ROBERT HEATH v. JOHN TURNER 217 



Number of Points can never actually constitute real 

 Magnitude," and whether '' Motion, or Fluxion, 

 can aciually exist, and be known, but by the next 

 Increment of Space gone over, in some real and 

 next Monnent of Time"? These are fundamental 

 problems indeed. Zeno is not mentioned in the 

 pamphlet, but the query involves Zeno's subtle 

 paradox of the ' ' arrow. " Nor is the answer given 

 devoid of interest. '* But Time, and Motion, flow- 

 ing over Space, . . . {since no Quantity can be 

 assign'd, or imagin'd so smalla but there will stili be 

 smaller) the respective Degree of Velocity of Motion, 

 or Fluxion (i.e. instantaneous velocities) of that 

 Flowing at any Instant of Time, and Point of Space 

 gone over, will be everywhere assignable by the 

 immediate Increments, as Effects of those preceding 

 Velocities, as has been shewn. Whence it will 

 follow, that certain Degrees of Motion, Fluxion, or 

 Velocity, exist at every instant of Time taken, and 

 Point of Space respectively described ; contrary to 

 the dijfferential Notion that P^oreigners have of this 

 Matter. " The weak spot here resides in the words 

 ''immediate Increments"; do immediate increments 

 exist in view of the statement in the above paren- 

 thesis ? The lack of a satisfactory arithmetical con- 

 tinuum Comes to view more fuUy in the antagonism 

 between geometrie increases and algebraic increases 

 exhibited in the following passage taken from the 

 pamphlet : 



"AH the Values of the geometrical Increases 

 flow'd over, in finite Time, can never be algebraically 



