24 Mr. C. Chree on the 



completely invalidates the conclusions drawn from the first 

 paper. After this it might seem unnecessary further to con- 

 sider that paper, but for Graetz's statement that it will still be 

 useful for giving comparative values of the conductivity, and 

 that it may throw some light on the trustworthiness of the 

 method. On page 90 is given the formula from which the 

 calculations are said to be derived. In it /j, x is incorrectly 

 given as 2*4043. In five out of six of the following tables of 

 data I is given as 9*8 centim. These tables give a summary 

 of the data obtained in the experiments on six different liquids, 

 the number of experiments on each varying from five to thir- 

 teen. I may safely assert that in most, if not all, of these 

 experiments it will be found that the values found by Graetz 

 for the conductivity are very far from satisfying his equation, 

 whether / be 9*8 or 8*9. {Singularly enough, however, taking 

 Z = 8'9, if the index of e be multiplied by '7 the equation will 

 in most cases be Yery nearly satisfied ; and in some cases a 

 still better result is obtained by multiplying the second term, 

 which is comparatively very small, by 10. I have calculated 

 out seventeen of the experiments, including the three from 

 which />! and^> 2 were calculated, and in only one did this emen- 

 dation fail nearly to satisfy the equation. Cutting Z= 9*8 

 centim. will be found to place Graetz's results in a worse light 

 even than 8*9. As the index of e consists of a series of fac- 

 tors, three or four of which are constants, it would seem 

 probable that Graetz calculated the value of the constant part 

 once for all. One of these factors is 7r, and it seems quite 



• • 22 



possible that this may have been put equal — , and the 7 may 



have been overlooked. If this explanation be correct the 

 decimal place also must have been misplaced, which might 

 easily occur. 



The product kl occurs in the index of e ; thus, as the second 

 term is very small, an error of the above nature, or in the 

 value of I, would not seriously have affected the relative values 

 of the conductivity provided the coefficient p x had been cor- 

 rect. A glance at the formula, however, will show that since 

 p l was incorrectly taken, no trustworthy results can be ob- 

 tained without repeating the entire calculation. The results 

 deduced when the correct values of p x and p 2 are inserted do 

 not seem very consistent, and it is scarcely worth while con- 

 sidering them here. 



In his second paper Graetz employs the amended coefficients, 

 and attributes the errors in the values obtained experimentally 

 to his having made the liquids traverse the pipe at velocities 

 exceeding the limits to which Poiseuille's law could be applied. 

 This explanation seems utterly inconsistent with observations 



