NEWTON S PRINCIPIA. 357 



The second series of Bossut s experiments showed that 

 the resistance in narrow or shallow canals was greater 

 than in an indefinite fluid. 



Du Buat deduced that the ratio of the resistance R in 

 a narrow canal to the resistance R in an indefinite fluid 

 was 



where C is the area of a section of the canal, B the area 

 of a section of the vessel. 



So many assumptions are made in the ordinary proof 

 that the resistance varies as the square of the velocity, 

 that it is no wonder if the law is found to be at variance 

 with experiment. We must proceed in a different man 

 ner if we wish to deduce the true law of resistance. The 

 difficulty of such an investigation is evident. Neverthe 

 less, by the skill of some eminent mathematicians, some 

 progress has been made. But the problem in its widest 

 form has not been solved. For such particular cases as 

 are most needed in practice, approximate solutions have 

 been found. One of these, and the most important, is the 

 pendulum. The innumerable applications of this instru 

 ment make its utility immense. Its very delicacy renders 

 it a very efficient test of our theories of fluid motion. The 

 resistance opposed to the uniform motion of bodies of cer 

 tain forms have also been investigated. 



(3.) In the year 1826 F. AY. Bessel published in the Royal 

 Academy of Sciences at Berlin a new method of determin 

 ing the length of the seconds pendulum. In the course of 

 it he pointed out an error in the old reduction to a vacuum. 

 He states * that &quot; if we denote by m the mass of a body 

 moving through a fluid, and by in the mass displaced, the 

 accelerating force acting on the body has, since the time 



* BaiJy on the Correction of a Pendulum. 



A A 3 



