118 
MINUTES OF PROCEEDINGS OF 
the cup of mercury. Now, to obtain the former, the latter of these 
times has to be subtracted from the reading of the instrument, and the dis- 
junctor enables us to do this by permitting us to break both currents 
(those through the first and second screens) simultaneously. The mode 
of procedure is then as follows :—The instrument being arranged, the 
two currents are simultaneously broken by means of the disjunctor, 
and the reading of the needle is recorded. The instrument is again 
adjusted, the projectile fired the velocity of which it is desired to 
determine, and the reading of the needle again noted ; the former arc 
is subtracted from the latter, and the corresponding time computed. It 
will be observed that by the use of the conjunctor any constant source 
of error (such, for example, as the error due to the time required to 
clamp the vernier needle) is eliminated, as the same error will occur 
both in the disjunctor and the projectile reading, and by subtraction 
will disappear. 
The disjunctor also enables us to ascertain the degree of regularity 
with which the instrument is working, as the accidental variations of 
the reading corresponding to the time 0, are of course the same as the 
variations which would occur in the reading corresponding to any 
other time. Major Navez lays down, as a rule, that observations 
should not be proceeded with when in a series of ten or twelve dis- 
junctor readings there is between two successive readings a difference 
greater than 0° * 25. 
6. It is of some importance to be enabled to put an exact estimate on 
the degree of reliance to be placed on the results of Major Navez’s 
beautiful instrument ; and, to do this, let us observe that the arc from 
which the required time is computed is the difference between two arcs, 
in our estimation of each of which we are liable to a small error. We 
have in fact the value of one arc <I> given by the equation 
= f — .....(1) 
where <p and <p' are each subject to probable errors (let us suppose) 
t and r' ; the probable error of $ is then r 2 -f r' 2 . If, after the satis¬ 
factory working of the instrument has been ascertained, and the 
probable error determined, we take a single reading with the disjunc¬ 
tor, and then with the projectile, r and r' are equal, and the probable 
error of the observation is r\/ 2. We have it, however, in our power, 
if it be thought necessary, to reduce even this error, for if the dis¬ 
junctor reading be taken, the mean of, say five observations, we have 
h' = and the probable error of # is which differs but 
slightly from r. An example will show how very trifling this error 
generally is. With an Armstrong 12-pounder shell, whose velocity is 
determined to be 1,181 feet per second, the value of r is found to be 
0°*06, and the disjunctor reading being the mean of five observations, 
the probable error of <1> is 0°*07. 
Hence the disjunctor reading being 42°*85, and the projectile 
reading 107°‘40, it follows that it is probable that in our determina¬ 
tion of 1181*2 ft. as the velocity at a point midway between the 
screens, we do not make an error exceeding 1 * 4 ft., that is to say, it is 
an even chance that the true velocity of the single observation lies 
between 1179*8 ft. and 1182*6 ft. As the round from which the 
above example is selected is one of a series of 10, the probable error 
in our determination of the mean velocity between the screens will 
be less than one-third of that just given, or the mean velocity may be 
assumed, as far as instrumental errors are concerned, to be practically 
correct. 
