424 Depression in Capillary Tubes. 



My antagonist has contended stoutly for the accuracy of 

 •00416, the depression in a bore of 0'6. Let us apply to this 

 instance, the test of my rules. As we both use the ultimate pro- 

 duct "015 for one element, and differ only in the sine of depres- 

 sion, if we substitute his number '75 for z in computing the limit 

 of y in the second rule in the article Fluids, we shall get 



_ -01443 



iising the same letters as above. Now in the article Cohesion, 

 I find A = 5"737 5 and hence a = '00419, very little different 

 from his number, which he admits may be carried to •00418. 

 And if he will compute voraciously, he will find that '00419 is 

 the most probable number ; for his method cannot reach beyond 

 probability. 



On the whole, his only argument has no foundation. My num- 

 ber is not wrong, because it is different from his. In the only 

 instance he has ventured to adduce, the difference of the two 

 nnmbers arises from the difference of the elements of calculation; 

 since these elements being substituted in the same formula bring 

 out the two depressions. But if '00416 be the true depression 

 with the elements '015 and '75, it can hardly be right in the 

 Table of 1809, with the elements '015 and -7353. 



But the inaccuracy and deficiency of the series, which have 

 already appeared in the foregoing examples, are most conspicuous 

 in the middle of the Table between the bores 0-2 and 0-4. As 

 an example, let us take the bore 0-3 in the Table 1809, the ele- 



10000 



ments being -015 and -7353. In this case q — ■ ^^ -, and 

 ox»t= 4-41176. 



Now, by the formula in your last Number, t — —^ = 



1- 10294: and we get, 



^ _ '000805 



- 85 



- 12 



Sum of negative terms . . . . — '000902 

 Positive terms = ^ = + '030077 



2.T.X 



Depression .. .. -029175 

 Applying to the same example the first rule in the article 

 Fluids, I have found/= 1 -'0301 ; and, xbeing 1-6627, we get 



the depression = ^ x/ = -030077 X (l-'0301) = -029171. 



The two rules therefore agree ; but as they are out of the pale, 

 their authority is zero. We must have recourse to the series. 



By 



