CONTINUOUS CALCULATING MACHINES. 
373 
error since exactly similar conditions to those occurring in practice must be ensured, 
and it may be fairly asked, What check is there upon the records of the large number 
of instruments of this kind in use ? 
It was for the purpose of obviating the defects of combined sliding and rolling 
action* that Professor James Thomson invented the disk- globe- and cylinder- 
integrator. This mechanism was at once applied by Sir William Thomson for 
purposes which had previously been deemed incapable of mechanical treatment, viz., 
the analysis required in connexion with tide-calculating machines. But, more than 
this, it was shown by Sir William Thomson that the combination for purposes of 
integration, now possible from the reduced friction, were not only applicable for 
calculating l<j)(x)\fj(x)dx, the integral of the product of two functions, but could in 
theory integrate linear differential equations of any order with variable coefficients.t 
In one application of the mechanism which has been devised by that gentleman for 
the solution of a differential equation two machines are employed. The fork of one 
sphere is connected with the cylinder of the second, and the fork of the second sphere 
with the cylinder of the first. Thus the motions g l and g« of the centre of the sphere 
are obtained, and by eliminating the latter, the former ((/j) is found to be the solution 
of the differential equation. This method requires the measurement of the movement 
of the fork, that is, of the centre of the sphere, to obtain the result. The use of the 
'position of the fork indicated on a scale at every instant in order to obtain a differential 
coefficient does not appear to have been proposed, and the author therefore ventures 
to suggest the following arrangement of the disk- globe- and cylinder-mechanism for 
that purpose. 
Figs. 3 and 4. 
Figs. 3 and 4 represent this arrangement in front and side elevation. The disk, as 
in the corresponding disk and roller mechanism, is driven by the wheel A, at a speed 
which varies as one variable quantity, and communicates a corresponding motion to 
the globe, and thus to the cylinder. The axis of the cylinder is prolonged, and upon 
it is cut a screw which works through a nut N. This nut forms the axis ol the second 
* 1 Proceedings of the Royal Society,’ vol. 24, p. 263. 
t Ibid., pp. 266, 271. 
3 c 
MDCCCLXXXV, 
