578 
Proceedings of the Royal Soeiety 
Any body wliich lias no rotation relative to a framing wliicli 
accomjilislies the conditions stated is devoid of absolute rotation, 
and if a body rotates relatively to any such frame it has the same 
rotation absolutely. 
The Law of Inertia here enunciated sets forth all the truth which 
is either explicitly stated or is suggested by the First and Second 
Laws in Sir Isaac Newton’s arrangement. 
By applying the Law of Inertia to the case in which the forces 
acting on the bodies vanish, the law becomes a remodelled substitute 
for the statement set forth by Sir Isaac Newton as the First Law of 
Motion in his arrangement. 
3, On a Modification of Gauss’s Method for determining the 
Horizontal Component of Terrestrial Magnetic Force, 
and the Magnetic Moments of Bar Magnets, in Absolute 
Measure. By Sir W. Thomson. 
4. On the Phenomenon of “ Greatest Middle ” in the Cycle 
of a Class of Periodic Continued Fractions. By 
Thomas Muir, M.A. 
1. The highest square in an integer H being A^ and 
H = A2 + D ; 
it is a familiar fact that the square root of H when expressed in the 
ordinary way as a continued fraction with unit-numerators takes 
the form 
A + - 1 
^2 
• + 
^2 
2A + - 
* <h 
-f--. 
the last element of the cycle of partial quotients being double the 
unique partial quotient A, and the cycle without this last element 
being the same when read backwards as when read forwards. It is 
also known that in the symmetric portion of the cycle no element 
