160 Prof. H. M'Leod and Lieut. G. S. Clarke on [Apr. 19, 



revolutions per minute 75 equal intervals ; but for the intermediate 

 numbers of rotations fractional numbers of intervals are necessary : for 

 97 revolutions 74-226 intervals are required. Great difficulties would 

 be found in dividing the circles in this manner : and the employment of 

 whole numbers of intervals would be equally inadmissible, 74 intervals, 

 for example, corresponding to 97*2973 revolutions. This difficulty may 

 be obviated by ruling on paper convergent lines, and then wrapping the 

 paper round a cylinder, so that one of the lines is parallel to the axis. 

 In this way circles traced round the cylinder are divided into any required 

 parts ; and between those circles, where numbers of equal intervals are 

 found, there will be every conceivable division between these numbers. 



This method of division possesses also the great advantage that equal 

 distances along the cylinder correspond to equal differences of numbers 

 of rotations : taking the above example, the circles on the cylinder where 

 72 and 75 equal intervals are found will correspond to 100 and 96 rota- 

 tions respectively ; on dividing the distance between the two rings into 

 four equal parts, numbers of spaces corresponding to the whole numbers 

 of rotations, 99, 98, and 97, will be found on the three intermediate 

 circles. The lines may now be converted into dots by erasing the portions 

 not required, or a screen with narrow slits placed in front of the cylinder 

 will effect the same object. 



Another arrangement may be employed by which fractions of rotations 

 may be measured. If the lines are viewed through a narrow slit in a 

 piece of black paper or thin metal attached to a tuning-fork or reed, 

 vibrating hi a plane parallel to the axis of the cylinder, the figures will be 

 perceived on looking through the slit. If the fork be now moved parallel 

 to the axis of the cylinder until the figure appears stationary, the numbers 

 of rotations may be read off from a graduated scale. 



When the figure is formed on circles, the circumferences of which are 

 not an exact multiple of the intervals, so that one division is smaller than 

 the rest, the figure is observed to make a sudden movement or jump at 

 the time of the passage of the small division. There seems to be no way 

 of preventing this ; but it is not found to have any practical objection ; 

 for when the crossings of the double curve remain stationary during the 

 remainder of the revolution, the proper position on the cylinder has been 

 obtained. After the jump the figure remains stationary, but in a slightly 

 altered position. 



In the employment of the tuning-fork means had to be devised for 

 readily setting it in vibration : the use of the violin bow is obviously in- 

 convenient ; and this was soon replaced by a fork with the distance be- 

 tween the prongs less at the top than at the bottom, and which was 

 started in the usual way by drawing a rod between the prongs. This 

 mode has ultimately been replaced by the use of a short piece of soft iron, 

 carried on an axis fixed between the prongs ; when forced between the 

 prongs the iron bar opens them to a sufficient extent, and on turning the 



