AS EXPLAINED BY THE HYPOTHESIS OF FINITE INTERVALS. 173 



seven constants, and determining tlieir values from the seven eiven 

 equations. With respect to the results we have deduced, there is little 

 doubt but that the values of b are very far from correct, as indeed any 

 person will perceive who will take the trouble to determine that quan- 

 tity in any case from the first three fixed lines. As to si^n, however 

 there can be httle doubt of its correctness; and, taken ^s ^ mean value 

 for the determining p and q, I have no reason to complain of the 

 sufficiency of the approximation. I have indeed adopted a process 

 not the most hkely to give results widely inconsistent with each other 

 but at the same time sufficient latitude is allowed for discrepancies far 

 greater than those which actually appear. We could not in reason 

 expect a coincidence in the results greater than that in the bases from 

 which they were deduced; and it appears to me, that as an approxi- 

 mation, we could not have anticipated results more nearly coinciding 

 had we known, a priori, that the formula from which they were de- 

 duced were accurate. 



I will point out a few of the discrepancies (omitting the consider- 

 ation of G). 



In FUnt Glass, No. 13, the greatest error from the result from B 

 E and H, which I shall caU the mean result, is .00002, or about 

 2oioo"' of the whole. 



In No. 23. it is .00003. 



In No. 30. it is .00009, or about ^- of the whole. 



In No. 3. it is .00005. 



In Crown Glass, letter M, it is .00004. 



In No. 9. it is .00005. 



In No. 13. it is .00006. 



In no case, then, except for water, does the error amount to a 

 figure in the fourth place of decimals, and hence, by what I have re- 

 marked above, in no case is there (my error. 



With respect, however, to the line G, the result is almost always 

 too great: the worst deviation, however, which is that for Flint Glass 

 No. 23. is .00015, or only an unit in the fourth place of decimals. 



