Expansion .0101 on 25 Inches,
.0105 on 26 Inches,
——
The Remainder .0004 is the Expansion with 4° on 1 Inch, above 25, i. e. on the 26th Inch.

362. 3d. To find the Expansion, with 4° on .1 above 25 Inches; add a Cypher and decimal Point to the former Answer, which then becomes .00004, viz. the Expansion, with 4° on one Tenth, above 25 Inches.

363. 4th. Lastly, to obtain the Expansion with 4°, on .19, above 25 Inches, say: If one Tenth of an Inch, above 25 Inches, gives this Expansion viz. .00004, what Expansion will nineteen Tenths above 25, give? answer .19 Tenths more; thus:

If .1:.00004::.19?
.19
———
00036
0004
———
.00076;then, in order to have

as many decimal Places in the Product as are contained both in the Multiplicand and Multiplier, add a Cypher and Point to the left, and the Product becomes .0000076 which, being divided by .1, gives a Cypher less. viz. the Expansion with 4° on .19 above 25 Inches.

THE FIRST TABLE:
shewing the expansion with HEAT
on inches of the BAROMETER.
degrees of the THERMOMETER, from 1 to 40, on farenheit’s scale.
9 10 11 12 13 14 15 16

1

 .00091 .00102 .00112 .00122 .00132 .00142 .00152 .00162

2

 .00182 .00204 .00224 .00244 .00264 .00284 .00304 .00324

3

 .00273 .00306 .00336 .00366 .00396 .00426 .00456 .00486

4

 .00364 .00408 .00448 .00488 .00528 .00568 .00608 .00648

5

 .00455 .00510 .00560 .00610 .00660 .00710 .00760 .00810

6

 .00546 .00612 .00672 .00732 .00792 .00852 .00912 .00972

7

 .00637 .00714 .00784 .00854 .00924 .00994 .01064 .01134

8

 .00728 .00816 .00896 .00976 .01056 .01136 .01216 .01296

9

 .00819 .00918 .01008 .01098 .01188 .01278 .01368 .01458

10

 .00910 .01020 .01120 .01220 .01320 .01420 .01520 .01620

11

 .01001 .01122 .01232 .01342 .01452 .01562 .01672 .01782

12

 .01092 .01224 .01344 .01464 .01584 .01704 .01824 .01944

13

 .01183 .01326 .01456 .01586 .01716 .01846 .01976 .02106

14

 .01274 .01428 .01568 .01708 .01848 .01988 .02128 .02268

15

 .01365 .01530 .01680 .01830 .01980 .02130 .02280 .02430

16

 .01456 .01632 .01792 .01952 .02112 .02272 .02432 .02592

17

 .01547 .01734 .01904 .02074 .02244 .02414 .02584 .02754

18

 .01638 .01836 .02016 .02196 .02376 .02556 .02736 .02916

19

 .01729 .01938 .02128 .02318 .02508 .02698 .02888 .03078

20

 .01820 .02040 .02240 .02440 .02640 .02840 .03040 .03240

21

 .01911 .02142 .02352 .02562 .02772 .02982 .03192 .03402

22

 .02002 .02244 .02464 .02684 .02904 .03124 .03344 .03564

23

 .02093 .02346 .02576 .02806 .03036 .03266 .03496 .03726

24

 .02184 .02448 .02688 .02928 .03168 .03408 .03648 .03888

25

 .02275 .02550 .02800 .03050 .03300 .03550 .03800 .04050

26

 .02366 .02652 .02912 .03172 .03432 .03692 .03952 .04212

27

 .02457 .02754 .03024 .03294 .03564 .03834 .04104 .04374

28

 .02548 .02856 .03136 .03416 .03696 .03976 .04256 .04536

29

 .02639 .02958 .03248 .03538 .03828 .04118 .04408 .04698

30

 .02730 .03060 .03360 .03660 .03960 .04260 .04560 .04860

31

 .02821 .03162 .03472 .03782 .04092 .04402 .04712 .05022

32

 .02912 .03264 .03584 .03904 .04224 .04544 .04864 .05184

33

 .03003 .03366 .03696 .04026 .04356 .04686 .05016 .05346

34

 .03094 .03468 .03808 .04148 .04488 .04828 .05168 .05508

