220 
MR. HEARN ON DISCREPANCIES OBSERVED 
I have therefore selected the preceding consecutive positive and negative experiments 
which have the times very nearly alike. 
The consideration of the resistance of the air might, however, at first sight, seem 
very necessary. Since the velocity is very small, we may, according to the conclu- 
sions of experimentalists, assume that the resistance varies nearly as the velocity ; 
dx . . . 
we ought therefore to introduce the term g-fi into the differential equation. The 
result shows that the time of vibration is very little affected by the resistance, but 
the resting point very considerably. Mr. Baily observes four extreme divisions, that 
is, he watches the motion for three successive vibrations, and then takes the means 
of successive pairs of extreme divisions. In this way he has three first means. He 
then takes the means of successive pairs of those first means, and thus obtains two 
second means; and lastly, he takes the mean of the second means, and this third 
mean is considered the resting point or place where the torsion rod would be in equi- 
librium. This proceeding, as I afterwards shall prove, does in general pretty accu- 
rately correct for the resistance of the air, and therefore we may consider Baily’s ‘rest- 
dx 
ing points’ as those which would arise from Mr. Airy’s theory, supposing the term 
for resistance had been introduced into his investigation. After this Mr. Baily com- 
bines his experiments in a very remarkable manner. Three successive experiments 
are combined in order to produce what he terms a single result ; and in combining 
them the means of the positive and negative resting points are taken, and means also 
of the times of vibration ; for such times it is found are never all exactly alike, and 
sometimes differ considerably. In order that the reader may at once see the method 
pursued, I have made the following extract from the tables ; — 
3rd Series. — 2-inch lead balls with bifilar silk lines ; distance =’177 inch ; upper 
distance T58 inch ; lower dist. T97 inch. 
1841. 
No. 
Position 
of the 
masses. 
Extreme 
divisions 
observed. 
1st Mean. 
2nd Mean. 
3rd Mean 
or resting 
point. 
Observed times. 
2 N. 
N for mean 
resting point. 
Feb. 26. 
T =44-500 
B = 29-880 
113 
Negative. 
126-90 
54-80 
119-00 
90-850 
86- 900 
87- 950 
88-875 
87-425 
88-150 
h m s 
At div. 85 
10 13 42-5 
21 24 
h m s 
At div. 90 
10 13 20 
21 48 
m s 
By div. 85 
16 28-5 
m s 
By div. 90 
16 25 
s 
493-148 
56-90 
30 11 
29 45 
8 14-25 
8 12-50 
114 
Positive. 
56-90 
155-40 
63-80 
106- 150 
109-600 
107- 900 
107- 875 
108- 750 
108-312 
At div. 105 
10 38 35 
47 24 
At div. 110 
10 38 51-5 
47 6 
By div. 105 By div. 1 10 
i 
16 51-5 16 53-5 
506-412 
152-00 
55 26-5 
55 45 
8 25-75 
8 26-75 
115 
Negative. 
15200 
30-60 
146-80 
91-300 
88-700 
91-400 
90-000 
90-050 
90-025 
At div. 85 
11 4 33 
12 24 
At div. 90 
11 4 19-5 
12 38 
By div. 85 
16 47 
By div. 90 
16 46 
502-998 
3600 
21 20 
21 5-5 
8 23-5 
8 23 
3rd Series. — 2-inch lead balls with bifilar silk lines; distance ='177 inch. 
1841. 
No. 
Pos. 
Observed 
Deduced. 
Results. 
Time of vibration. 
Resting point. 
Distance. 
Time =N. 
Deviation =D. 
Distance = d. 
Single. Daily. 
Feb. 26. 
113 
493-148 
88-150 
10-9936 
109972 
114 
+ 
506 412 
108-312 
11-0008 
502-242 
9-612 
6-0199 5-6946 
log.C = 6-360356. 
115 
502-998 
90-025 
