30 Or the Variations in Personal Equation 
e was the distance measured on the tape between consecutive marks of the 
key. 
p the length on the tape of the nearest corresponding 10 seconds recorded by the 
pcnduhim pen. 
Had the pendulum been beating exactly one second, 10 x - seconds would 
have been the true length of the estimate ; actually the period as found by com- 
jiarison for a long run Avith a watch was, 
before Experiments G and D ( 6th December) 1"020 seconds 
after „ „ (16th „ • ) 1-019 
so that the length of estimate with sufficient accuracy is 10'2 x seconds. It is 
the factor - that will be used throughout the reductions. 
P ^ 
,_ P , 
r\ i\ l\ t\ ;^ ^ 1^ in f\ !\ i\ r\ ■ 
L_r-i I l_r 
h c a 
Fig. 2. Shows a small piece of tape, and tlie points from which the measurements were made. 
If the amplitude of the pendulum was rather small, it was sometimes notice- 
able that the intervals between the second marks were alternately longer and 
shorter; this was due cither to slight deformation in the shape of the mercury 
bead or (what is really the same thing) from the centre of the bead not having 
been placed exactly under the equilibrium position of the platinum pointer. But 
in taking for measurement the even number of 10 seconds, such errors would be 
inappreciable. 
In both experiments the beginning and end of the estimate were, recorded by 
sharp taps on the key (at a and b respectively in Figure 2); a long drawn tap 
(c in figure) then followed to make a break before the next estimate was recorded. 
The interval between the h tap of one observation and the a tap of the following 
varied from l^ to 2^ seconds. This method of record soon became quite auto- 
matic, and very few mistaps occurred. 
The measurem(;j^its on the tape were made from the sharp beginnings of the 
marks, which correspond to the making of the electric contact at the beginning of 
the tap on the key. 
In Experiment G the counting was sotto voce," the first tap being made on 
the count "nought," the last on "ten"; in order that the counts might be quite 
uniform the word " sen " was used instead of the two-syllabled " seven." The 
counting was usually done in step to a slight beat of the thumb on the key (not 
hard enough, of course, to make contact), and it was fairly easy to keep the 
attention concentrated during the counts. In Experiment D there was no counting 
and it was far harder to keep one's mind fixed ; in foct the mental effort required 
was quite noticeable, and I found that a greater interval of rest was required 