35

 .03185 .03570 .03920 .04270 .04620 .04970 .05320 .05670

36

 .03276 .03672 .04032 .04392 .04752 .05112 .05472 .05832

37

 .03367 .03774 .04144 .04514 .04884 .05254 .05624 .05994

38

 .03458 .03876 .04256 .04636 .05016 .05396 .05776 .06156

39

 .03549 .03978 .04368 .04758 .05148 .05538 .05928 .06318

40

 .03640 .04080 .04480 .04880 .05280 .05680 .06080 .06480
THE FIRST TABLE CONTINUED:
shewing the expansion with HEAT
on inches of the BAROMETER.
degrees of the THERMOMETER, from 1 to 40, on farenheit’s scale.
17 18 19 20 21 22 23 24

1

 .00172 .00182 .00192 .00203 .00213 .00223 .00233 .00243

2

 .00344 .00364 .00384 .00406 .00426 .00446 .00466 .00486

3

 .00516 .00546 .00576 .00609 .00639 .00669 .00699 .00729

4

 .00688 .00728 .00768 .00812 .00852 .00892 .00932 .00972

5

 .00860 .00910 .00960 .01015 .01065 .01115 .01165 .01215

6

 .01032 .01092 .01152 .01218 .01278 .01338 .01398 .01458

7

 .01204 .01274 .01344 .01421 .01491 .01561 .01631 .01701

8

 .01376 .01456 .01536 .01624 .01704 .01784 .01864 .01944

9

 .01548 .01638 .01728 .01827 .01917 .02007 .02097 .02187

10

 .01720 .01820 .01920 .02030 .02130 .02230 .02330 .02430

11

 .01892 .02002 .02112 .02233 .02343 .02453 .02563 .02673

12

 .02064 .02184 .02304 .02436 .02556 .02676 .02796 .02916

13

 .02236 .02366 .02496 .02639 .02769 .02899 .03029 .03159

14

 .02408 .02548 .02688 .02842 .02982 .03122 .03262 .03402

15

 .02580 .02730 .02880 .03045 .03195 .03345 .03495 .03645

16

 .02752 .02912 .03072 .03248 .03408 .03568 .03728 .03888

17

 .02924 .03094 .03264 .03451 .03621 .03791 .03961 .04131

18

 .03096 .03276 .03456 .03654 .03834 .04014 .04194 .04374

19

 .03268 .03458 .03648 .03857 .04047 .04237 .04427 .04617

20

 .03440 .03640 .03840 .04060 .04260 .04460 .04660 .04860

21

 .03612 .03822 .04032 .04263 .04473 .04683 .04893 .05103

22

 .03784 .04004 .04224 .04466 .04686 .04906 .05126 .05346

23

 .03956 .04186 .04416 .04669 .04899 .05129 .05359 .05589

24

 .04128 .04368 .04608 .04872 .05112 .05352 .05592 .05832

25

 .04300 .04550 .04800 .05075 .05325 .05575 .05825 .06075

26

 .04472 .04732 .04992 .05278 .05538 .05798 .06058 .06318

27

 .04644 .04914 .05184 .05481 .05751 .06021 .06291 .06561

28

 .04816 .05096 .05376 .05684 .05964 .06244 .06524 .06804

29

 .04988 .05278 .05568 .05887 .06177 .06467 .06757 .07047

30

 .05160 .05460 .05760 .06090 .06390 .06690 .06990 .07290

31

 .05332 .05642 .05952 .06293 .06603 .06913 .07223 .07533

32

 .05504 .05824 .06144 .06496 .06816 .07139 .07456 .07776

33

 .05676 .06006 .06336 .06699 .07029 .07359 .07689 .08019

34

 .05848 .06188 .06528 .06902 .07242 .07582 .07922 .08262

35

 .06020 .06350 .06720 .07105 .07455 .07805 .08155 .08505

36

 .06192 .06534 .06912 .07308 .07668 .08028 .08388 .08748

37

 .06364 .06716 .07104 .07511 .07881 .08251 .08621 .08991

38

 .06536 .06892 .07296 .07714 .08094 .08474 .08854 .09234

39

 .06708 .07078 .07488 .07917 .08307 .08697 .09087 .09477

40

 .06880 .07260 .07680 .08120 .08520 .08920 .09320 .09720
THE FIRST TABLE CONCLUDED:
shewing the expansion with HEAT
on inches of the BAROMETER.
degrees of the THERMOMETER, from 1 to 40, on farenheit’s scale.
25 26 27 28 29 30 31 32

