306 delation hetween the Specific Grai'Uies and 



ought necessarily to be as nearly equi-differcntial as is con- 

 sistent with the nature of the thing- This, however, is by- 

 no means the case with that which is here employed. The 

 differences between the successive terms of the harmonic 

 series one-half, one-third, one-fourth, one-fifth, one-sixth, 

 &CC., are one-sixth, one-twelfth, one-twentieth, one-thir- 

 tieth, &c.; or such that they arc constantly to each other 

 as the products of the terms between which they fall ; and 

 their inequality, therefore, becomes very soon exceedingly 

 great. 



It will perhaps, however, be more intelligible to some of 

 otif readers, if we explain this matter in other words. The 

 first objection, then, which must naturally occur to every 

 one with regard to this method of denominating strengths, 

 is, that in one part of the series the difference between those 

 of two denominations immediately succeeding each other- 

 is vastly too great, whilst at another part of it this differ- 

 ence is as disproportionally minute. Let us suppose, for ex- 

 ample, that spirit of any particular kind, of proof strength, 

 is worth 12s. per gallon. Then, what is meant by Clarke's 

 *' one to two," or that spirit of which 2 gallons would 

 make 3 of proof, would be worth 12 multiplied by 3 di- 

 vided by 2, or 18s. per gallon; and what is meant by his 

 ** one to three," or that of which 3 gallons would make 

 4 of proof, would be worth 12 multiplied by 4 divided 

 by 3, or 16s. per gallon only. The difference between the 

 strengths and values of these two kinds of spirit is enor- 

 mous when regarded in a commercial point of view ; and 

 yet we have no denomination accorfling to his system (with- 

 out using more complex ratios and higher terms) for any 

 intermediate strength. If we w^islied to express the strength 

 of a spirit of the same kind which was in this respect worth 

 17 s. per gallon, we have no name for it. Now let us look 

 at two other terms of his scries, and see what is the differ- 

 ence in value between his " one to nine" and " one to ten." 

 The former of these is worth 12 multiplied by 10 divided 

 by 9, or 13s. 4d.; and the latter, 12 multiplied by 11 di- 

 vided by 10, or somewhat less than 13s. 2i-d.; so that 

 here the difference is but little more than 1 J-d. a gallon, in- 

 stead of 2s.; and the further we proceed according to this 

 system, the more the disproportion increases. But this is 

 not all. There are many kinds of spirit which are above 

 his " one to Iwo," though we have not yet discovered any 

 which would require an equal measure of water to reduce it 

 to proof; and there are, on the other hand, faints and low 

 vincB which are wortii preser\ing, which are below his 



*' one 



