70 PROFESSOR C. V. BOYS ON THE 
detail that might conduce to greater accuracy. I am still convinced that G may be 
determined with an accuracy of 1 in 10,000 by means of apparatus such as I have 
described. 
In the general design I am unable to suggest any improvement. The weakest spot 
is caused by the resistance of the air making time work difficult, especially where 
visible shaking interferes with the usefulness of oscillations of small amplitude. I 
doubt if a practical gain is to be obtained by the use of hydrogen, and I am sure that 
a high vacuum is out of the question. The only remedy, therefore, is to employ 
larger suspended balls, and with them a longer beam. For the same argument that 
shows that with any length of beam the limit of sensibility imposed by the strength 
of the fibre is increased by reducing the weight of the suspended balls, for the rigidity 
of a fibre varies nearly as the square of its strength, shows also that if the fibres are 
not far from their breaking weight, the size of the balls cannot be increased without 
reducing the sensibility. _ But increase of size would be advantageous because, while 
the forces depend upon the cube of the diameter, the resistance to movement depends 
upon the square. The result is a less serious decrement with larger balls. Now, in 
order to employ these -and yet maintain the period with the necessarily stronger 
fibre, a longer beam must be employed. Of course, unless the diameter of the large 
attracting balls are increased in the same proportion the angle of deflection will fall. 
I do not think that the beam needs to be lengthened to more than about two 
inches. If this length were adopted it would be better to aim at 5 centims., for since 
this is half a decimetre, a more accurate determination of the length could be obtained 
by reference to the standard decimetre at Sevres, than would be possible if it were not 
very nearly an exact submultiple. Whether or not the lead balls and the whole 
apparatus should be doubled in size is a mere question of cost. The expenses 
would run up very rapidly with very moderate increase of sensibility. I should feel 
disposed to be content with lead balls about six inches in diameter, but I would 
certainly have an Elmore tube for the centre one T, and, by preference, for the large 
eylinder C. The slight diminution of angular deflection which would result from this 
change, would be more than compensated by the doubled optical definition, but there 
might be some difficulty in obtaining a thin rectangular mirror 5 X 1 centims., in 
which no optical defect could be detected. 
It may appear that I am reversing all my arguments and practice in now advocating 
an increase of size, but it must be remembered that the object is not so much to 
increase the sensibility, or even to be able to make better geometrical determinations, 
for both of these, in my apparatus, exceed the square of the periods in the degree of 
accuracy with which they are known. The object is solely to be less influenced by 
the viscosity of the air, but this would not have limited the accuracy of my periods so 
seriously if I had not been disturbed by trains. 
I should have had less confidence in this doubling of the size, if my supposition 
that the disturbing moments, due to convection, were proportional to the seventh 