1

 .00253 .00263 .00274 .00284 .00294 .00304 .00314 .00324

2

 .00506 .00526 .00548 .00568 .00588 .00608 .00628 .00648

3

 .00759 .00789 .00822 .00852 .00882 .00912 .00942 .00972

4

 .01012 .01052 .01096 .01136 .01176 .01216 .01256 .01296

5

 .01265 .01315 .01370 .01420 .01470 .01520 .01570 .01620

6

 .01518 .01578 .01644 .01704 .01764 .01824 .01884 .01944

7

 .01771 .01841 .01918 .01988 .02058 .02128 .02198 .02268

8

 .02024 .02104 .02192 .02272 .02352 .02432 .02512 .0259?

9

 .02277 .02367 .02466 .02556 .02646 .02736 .02826 .02916

10

 .02530 .02630 .02740 .02840 .02940 .03040 .03140 .03240

11

 .02783 .02893 .03014 .03124 .03234 .03344 .03454 .03564

12

 .03036 .03156 .03288 .03408 .03528 .03648 .03768 .03888

13

 .03289 .03419 .03562 .03692 .03822 .03952 .04082 .04212

14

 .03542 .03682 .03836 .03976 .04116 .04256 .04396 .04536

15

 .03795 .03945 .04110 .04260 .04410 .04560 .04710 .04860

16

 .04048 .04208 .04384 .04544 .04704 .04864 .05024 .05184

17

 .04301 .04471 .04658 .04828 .04998 .05168 .05338 .05508

18

 .04554 .04734 .04932 .05112 .05292 .05472 .05652 .05832

19

 .04807 .04997 .05206 .05396 .05586 .05776 .05966 .06156

20

 .05060 .05260 .05480 .05680 .05880 .06080 .06280 .06480

21

 .05313 .05523 .05754 .05964 .06174 .06384 .06594 .06804

22

 .05566 .05786 .06028 .06248 .06468 .06688 .06908 .07128

23

 .05819 .06049 .06302 .06532 .06762 .06992 .07222 .07452

24

 .06072 .06312 .06576 .06816 .07056 .07296 .07536 .07776

25

 .06325 .06575 .06850 .07100 .07350 .07600 .07850 .08100

26

 .06578 .06838 .07124 .07384 .07644 .07904 .08164 .08424

27

 .06831 .07101 .07398 .07668 .07938 .08208 .08478 .08748

28

 .07084 .07364 .07672 .07952 .08232 .08512 .0879 .09072

29

 .07337 .07627 .07946 .08236 .08526 .08816 .09106 .09396

30

 .07590 .07890 .08220 .08520 .08820 .09120 .09420 .09720

31

 .07843 .08153 .08494 .08804 .09114 .09424 .09734 .10044

32

 .08096 .08416 .08768 .09088 .09408 .09728 .10048 .10368

33

 .08349 .08679 .09042 .09372 .09702 .10032 .10362 .10692

34

 .08602 .08942 .09316 .09656 .09996 .10336 .10676 .11016

35

 .08855 .09205 .09590 .09940 .10290 .10640 .10990 .11340

36

 .09108 .09468 .09864 .10224 .10584 .10944 .11314 .11664

37

 .09361 .09731 .10138 .10508 .10878 .11248 .11618 .11988

38

 .09614 .09994 .10412 .10792 .11172 .11552 .11932 .12312

39

 .09867 .10257 .10686 .11076 .11466 .11866 .12246 .12636

40

 .10120 .10520 .10960 .11360 .11760 .12160 .12560 .12960

The 5th Step, applied in the first Example.

364. Add this, to the former Expansion, thus: