THE ROYAL ARTILLERY INSTITUTION. 
179 
130 656, an amount of error to which this method is liable, unless we carry 
the interpolations one place of figures further. It is on this account that, 
although the actual measurements of the records on the cylinder of the 
chronograph do not go beyond the ToVoth or -goVoth of a second, yet, in 
interpolation the consideration of To^oth or even a smaller part of a second 
is retained, in order to give greater facilities for the adjustment of column A 2 
by the application of small corrections, and consequently greater accuracy 
when the time is expressed in seconds carried to three places of decimals. 
The above is an exact representation of the method adopted when the 
utmost care is required in calculating the time occupied by the projectile in 
passing from screen to screen. First of all, from some line drawn on the 
paper parallel to the axis of the cylinder, the clock records are measured and 
placed in one column; and the screen records are measured and placed 
in another column. The measurements for the clock should extend over five 
or six seconds, and overlap the screen records both ways. Both columns 
are then differenced as in (I). Small corrections are made, where needed, 
to introduce regularity in the column A 2 , and the figures are carried one 
place of decimals further than the measurements. The screen marks thus 
adjusted are left till a proper time-table has been constructed. By interpo¬ 
lation as in (HI), the distance described by the clock tracing point at the 
end of every half-beat is found. By another interpolation, the space 
described by the clock marker at the end of every Voth of a beat is found, 
as in (IV). In all cases it has appeared at this point, that the column of 
second differences was nothing, or extremely small, so that the rule of pro¬ 
portional parts could be used to determine fractions of a second less than 
•loth of a second. This completes the time-table. We have now to deter¬ 
mine by its help, the times corresponding to the spaces described by the 
screen tracing point when the first, second, &c. screen was passed : thus, 
referring to Bound 1, we find that 
the corrected reading for the sixth screen was. 41*325 
and referring to the time-table we find corresponding to beat 5*4 41T05 
•220 
with a difference of 771 corresponding to -^th of a beat. Therefore the 
sixth screen was passed by the shot at 5*4000+ T V -frr = 5*4285 in beats of 
the clock. 
The necessity for the introduction of small corrections may spring from 
one or more of the following sources. The reading off from the original 
records cannot be exactly true. The thread may bend at one screen 
rather more than at another before breaking. The distance apart of the 
screens may not be exactly equal. The supporting poles may not be quite 
vertical. The projectile may strike a thread directly at one screen, at the next 
it may pass midway between the two threads. Now if some errors be con¬ 
stant throughout the experiment, and if others enter only occasionally into 
the records, they are of no moment, because the constant errors vanish, and 
the occassional errors are corrected in the process of differencing. The 
only errors to be feared are those which follow some law, for if there 
were such, they would combine with the law of motion of the projectile 
and so escape detection. But there is little danger of such errors in 
the use of the chronograph here described, for the records of the clock 
