i^4 of projectiles,

and drawing a line through the points agpby, it will be thescaie of spaces in tile times of the retarded movements ofimpulsion.

158. Having constructed this scale (156, 157), the resultof the experiments should be examined to lee that there be noerror, and as it is the scale of a retarded movement, it sliouldhave the properties expressed in the treatise on moving bodies :in the first place, the line agp by should be a curve concavetowards the directrix, and the differences p m, bo, Ly be-tween the ordinates, should decrease in a regular progressionfrom a to y ; wherefore, if the scale be a right line, or acurve convex toward the directrix, it is a proof that someerrors have been committed in making the experiments, orin taking the results. But if they differ a little in one ortwo points only, it is immaterial, since small errors are ine-vitable ; when this occurs, the differences should be judici-ously corrected. To this end, deduct the second differencesfrom the first: and if the results be still erroneous, take thethird differences ; in the latter, the least irregularity incarrying on the experiments will considerably disturb theorder of progression. To set this matter in a clear point ofview, suppose the following to have been the result of theexperiments.

Spaces passed through by the Shot from the impulsive motionin corresponding times.

Differences.

Seconds of ‘Titnei

Fat.

First.

Second.

Third.

1

—

1302

—

—

—

—

%

—

2394

I0Q2

—

—

3

—

33 10

916

176

— '

4

—

4082

—

772

144

32

5

—

4730

—

648

124

20

6

*

5284

—

554

94

30

If no error be perceptible in the first ; but in the second,the progression does not decrease regularly, and in the thirdthe difference after decreasing from the first term 32 to thesecond 20, increases from the second term 20 to the thirdterm 30, to correct these errors, let the results be modified asjbelow; then will all the differences decrease in a regularprogression and be sufficiently accurate.

Results