CONTINUOUS CALCULATING MACHINES. 
371 
It now, therefore, becomes necessary to examine the defects of the disk and roller 
in view of both the foregoing purposes. These defects may be said to be of two 
kinds— 
(1.) Those which are the result of the principle of action itself. 
(2.) The limited range of action of the instrument. 
(1.) The very conditions under which the disk and roller works are contradictory. 
On the one hand the roller must slide sideways, that is, in a perpendicular direction 
to its plane of rotation, or the relative velocity cannot be changed. On the other 
hand no sliding or slipping must take place in the direction of its rotation, which must 
be only a motion of pure rolling contact. The roller has to work upon continuously- 
changing circles, and nothing in the nature of a toothed or serrated edge is admissible. 
Such a serrated edge has, indeed, been introduced by some inventors, and the sur¬ 
face of the cone or disk on which it works made, as of course it must be, of softer 
metal. This was so in the instrument of Moseley for integrating the work of a 
steam engine; but it is a significant fact that the committee speak of the ‘ slight 
furrows’ caused in consequence upon the driving cone. # Now it is easy to see that 
these slight furrows must introduce an error, as the position of the roller continually 
changes, and quite vitiate the differential principle of action. The force of friction 
which must therefore be employed to ensure rolling contact leads to the three 
following defects:— 
(i.) Grinding action between the edge of the roller and face of the disk. 
(ii.) Necessity for the application of force in order to change the position of 
the roller. 
(iii.) Error in numerical results. 
(i.) The first of these is well known, and is in fact illustrated in an extreme case by 
every mortar or pug mill. As the edge, which must initially have some appreciable 
thickness, however slight, grows wider, the evil increases, and the size of the roller 
altering the accuracy of its record is destroyed. This must take place rapidly in the 
case of the steam engine integrator, where such a wide range of motion occurs at 
every stroke of the engine. 
(ii.) The second defect is a serious one where the instrument is employed for 
ergometrical purposes, as even allowing that the friction may be always constant at 
one portion of the disk, it cannot be so where the conditions of rolling are different. 
Where the disk and roller is employed as a screw for the converse process, the same 
actual side friction must also take place, though it is not so apparent. The objects for 
which it has been more frequently suggested or employed require the use of a clock, 
and the author has, in endeavouring to apply the principle to the above-mentioned 
entirely distinct in principle from the two already discussed, but its application is only suitable for 
numerical and discontinuous calculation; and as, moreover, it involves no new mechanical arrangement, 
it is not alluded to until hereafter (p. 385), when discussing the other purposes of the new mechanism. 
* 11th Report of the British Association, p. 321. 
