MESSRS. R. H. FOWLER AND C. N. H. LOCK ON 
9,4.9 
j-j rt 
k > 45 degrees. If necessary, similar curves are drawn for otlier values of k (rounds 
III. 11, III. 16) and the true values of k, sin \rt and <dT (the length of the half-period) 
finally settled by interpolation. 
If required a curve can be calculated by the exact formula (10) after g has been 
determined by (19), but the change of shape is negligible unless sin \ol and, therefore, g 
is very large. An example of the effect of including g is shown in fig. 3 for III. (11), 
but round III. (11) and its companions are the only ones in which g had any sensible 
effect. Rounds IV. (8 and 9) illustrate the effect of a considerable alteration in b 
(representing the initial disturbance) in causing, when s < 1, a considerable change in 
period but only a small change in amplitude. The fit obtained between calculated 
and observed curves is generally good. The selected curves in fig. 3 are a fair sample 
of the whole. 
When the minimum yaw (3 is not zero the curve is first calculated as above, as if 
j3 ~ 0, and then corrected by (33), using the observed value of (3, which is obtained 
like ol from a rough curve. An example of such curves will be found in fig. 3 for the 
second half-period of IV. (8) and the second and third half-periods of III. (16). After 
the (3 correction has been put on, the value of k may require readjustment to obtain 
the proper fit. 
The values of k, sin \a and iiT so determined are given for each half-period of each 
round in Table II., together with sin|/3 and X obtained from the equation X = K/QT. 
We then obtain s, q and b from equations (15)-(17).* From the values of s and q and 
the other observational data we can calculate / M sin ^ as a function of vja and § from 
formulae (3) and (4). The results are shown in figs. 1 and 2, and Tables I. and III., 
and have already been discussed. 
The damping effects appear in the variation of the various constants from one 
half-period to another. In general, s increases approximately at the rate required by 
theory, i.e., inversely as the square of the velocity at the middle point of the half- 
period:f 
* When k is much less than 45 degrees the method breaks down, as k cannot be determined satisfactorily 
from the observational curves. The method explained in (A), p. 343, could then be employed. This is 
equivalent to assuming q = 0 and using formula (16) to determine k given sin \cl and A. Under these 
conditions sin Ja is so small that the value of q does not appreciably affect either the value of s or the shape 
of the curve of/ M against S. 
| Theoretically, s should increase while q should remain roughly constant. But sin \cl is common to 
the first and second half-period, while A is determined mainly by the shape of the curve near the maximum. 
Hence, in general, k alone varies between the first and second half-periods. It appears that the result of 
varying k only in formulae (15, 16) is to produce a fictitious decrease in q while the increase of s is diminished 
as may be seen in Table II. For this reason mean values for the whole period are used in constructing 
figs. 1 and 2. 
