436 The Originalily of Daniel's Life -Preserver disputed. 



Fifth : and in the other Si. hoiia, we have For the Commen- 

 surable Systems mentioned, as I'ollows, viz. 



Schol. 9« = 112Z; = 8— r= — 2&2S6692 

 3 19 4 — 3-694570 



5 43 8 —2- 1^0990 



6 12 2 —1-000655 



8 fi7 12 — l-TO'ltiOl 



9 74 14 — 2-38-^017 

 10 50 10 — 3-04b031 



12 31 6 —2-651765 



13 55 10 — 1-9312S1 

 Which results, it will be observed, are much more exact 



than those which I before gave, owing to too few places of 

 decimals having been used, as my able friend, the Rev. C.J. 

 Smyth, long ago pointed out to me, after recalculating and 

 enlarging M. Saiiveur's Tal)le of Commensurable Systems, 

 and which it were much to be wished that he would publish. 



The Temperament of the Fifth or — r being thus ob- 

 tained, for any Commensurable System, we have only to 

 consider 5 as = i, — / = o, and z/ = i, and all the other 

 Temperaments and the Wolves of any such system will 

 readily be obtained from the Theorems at page 41 of the 

 36th volume, or from the Corollaries that follow at page 371. 



If we select the 6th Scholium as an example of the use 



of Theorem 8, we have — = -— - = -— ,and-0301029.9957 



-K-6 — -0045267,3834 = -0004904,2825 = — r, the re^ 

 ciprocal logarithm of the flat tcm]ieran)cnt of the Isotonic 

 System: from which if we take -0004901,0713 the recipro- 

 cal logarithm of 2, we have 3-21 12 (or yV of 38,5342 the 

 reciprocal logarithm oi m), or £ -[- |'"i ^s the proper flat- 

 tening of the Equal Temperament. 



Allow me here to correct two errata in the 5'.h Scholium, 

 p. 46, of volume xxxvi. bottom line and line 6 from the 

 bottom, for flat read sharp. 



I am, sir. 



Your obedient servant. 



Upper Crown Street, JoHN FaREV, Sen. 



Dec. 4, 1811. 



LXXX. The Originality of Daniel's Life-Preserver disputed. 



To Mr. Tilloch. 



Sir, J. HE advantages that have accrued to the public, from 

 the institution of the Society for the Encouragement of Artsr- 



and 



