Depression of Mercury in CupUlary Tubes. 425 



By making qx"" — 4-41176, we get this equation, 



•7358 = 1-6627 7/ + 02285 y' +0'215?/5 + 0-149 y". 



In computing tliese coefficients, 5 terms of the first series were 



used ; 6 terms of the second ; 5 of the tliird ; and all the terms 



set down of the fourth. The solution of the equation is, 



y = 0-4292; the proof, . . -71363 



1807 



313 



40 



-73523 

 We now get the depression = -068 x y = -0291S5, very near 

 the former values ; and the difference is on the right side, y being 

 too great. Now the number in the Table is -02906 ; and no 

 reasonable man can doubt that there is an error. 



I have now refuted the arguments, or surmises rather, of my 

 antagonist; and have shown him that his series is not infallible. 

 My rules have been laboriously vindicated with the lingers at least, 

 if not with the head. As to the so vaunted method of computa- 

 tion by the series, there can be but one opinion. It is inelegant ; 

 operose; unsatisfactory and unscientific, since it affords no means 

 of ascertaining the degree of the approximation but sheer calcu- 

 lation, which in many cases is impracticable. 



We hear much of refinements in the mathematics. Does this 

 allude to the results of calculation ? Now my rules are greatly 

 more simple and easier in practice than his, which can hardly 

 be a fault. It must then allude to the process of investigation. 

 But I have always understood that pains must be taken to search 

 into the properties of the quantities under consideration, in order 

 to obtain simple and effectual rules. 



It is proposed to combine the series with Laplace's method 

 of approximation. The attempt will be successful, if it be ex- 

 ecuted with judgement and patient labour. But is it any thing 

 new to assist an approximation by the method of development ? 

 The density of the air, considered as a function of the refraction 

 it causes, has been expanded in a series ; and by this means, 

 with some helps, we have got a new rule for calculating the re- 

 fraction of the atmosphere: but we have obtained nothing new 

 in point of mathematical method. New applications do not make 

 new methods; and new names do not constitute new things. 

 The theorem of Taylor, or of M'Laurin, has received no addi- 

 tions, even although the mode should prevail of designating such 

 well-known operations by the (|uaint phrase of the Universal, 

 Solvent y or the sonorous epithet of the Taylorinn 7'hcuiem. 



I have the honour to be, tVc. 

 .Ii.no II, IWl. J. IvOKV. 



1*. S. All imperfect method and cxccplinnublc calculations aie 

 Vol.57. No. 2J'<.Junc l:>21. 3 II bad 



