316 



On the Adhesion of the Particles 



are as the squares of the same lines, it is evident that the weight of the 

 small sphere mentioned above must be 1000 times less than the weight 

 of the large sphere (the cube of 10 being 1000 and its square 100), 

 consequently the smaller sphere ought to weigh in water only 3068.465 

 grains (deduction being made for the effect of the viscosity of the 

 liquid), and its surface would be 3.68 square inches. 



Since the diminution of weight which was due to the viscosity of 

 the liquid was only i grain when the surface of the sphere was 368 

 square inches, it is evident that this diminution ought to be 100 times 

 smaller, or of a grain, in the case of the smaller globe which has 

 100 times less surface ; now of a grain in the case of a body which 

 weighs only 3068.465 grains is -. of the real weight of the body 

 in water, and by this amount the weight will be diminished on account 

 of the viscosity of the liquid. This quantity is precisely 100 times 

 more considerable, relatively to the weight of the body in water, than 

 we have found it to be in the case of a body 10 times as large. 



Hence we may conclude (and this can also easily be shown by a rigor- 

 ous demonstration) that when a solid sphere heavier than water is sub- 

 merged in this liquid, the decrease of weight due to the viscosity of 

 the liquid is inversely proportional to the diameter of the sphere. 



For example, if, when the diameter of the sphere was 10.8233 

 inches, the decrease of its weight in water due to the viscosity of 

 that liquid is to its weight in the same liquid in the ratio of I to 

 3068465 ; 



When the diameter is reduced to 

 1.08233 of an inch 

 0.108233 

 0.0108233 

 0.00108233 

 0.000108233 

 0.0000108233 

 0.00000108233 



The diminution of weight due to 



the viscosity of the liquid will be to 



the weight of the body in water 



to 



306846.5 

 30684.65 

 3068.465 

 306.8465 

 30.68465 

 3.068465 

 0.3068465 



And in this last case it is evident that the minute body must of 

 necessity remain suspended in the liquid. 



I know very well that these long numerical calculations must seem 

 superfluous to geometers accustomed to algebraic calculation ; but many 

 persons who are unacquainted with algebra desire to have brought 

 within their reach satisfactory proofs of the truth of a conclusion 

 which is given out to them as certain, especially when it is to serve as 



