240 . PHILOSOPHICAL TRANSACTIONS. [aNNO IQqS. 



lib. 1 5, cap. 10, p. 566, from whose hint I suppose, Piso and Marcgrave inquired 

 more after it in Brasil ; from whose inquiries we may have as good an account as 

 they give us. 



/Account of a Monstrous Calf with ttuo Heads. . Communicated by the Right Hon. 

 Sir Robert Southivell, V. P. R. S. N° 238, p. 79- 



This monstrous calf had a perfect large head, and on the right side of that 

 another almost as large; from the roof of which hung down a piece of flesh 

 with the shape of a tongue upon it, and a row of teeth, as on an under-jaw, 

 which occasioned the man, who showed it, to say it had 3 heads. 



On the Division of the Monochord, or Section of the Musical Canon. By Dr. 



Jf'allis. N° 238, p. 80. 



Any string or cord of a musical instrument open, or at its full length, will 

 sound what is called an octave, or diapason, to that of the same string stopped 

 in the middle, or at half its length. Hence it is that we commonly assign to 

 an octave the duple ratio, or that of 2 to ] ; because such is the proportion of 

 lengths, taken in the same string, which gives those sounds. And on a like 

 account we assign to a fifth, or diapente, the sesquialter ratio, or that of 3 to 

 2; and to a fourth, or diatesseron, the sesquitertian, or that of 4 to 3; and to 

 a tone, which is the difference of a fourth and fifth, the sesquioctave, or that 

 of 9 to 8 ; because lengths, taken in the same string, in these ratios, give such 

 sounds. And universally, whatever ratio of lengths, taken in the same string, 

 equally stretched, gives such and such sounds, just such ratios of gravity we 

 assign to the sounds so given. 



But when an eighth or octave is said, in common speech, to consist of 12 

 hemitones, or 6 tones, this is not to be understood according to the utmost 

 rigour of mathematical exactness, of such 6 tones as called the diazeuctic tones, 

 or that of la mi, which is the difference of a fourth and fifth; but is exact 

 enough for common use. For 6 such tones, that is, the ratio of 9 to 8, 

 repeated 6 times, is somewhat more than that of an octave, or the ratio of 2 

 to 1; and consequently such a hemitone is somewhat more than the l'2th part 

 of an eight or octave, or diapason. But the difference is so small that the ear 

 can hardly distinguish it; and therefore in common speech it is usual so to speak. 

 And accordingly, when we are directed to take the lengths for what are called 

 the 12 hemitones in geometrical proportion, it is to be understood not to be so 

 in the utmost strictness, but to be accurate enough for common use; as for 

 placing the frets on the neck of a viol, or other musical instrument, wherein a 



