204
EXPERIMENTS WITH
TRACT 3G.
the several angles of inclination, where s denotes the sine, inorder to compare with the resistances, and we shall find thevalues of s u , for the several angles, to be thus:
An-
gles
Values of
5 2C
Exper.
Resist.
Dills.
5°
8
19
11
10
32
52
20
20
133
158
25
30
302
331
29
40
508
533
25
50
710
724
14
60
866
868
2
70
958
957
-i
80
995
994
-i
90
1000
1000
0
Here it appears, that the valuesof s zc agree with the ratios ofthe resistances, from 90° to 60°very nearly ; but that from 60°to 30°, the differences increase,and from 30° to 0, they decreaseagain, the greatest differencebeing at 30°, where it is -f T ofthe whole.
54. Instead of the index 2c, in the function then, it islikely that we shall succeed better if we assume the indefiniteone nc, by adapting its result to the resistance for the ex-perimented angle of 30°, that is, to ascertain what n mustbe, so as that the function s" c may agree with the resistanceat 30°, viz, by making s" c = 331. Now this equation inlogarithms is ?icx log. j = log. 331 , and hence n = log ' 331— 1‘842 nearly. Then taking always s 1 ’ 8 * 2 ', there resultsthe following numbers:
An-
gles
Values ol
s 1*542C
Exper.
resist.
Diffs.
5°
11
18
7
10
42
52
10
20
156
158
2
30
331
.'31
0
40
536
533
-3
50
730
724
-6
60
876
868
-8
70
962
957
-5
80
995
994
-1
90
1000
1000
0
velocity of 12 feetsquare inches, or f
Here the differences being allvery small, it may be concludedthat the function s l ' 84 “ is an ex-pression for the resistance, suffi-ciently near the truth, for all theangles of inclination. And thisbeing multiplied by ‘841, tobring it to ounces, will give•84 Is 1 ’ 842 ' for the resistance, inounces, for any angle, whosesine is s, and cosine c, for thein a second, on a plane surface of 32of a square foot.