316 Mr Fowler and Mr Lock, The origin of 



The greatest possible value of the spread is of course ^tt which 

 occurs when the three values of (ft^ are of the form 



a, a + ^TT, a + |77. 



It is thus equally probable that the spread of a group of three will 

 or will not exceed 147° on a basis of random distribution. In the 

 twenty-one groups the spread only twice exceeds and once equals 

 147°, and the average spread is only 70°. The probabihty with a 

 random distribution that any ividividual spread should be less than 

 or equal to 70° is only 0-113. The probability that the average of 

 twenty-one spreads shall be as small as 70° will be excessively 

 small. 



We may therefore be fairly confident on the evidence of the ||| 

 spread that the main part of the angular velocity of the axis of " 

 the shell is due to some cause which operates in or nearly in the 

 same plane for all rounds fired under the same conditions. This 

 conclusion is supported by the results of two five-round groups of 

 similar shells fired from another type of gun*. In each case the 

 spread of the five values of <^q was less than 30°. 



We are, however, justified in concluding that there are other 

 regularities in Table II. It is arranged in order of muzzle velocities 

 for the shells of each type, fired from the gun of each twist of 

 rifling. Thus the table consists of eight sets of such arrangements 

 separated by spaces. In each such set which is sufficiently complete 

 there is a well-marked progressive change noticeable in the mean 

 value of cf)Q as the velocity changes through the set. 



Finally, compare together the mean values of ^q for all groups 

 at the same muzzle velocity from the same gun, irrespective of the 

 type of shell. We obtain the following sets of numbers. For the 

 gun rifled 1 in 40, 



The numbers in brackets on the left specify the muzzle velocity to 

 which the group belongs. These mean values of 0q are obviously, 

 with one exception, heavily correlated. We may say in fact that 

 the main part of the initial disturbance consists of an angular 

 velocity of the axis of the shell located in a plane which varies 

 httle from round to round or even with changes in the centre of 

 gravity and moments of inertia of the shell, but which changes 



* Gun: 16-pdr, 9-cwt. 



