252 NEWTON S 



If we neglect the variations of a with t this is the equation 

 to a parabola. The terms in y thus neglected are of the 

 order * 2 . 



Newton takes these figures to be accurate enough for 

 practical purposes, and we might now proceed to deduce 

 the resistances at O from the difference of the arcs. But 

 we have said enough to illustrate Newton s method. It 

 is not so convenient for use as the more modern formula. 

 But it is remarkable that the two methods are of equal 

 degrees of approximation. Thus Newton arrived at as 

 accurate a result as that which we now use, the only 

 difference being that he expressed his result, according to 

 the custom of the age, in a geometrical form. 



We must now deduce the true law of resistance from a 

 combination of theory and experiment. It is clear from 

 what precedes, that the observations must be made on the 

 decrements of the arcs. Newton suspended a wooden ball 

 weighing 57-/g- ounces troy, its diameter being 6J- London 

 inches, by a fine thread on a firm hook, so that the distance 

 between the hook and the centre of oscillation of the globe 

 was 10 feet. He marked on the thread a point 10 feet 

 1 inch distant from the centre of suspension, and even with 

 this point he placed a ruler divided into inches, by the 

 help whereof he observed the lengths of the arcs described 

 by the pendulum. Then he numbered the oscillations in 

 which the globe would lose \ part of its motion. In the 

 following table the first column represents the first arc, or 

 space the pendulum was drawn aside from the perpen 

 dicular ; the second column the number of oscillations .. 

 the third column the last arc, which is always ^ less than 

 the first ; and the fourth column the difierence between 

 the first and last arcs ; 



