242 PHILOSOPHICAL TRANSACTIONS. [aNNO IQqS. 



9 to 8 ; or this the lesser, as 10 to Q, and that the greater, as Q to 8, or some- 

 times this and sometimes that, as there is occasion, to avoid what is called a 

 schism, is somewhat indifferent ; for either way the compound will be as 5 to 4, 

 and the difference, which is called a comma, as 81 to 80. That is, |- x V° = 



I V ^ — ' " — * A nd ' " \ ( " ' 



Lastly, if from that of the trihemitone, or lesser third, la, mi, fa, whose ratio 

 is as 6 to 5, we take that of the tone la, mi, which is the difference of a fourth 

 and fifth, as Q to 8, there remains for the hemitone mi, fa, or la, fa, that of l6 

 to 15. That is f ) 4.(44 = 44. Or, the trihemitone, or lesser third, whose 

 ratio is as 6 to 5, may be divided into three near equals, by taking triple num- 

 bers in the same ratio, 18, 15, and interposing the two intermediates 1 7, 16, 

 which will therefore be as 18 to 17, and as 17 to 16, and as 16 to 15; that is, 

 JL^ X -\^ X -rf = -ri- = -T- Where also the greater tone, whose ratio is as Q to 8, 

 or 18 to 16, is divided into its two near equals, commonly called hemitones, 

 that of 18 to 17, and that of 17 to iS; that is, J-f x+1 = if = A. 



And the lesser tone, that of 10 to 9, or 20 to 18, may be in like manner 

 divided into that of 20 to 12, and that of 19 to 18 ; that is, ^ X -M- = if = '^. 

 Which divisions of the greater and lesser tone answer to what is wont to be 

 designed by fiats and sharps. 



So that by this computation of these eight notes, la, fa, sol, la, mi, fa, sol, 

 la, their ratios stand thus ; that of la, fa, or mi, fa, is as I 6 to J5 ; that of fa, 

 sol, as 10 to 9, and that of sol, la, as 9 to 8, (or else that of fa, sol, as 9 to 8, 

 and that of sol, la, as 10 to 9) that of la, mi, as 9 to 8, And if either of 'the 

 tones, greater or less, chance to be divided (by fiats or sharps) into what they 

 call hemitones, their ratios are to be such as is already mentioned. 



There may be a like division of a fourth, or diatesseron into two near equals : 

 and of some others of these into three near equals. Which might be of use 

 for what they were wont to call the chromatic and enarmonic music. But these 

 species having been long since laid aside, there is now no need of these divi- 

 sions in the modern music. 



On the Poisonous QuaHlies of Hemlock water-drop-iuort.* By Dr. T^aughan. 

 Cornf/nmicated by Mr. Ray. N° 238, p. 84. 



Eight young lads one afternoon went a fishing to a brook in Ireland, and there 

 meeting with a great parcel of oenanthe aquatica succo viroso, they mistook the 



* Q?n;inthe crocata, Linn. Oilier inslance? of the deleterious effects of this vegetable are re- 

 corded in the 4Uii and 5(ith vols, of these Transactions. The medical reader is further referred to 

 the 7th vol. of Dr. Foart Siramons's Medical I'acts and Observations, for other proofs of the poisouou* 

 ojieration of this plant. 



