1876.] an Integrating Machine. 263 



suggestion, which appears to be both interesting and important, pro- 

 posing the attainment of the desired conditions of action by the mutual 

 rolling of a cone and cylinder with their axes at right angles. 



The idea of using pure rolling instead of combined rolling and slipping 

 was communicated to me by Prof. Maxwell, when I had the pleasure of 

 learning from himself some particulars as to the nature of his contri- 

 vance. Afterwards (some time between the years 1861 and 1864), while 

 endeavouring to contrive means for the attainment in meteorological 

 observatories of certain integrations in respect to the motions of the 

 wind, and also in endeavouring to devise a planimeter more satisfactory 

 in principle than either Sang's or Amsler's planimeter (even though, on 

 grounds of practical simplicity and convenience, unlikely to turn out 

 preferable to Amsler's in ordinary cases of taking areas from maps or 

 other diagrams, but something that I hoped might possibly be attain- 

 able which, while having the merit of working by pure rolling contact, 

 might be simpler than the instrument of Prof. Maxwell and preferable 

 to it in mechanism), I succeeded in devising for the desired object a new 

 kinematic method, which has ever since appeared to me likely sometime 

 to prove valuable when occasion for its employment might be found. 

 Now, within the last few days, this principle, on being suggested to my 

 brother as perhaps capable of being usefully employed towards the deve- 

 lopment of tide-calculating machines which he had been devising, has 

 been found by him to be capable of beiug introduced and combined in 

 several ways to produce important results. On his advice, therefore, I 

 now offer to the Eoyal Society a brief description of the new principle 

 as devised by me. 



The new principle consists primarily in the transmission of motion 

 from a disk or cone to a cylinder by the intervention of a loose ball, 

 which presses by its gravity on the disk and cylinder, or on the cone and 

 cylinder, as the case may be, the pressure being sufficient to give the 

 necessary frictional coherence at each point of rolling contact ; and the 

 axis of the disk or cone and that of the cylinder being both held fixed 

 in position by bearings in stationary framework, and the arrangement of 

 these axes being such that when the disk or the cone and the cylinder 

 are kept steady, or, in other words, without rotation on their axes, the 

 ball can roll along them in contact with both, so that the point of rolling 

 contact between the ball and the cylinder shall traverse a straight line on 

 the cylindric surface parallel necessarily to the axis of the cylinder — and so 

 that, in the case of a disk beiug used, the point of rolling contact of the ball 

 with the disk shall traverse a straight line passing through the centre of 

 the disk — or that, in case of a cone being used, the line of rolling con- 

 tact of the ball on the cone shall traverse a straight line on the conical sur- 

 face, directed necessarily towards the vertex of the cone. It will thus 

 readily be seen that, whether the cylinder and the disk or cone be at rest or 

 revolving on their axes, the two lines of rolling contact of the ball, one 



