256 
DR. J. YOUNG AND PROFESSOR G. FORBES ON THE 
Taking this as a first approximation to the value of 4 f which is to be adopted, we 
find 
6*!= 9,8.90 
So=B2,309 
£ ' 
§ x -j-Sg— 42,199 
s=- i y J +i/= 21,100+ 41 = 21,141 (assuming f x is sufficiently near to the correct 
value of f). 
The value of 4 f corresponding to this value of s is 
1931 
4j^=329 + Q237 ^ 336. 
The value for 4/' which we must adopt is the mean of these two, 4 f Y and 4 f 2 . 
4/’= 1(325+ 336) = 331 
[We might adopt this improved value for f to find a truer value for s, and thence 
we might get a still nearer approximation to the correct value of f In practice we 
find that no greater accuracy would be thus attained.] 
Substituting now in equation (A) we have 
“=11,210; §-{^ 2 +i/j=24,108-21,141 
= 2,967 
v 3 =(ll,210) 3 -166 x 2967 
and 
^=11,188. 
We have neglected all account of the position of the decimal point up to this stage. 
It is easy to see that the above value of v means that the cylinder of the chronograph 
is, at the instant of equality of the lights, rotating at a speed which if uniform would 
accomplish IT 188 revolutions per second. At the same instant the cylinder rotated 
0*2406 of a revolution in the time taken by the toothed wheel to complete 100 revo¬ 
lutions. Hence the speed of rotation of the toothed wheel is 
1T188 
- = 465*00 revolutions per second. 
0‘002406 
The value of v is calculated by the help of seven-figure logarithms. 
Having now studied in detail the method of reduction of this particular observation, 
the following systematic form for the tabulation of results will easily be understood ;— 
