64 H. G. Fourcade.—On the [April 26, 
The greater accuracy of the first method over the second is thus 
measured by 
a quantity which is always positive and increases with 6, so that 
the advantage of the method increases with the imperfection of the 
instrument. 
In practice, however, it was found that repeating instruments are 
affected with constant and periodic errors the source of which has 
not hitherto been satisfactorily. explained. Col. A. R. Clarke 
(Geodesy, p. 18) summing up what is known on the subject says: 
‘¢ There are, however, other sources of error at work; the whole 
apparatus is not rigid as it is in theory supposed to be, and the play 
of the several axes doubtless affects the work with some constant 
error. Moreover it is a principle in observing generally, that to 
repeat the same observations over and over, under precisely the same 
circumstances, is a mere waste of time, the eye itself seems to take 
up under such circumstances a fixed habit of regarding the object 
observed, and that with an error which is for the time uniform. 
In some repeating circles a tendency has been found in the observed 
angle to continually increase or decrease as the number of repetitions 
was increased.” 
“W. Struve, in his account of his great arc in Russia, observes 
that if in measuring an angle the repetition be made first in the 
ordinary direction, and then again by reversing the direction of 
rotation of the circle, the two results differ systematically. Accord- 
ingly it became the practice to combine in measuring an angle 
rotations in both directions. Nevertheless there was no certainty 
that,even then the error was eliminated, and the method of repetition 
wagjsoon abandoned.” 
It remains difficult to understand why personal errors should 
become larger or more variable when bisecting a signal for the purpose 
of repetition than they are when the same operation is performed for 
the purpose of reiteration, and it is equally obscure why the play 
of the'axes should be greater. No doubt, the play of the axes would 
be more marked in an instrument like the repeating circle with its 
multiplicity of axes and complication of parts, but it is extremely 
a 
