TRACT 37.

OF GUNNERY.

297

that these numbers, for the value of n, ought to exhibit thefirst force of the inflamed powder, when it is supposed to oc-cupy the space only in which the bare powder itself lies;whereas it is manifest, that the condensed fluid of the charge,in these experiments, occupies the whole space between theball and the bottom of the gun bore, or the whole space takentip by the powder and the bag together: which exceeds theformer space, or that of the powder alone (besides the dif-ferent lengths in the bore, which has been accounted for byusing h for a in the theorem) at least in the proportion of thecircle of the gun bore, to the same as diminished by thethickness of the surrounding flannel of the bag that containedthe powder; it is manifest then that the force was diminishedin the same ratio on that account. Now, by gently com-pressing a number of folds of the flannel together, it hasbeen found that the thickness of the single flannel was equalto the 40th part of an inch; the double of wdiich, ^ or '05of an inch, is therefore the quantity by which the diameterof the circle of the powder within the bag, was less than thatof the gun bore. But the diameter of the gun bores was 2 - 02inches; therefore, deducting the '05, the remainder 1’97 isthe diameter of the powder cylinder within the bag: and be-cause the areas of circles are to each other as the squares oftheir diameters, and the squares of these numbers, 1'97 and2'02, being to each other as 388 to 408, or as 97 to 102;therefore, on this account alone, the numbers before found,for the values of n, in the last column of the table, must beincreased in the ratio of 97 to 102, or nearly the part;which increase being made, the numbers for the value of nwill be as in the annexed tablet, so far as includes the effectof this cause of increase.

Powder.

The Guns.

02

i

2

3

4

4

1244

1255

1303

1296

8

1388

1521

1707

1752

16

1612

1606

1758

1773