282

THEORY AND PRACTICE

TRACT 37.

142. In these four examples, the results'are various, bothfor the strength of the wood, and the time of penetration,though the data, from which they are computed, are the me-diuins of several experiments; doubtless, the consequenceof several unavoidable circumstances, as, the irregularityamong the different experiments, and the different blocks ofthe wood, and the resistance of the wood not being exactly ^constant quantity, owing to the condensation and elasticityof the parts of it driven in before the ball. In this uncer-tainty, we may take a medium among all the four results,both for the strength of the timber, and the time of penetra-tion, as follows.

Values of f.

of t.

24000

480

18000

480

14062

300

1 3200

398

4)69262

4) J 658

f zz 17.31.5 mediums. 415 . . . t —

So that, the mediums among these 4 cases, give us partof a second, for the time of the ball’s penetration ; and 17315for the strength of the timber, or that its resistance is to theforce of gravity, as 17315 to 1.

Otherwise.

143. The calculation mav be otherwise instituted thus.Putting, as before, d for the ball’s diameter, and f for thestrength or firmness of the matter in the obstacle ; then shalld*f be proportional to the resistance; which resistance let beexpressed by the weight of a column of water of the samediameter d as the ball, and the height f y its specific gravitybeing 1 ; add let the specific gravity of the matter of theball be denoted by n, which in the present case is 7| nearly;and a = ‘7854. Then ad 1 will be the area of the section,and \and l the weight of the ball; so that the resistance willbe to the weight of the ball, as adf to \and 3 , or as f to \nd ,