On the Origin and Practice of Lithography. 215 



the descending Octave to D, and it will thence appear, that 104 

 Schismas compose the Interval CD ; then, since E the Third 

 above C, is 197, a fifth tuned upon or added to tliis, gives 555 

 forB; and so on, through the whole 3.9 Notes; which Notes 

 arranged, are as follows, viz. 0(1), 11, 36, 47(1). 57(2), 93, 

 104(11), 140, 150, l(il(3), 197(111), 208,2.33,244, 254(4), 

 265, 2.90, 301(IV), 311(5), 322, 347, 35S(V), 3G9, 394, 405, 

 415(6), 451 (VI), 462, 498, 508(7), 51.9, 54-J, 555 (VII), 

 565(8), 566, 576, 591, 601, 602, and 612(V1II). Where the 

 numeral designations of the Intervals are sliovai in parentheses ; 

 viz. 1, I, 2, II, 3, &c. ; answering to C, C*, Db, D, Eb, &;c. and 

 the Sehisinas fall between 565 and 566 aiid 601 and 602. 



" By adding 6 12 to each of the above 39 numbers, and setting 

 them down as a second Octave above this, and then going suc- 

 cessively through the arithmetical subtraction of every number 

 above given, from each of the 39 numljers next greater than it, 

 every possible Intcival on this Organ, will thus be shown or 

 measured, without the least fractional differences or errors. It 

 is hoped, therefore, that the chief (I'lfficulty heretofore opposed, 

 to the readily understanding of the enlarged or true Scale of 

 Music, is now removed. 



" It may be proper to add, that the Schisma Unit, above de- 

 scribed, taken from a true Filtb, produces the proper Equal 

 Temperamtvl Fifth, being 357 ; of which tempered Fifth, this 

 Organ furnishes live Examples ; viz. E« c', E'cb, B'* g', B' gb, 

 and G'*e'b, either of which will exhibit to the ear, the true ef- 

 fect intended, as to deviation from perfection ; but none of them 

 fall in the proper places of the scale, for the Isotonic System of 

 Temperament, whose Noces must all be multiples of 357, abating 

 Octaves; because 357, multiplied by 12, is exactly equal to 

 612 multiplied bv 7, and multiples also of 51, the Half-note of 

 this System ; because 5 1 multiplied i)y 12, makes 612. So with 

 regard to any other Tempered Systems, their Intervals may be 

 expressed in these numbers and decimals; thus, in the Mean-Tone 

 System, where the Fifths are flattened | of a Comma, or 2*75, 

 the FiftHi is 355-25, four of which CG, Gd, da, p.e, make 1421, 

 from which take 2 Octaves or 1224, and 197 remains, for the 

 perfect major Third CE, see Phil. Mag. xxwi. pp. 39 and 374. 



HowUmd-btrett, JMiircli 25, 1017. 



LVIII. Notice on the Origin and Practice of the new Invention 

 oj Lithography. 



Aloys Sennefelder, a singer at the theatre of Munich, was 



the first who observed the property which calcareous stones pos- 



O 4 sess 



