6 PROFESSOR C. V. BOYS ON THE 
each will be independent of the linear dimensions, and so the temperature differences 
of corresponding pairs of points or of the two sides will be proportional to n. In con- 
sequence of this difference of temperature the included air will be warmer on one side 
than on the other and will circulate. The linear velocity of circulation will depend 
upon the difference of pressure between the ends of the upcast and downeast sides 
divided by the resistance due to viscosity, 7.e., in such cases as we are concerned with, 
where the pressures and velocities are infinitesimal, and practically all the energy is 
expended in overcoming viscosity and none in imparting energy of motion to the gas. 
The difference of pressure varies as the height multiplied by the difference of tem- 
perature, or as 7? : 1. The effect of viscosity is proportional to the length of the 
channel, and inversely as its area; it varies, therefore, as n~! : 1. The velocity of 
circulation will vary as 1*/n~1, or as n? : 1. In order to ascertain what disturbing 
effect this movement may have upon the suspended part of the apparatus, we may 
either consider that the force depends upon the product of the area into the velocity 
gradient or rate of shear of the surrounding air, 2.e., that it is proportional to n? x n°, 
or 7‘, in which case, since the force is to be multiplied by an arm also n times as long 
in order to obtain the couple, this becomes n* ; or without considering the velocity at 
all we may consider the suspension as part of the boundary of the gas receiving its 
share of the drag which is felt by the surrounding tube. The proportion must be the 
same in the two cases. The force causing the drag is proportional to the difference in 
temperature of the air columns multiplied by their area, or to n*, and, therefore, the 
drag on the suspension varies as 7* and the couple produced as n°, as before. From 
this it would appear that no gain or loss results from a diminution of size. It must, 
however, be remembered, that, as apparatus is made larger, the three-fold increase in 
velocity in the air-current may well bring it up to such a value that its square can no 
longer be considered inappreciable. When the velocity is sufficient for the effect of 
impact to be felt, then the couple will follow a law depending upon a higher power 
of n than the fifth which, with increase of velocity, will approach the eighth power of 
the linear dimensions. 
I do not anticipate with my design, which with its double tube and protecting 
screens is eminently favourable for the attainment of a uniform temperature im the 
inside, that the ai velocity will ever approach that in which the square becomes 
appreciable, so that in a suitable underground observing room I should not expect any 
loss of definiteness to follow a moderate increase of size ; nevertheless, I should feel 
doubtful as to the result if the dimensions were increased inordinately. Practically, 
however, smallness has a very great advantage, owing to the length of time which 
must elapse between the carrying out of any operation in which the apparatus is 
handled or otherwise warmed by manipulation, and its acquiring such a steady state 
again as to be fit for the observer to make the delicate observations of the movements 
of the suspended system. I have even considered three days to be necessary for my 
small apparatus to be ready for observation of deflection and period after making the 
