852 
exceptions took place in the immediate neighbourhood of the middle 
thread, always took place bevond it, calling the change in the per- 
sonal error by the bisection A', such that a positive value means 
an accelerated observation, we shall have: 
Thread Clamp West Clamp East WAE + ne 
Dar ET ANGER LE At AT 
I] + All —All + A! if All —4A' 
UI + All —_ All + A 5 AIll — 34! 
v ER CEA A AT Se 
VI —AVI +A’ +AVI es AVI — $A! 
VII AME en EV ? AVI — 34! 
By a change in the personal error after the bisection the sum 
W +E thus obtains a constant value differing from zero for all 
the threads and our result might be explained by assuming that 
after the bisection H. estimated the times of transit O%.08 too late, 
K at first in 1864 0s.03, later on 0=.10 too late. The signs as found 
are such as might be expected according to the suggested explanation, 
whereas, if assume that the bisection made before the 
middle thread, our result (see the discussion further down) would 
mean an accelerated observation in consequence of the bisection. 
To begin with, therefore, the above supposition appeared to us a 
very probable one, but on further consideration we hesitated to adopt 
it definitely, especially in view of the relatively large retardation 
which would have to be assumed and the great influence which the 
retardation, as shown by the last column of the table, exercises on 
the derivation of the intervals themselves. For the quantities 
+ 1(W—E) (+ for threads I—III and — for V—VII), which in 
normal observations immediately give us the corrections of the 
thread-intervals, must now be corrected by half the retardation and, 
by working out the more general supposition that in p cases the 
bisection was made before and 1—p cases after the middle thread, it 
appears that the value which will be found for the retardation itself 
entirely depends on the supposition made as to the moment of the 
bisection. The result from the general supposition is given in the 
we was 
following table: 
