48

DEDUCTIONS FROM THE

TRACT 34.

in which last line of means are found by adding into onesum the numbers in each column, and dividing that sum bythe number of those parts. And thus we have obtained themediums of the mediums for each day, which must be verynear the truth. But to find how near they are to the truth,and to correct them, let these be collected and ranged as inthe second column of the following table of the heights of

wt.

oz

Irregular

Regular

Correct

means

means

cliffs

diffs

means

2

4

6

8

10

12

14

16

18

20

1'82

ST 54'3 85’666-95

8- 27

9- 5110-9912-2213-23

1-33

T23

1-28

1'29

1-32

1-24

1-48

1-23

1-01

1-27

1-27

1-27

1-27

1-27

1-27

1-27

1-27

1-27

1-85

3- 12

4- 39

5- 66

6- 938-209-47

10-74

12-01

13-28

2-18

3- 45

4- 72

5- 99

7- 26

8- 53

9- 80

11- 07

12- 34

13- 61

charges, or column of irregular means. Then take thedifferences between each of these, and place them in the 3dcolumn, or irregular differences ; which would have been allequal if the mediums had been regular. Find then a me-dium among these unequal differences, by dividing theirsum by the number of them, and it will be found to be 1-27,which set in the 4th column of regular or equal differences.Then, as the numbers in the 3d column, the nearest to thismean T27, are the differences between 6, 8, and 10 ounces,,by supposing 5-66 to be the true length of the 8 oz charge,all the others are formed from it, by adding and subtractingcontinually the mean or common difference 1-27, and areplaced in the 5th column ; which will therefore consist ofthe true regular length of each charge, including both thepowder and the neck of the flannel bag which contained it,as indicated by the marked divisions on the rammer bywhich the charge was pushed home in the gun bore.