4617 . 610 4773 4575 . 860 4558 496.O
i 5427 5298 || 365 5.358 465 t | . 615 4819 4554 || . 865 4545 49 to
32 2396 £337 || . .370 5391 4689 || 62o 4866 4538 || .876 4358 4862
5. 25 3362 B373 || 6.375-542d 4725 || 6.025 4.315 4527 iſ 6.875 #575-45ſ;
: 50 B334 B456 . 38o 5444 4.775 . 630 4964 452 .880 4598 477
* 55 5283 5435 . 565 54.64 48.19 . 635 ×o 14 452O . 835 4.625 4729
. 140 3239 546 O . 39() 543O 4.866 . 64 O 5064. 4525 . 39C 4657 4-690
- . 142 B 193 5489 . 595 549 1 49 15 . 645 5 i3 4535 . 895 4693 4655
6. 150 ± 146 3496 || 6.400 54.96 4965Tá.650TE 16 1 4.545) iſ 6,500 4753 4.63%
155 5097 5507 .405 54.96 50 15 . 655 5207 4569 . 905 4774 4598
. 16O 504.8 E5 14 || .4 to 5492 5065 . 660 525O 4593 || . 91 O 482O 4576
t 65 49.98 55,16 .4 15 5433 51 14 . 665 529 tº 462 . 915 4867 4.559
. 17 O 4949 55 13 .42O 54.69 5 162 . 670 5329 4.654 . 92O 49 13, 4548
6.175. 4900 5505 || 6.425, 5450 B308 || 5.675 5563 465 TT 6.525. 4565 4542
. 180 4852 5495 .43O 5426 5252 . 680 B593 4.75 i . 93O 5C, 15 454
. 185 4.805 5476 . 435 53.98 5294 . 685 54 19 4774 . 935 5065 4546
. 19 O 4759 5454 . 440 5366 5532 . 690 544 O 48 1.9 . 94 O 51 14. 4556
. 195 47 16 54.23 .445 5331 5567 .695 5456 4.866 . 945 5162 457
6.200. 4676 53.98 || 6.450 5292 5558 || 6.700 54.67 45 15 || 6.950 B207 459:
.2O5 4639 5364 . 455 5250 54.25 . 705 5473 4965 . 955 5250 4616
. 2 to 4 106 5327 . 460 52O5 5448 . 71 o 5474 50 15 . 960 5200, 4646
.2 15 4576 5287 . 465 5158 54.67 . 715 547 O 5064 . 965 5326 4680
.22O 455C 524.4 .47o 51 to 54.79 .72O_546O 5113 . 970 5.359 47 18
5.225 4529 BT58 || 5.475 T506 T5487 || 6.735TB445-516 TT6.975–558; 4775
. 230 45 12 515 . .43o 50 it 549 . 730 B425 52O7 . 93O 54 t t 4803
. 235 4500 5 1 O3 . 485 4961 5489 . 735 54 oo 5250 . 935 3430 4850
24 O 4493 5054 . 490 49 12 5482 .74 O 5372 529 . 99 O 5444 4898
. . 245 4491 3004 . 495 4.864 547 O . 745 53.59 5328 . 995 3452 4947
6.25o 4493 4954 || 6.500 4315 B454 Tă.750–5503 E352Ty. Soo 5455 4997

F R E S N E L
I N T E G R A L S
S X C S X C S X C S
4997 || 7.25o 5338 4719 |7.5oo 576O 4607 || 7.750 5038 4591
5047 .255 5367 4759 ,505 T52O5 4629 .755 5087 4599
5O96 .26O 5592 4803 .5 to 5247 4656 .760 5 135 4513
5 144 .265 54 12 4849 . 515 5286 4.638 .765 5.182 4652
5 191 .27O_5426 4897 .520 552 4723 . 770 5225 4657
5234 || 7.275 54.34 4946 || 7.525-535 tº 4753 ||7.775 5265. 4687
5275 .280 5437 4996 .53o 5576 4806 .78o 55oo 4.722
5313 .285 5434 5046 . 535 5596 4352 .785 533 ( 4761
5347 .29O 5426 5095 . 54 O 54 O 4900 . 790 5558 43O4.
5577 .295 54 12 5144 .545 54 19 495O .795 5579 4349
54.02 || 7.5oo 5393 5190 || 7.55o 54.22 500 TET.8oo_5395 4.896
3422 .305 5363 B233 . 555 54 18 5051 .805 54.05 4945
5437 . 3 to 5339 5273 .56O 54O9 5098 . 8 1 O 5408 4995
5446 . 3 15 5505 55 to .565 5394 5.146 . 8 15 54.05 5045
o 5450 . 32O 5267 5343 .57O 5374 B 192 . 82O 5596 5O94
7. O75 4964. 5448 || 7.325-5226,5370 T. B75 T5348.5235Tº. 825 B581–5142
. O3O 4914 5441 .33o 5182 5394 .58o 5318 5274 . 830 5560 5.188
. O85 4.866 5429 .335 5 135 54 12 .585 5283 53 to .835 5334 5251
. O90 43 19 5411 . 34o 5087 5425 .590 5244 534.1 . 840 5505 5270
. O95 4775 5388 . 345 5037 54.32 .595 520 1 5.568 . 845 5.268 5305
7. TOQ 4.755 536O || 7.550 4987 9433 ſ. 600 5 1565389 || 7,850 5228, 53.35
. 1 OB 4695 5328 . 355 4938 5428 . 605 51 O9 5404 .855 51.85 5360
. 1 1 O 466O 5292 . 360 4389 5418 . 6 1 O 5060 5414 . 860 5 139 5380
. 115 4.650 B252 . 365 4842 54O2 . 615 501 O 54 18 . 865 5091 5594
. 12O 46O5 5209 . 370 4796 538 .62O 496O 54 16 . 870 3042 54O2
7. 125 4585-5164. Tz. 375 T4753 B354 || 7.625-451 TEAC&T/.875 4952 E4S4
. (3o 4569 51 16 .33d 4714 5523 .63O 4865 5394 . 880 4.942 54OO
. 135 4559 5067 . 385 4679 5288 .635 4.817 5375 . 885 4.895 5390
. 14O 4555 50.17 . 590 4648 5249 .640 4773 5350 . 890 4846 5373
. 145 4556 4967 . 595 4622 52O7 . 645, 47.33 332O . 895 4.8O1 5351
7. 150 4563 4518 || 7.400T 460 T516 LT7.650T 4607-5285 IT. Soo T475c) B323
. 155 4575 4869 .405 4585 51 13 . 655 4665 5247 . 905 4722 5291
. 16O 4592 4822 .4 to 4575 5064 .66O 465& 5205 , 9 to 4688 5254
. 165 4615 4777 . 415 4571 50 14 , 665 4617 5160 . 915 4659 52.13
. 17O 4645 4736 .42O 4572 4964 .67O 4601 51 12 . 920 4-656 5169
7. 175 4675 4698 || 7.425. 4580 4515 || 7.675-455. Boé, IE7.925–4518–542:
. 18O 47 ft 4664 .43o 4593 4867 . 680 4536 50 13 . 93C 4606 5074
. 185 475 4634 . 455 46 12 462O . 685 4588 4963 . 935 46OO 5025
. 190 4794. 4608 .44C 4635 4776 . 690 4595 49 14 . 940 4-6OO 4975
. 195 4839 4587 . 445 4664 4735 , 695 4609 4866 . 94-5 4-605 4925
7.200–4887. 4572 TV.450T4697-4658 T.705 T4638-4820 || 7.555–4615. 4577
.2O5 4956 4562 .455 4735 4666 .705 4652 4777 .955 4.638 483d
.21 O 4986 4558 .460 4776 4637 .7 to 4682 4.737 . 960 4662 4787
.2 15 5056 456O || .465 4820 46 13 .7 15 47 16 4700 . 965 4692 4747
.22O 5086 4567 .47O 4867 45.95 . 720 4755 4668 , 970 4726 47 to
7.225 T51.34 4580 TV.475-4915, 4583 ||7.725. 4797. 464 II",375.T.4764-4575
.23o 518 4593 . 430 4964. 4576 .750 4842 4620 . 980 4806 4651
.255 5225 4622 . 485 50 14 45.75 .755 4389 4604 . 985 4351 463o
.24C 5266 4.650 . 490 5064. 4580 .74O 4938 4593 990 4899 46.15
.245 5505 4682 . 495 5 13 459 | , 745 4988 4589 , 995 4.948 4606
7.25o 5338 4715 IT.BööTBT55 Höö7T".75d 5635-455TT5.665-4555-45C2