( oraeti 



II 

 Comma. 



Kxplana- 

 tion of 

 Table III. 



COM 



Table III. 



18 



COM 



This Table is computed for the elliptical orbits of 

 comets, as the last was for parabolic orbits. The greater 

 axis of the ellipse, determined in parts of the radius of 

 the earth's orbit, is supposed to be known, and from 

 this we may easily find, by the Table, the time of a re- 

 volution in days and decimals of a day. 



The greater axis of the elliptical orbit is expressed in 

 the following Table by 1000, and the time of a half re- 

 volution by 500,000, so that the time of a whole revo- 

 lution will be 100,000. We have then only to make 

 the following proportions : 



1. As 1000 is to the greater axis of the elliptical or- 

 bit of the comet, so is the number contained in the first 

 column of the Table to a fourth proportional, which will 

 be the distance of the comet from the sun in parts of 

 the radius of the earth's orbit. 



2. As 100,000 is to the time of a complete revolution 

 of a comet, so is the number contained in the second 

 column of the Table to a fourth proportional, which 

 will be the time, corresponding to the distance, ex- 

 pressed in days and decimals of a day. 



Example. — Let the greater axis of the elliptical or- 

 bit of a comet be 6'.287, and the time of a complete re- 

 volution 5.575 years, which was the case with the 

 famous comet of 1770, the only one which is known 

 to have moved in an elliptical orbit, and let the distance 

 be 12, then we have 



1000 : 6.287 = 12 : 0.075404, 

 the distance of the comet from the sun in parts of the 

 radius of the earth's orbit ; and 

 Years. 

 100000 : 5.575 = 280 : 0.01561, 

 which is 5 days, 16 hours, 44', the time which has 

 elapsed since its passage of the perihelion, or the time 

 which will elapse before it reaches its perihelion. 



The preceding Tables were principally computed by 

 M. Schulze. (o) 



COMETARIUM, is the name of a machine invented 

 by Dr Desaguliers, for explaining the phenomena of the 

 motions of comets. The fullest and most perspicuous 

 description of this machine will be found in Ferguson's 

 Astronomy , vol. ii. p. 17- 



COMETES, a genus of plants of the class tetrandria, 

 and order Monogynia. . See Botany, p. 126. 



COMMA, in Music, is a name very anciently applied 

 to the interval which is the difference between the ma- 

 jor and the minor tone, and which is still very often 

 used alone, without further addition, in musical writ- 

 ings; but which is not a commendable practice, for 

 want of precision, since two other small intervals very 

 often occur that pass also by this name, viz. the minor 

 comma, and that of Pythagoras, besides a multitude of 

 others, of less frequent occurrence or use, which diffe- 

 rent writers have called commas, as in the Table there- 

 of which we have subjoined. 



Comma Major, or Comma (c), is an interval whose 



80 . 2*5 

 ratio is •— -; the component primes of which are ; 



ol * 3 4 



its common logarithm is .9946049,6811 : in the bina- 

 ry logarithms of Euler, or decimal of an octave, it is 

 .01792190 : it is the unit of the comma logarithms: 

 where the schisrda is the unit, it is =11.0078624: in 

 1 he new notation it is 1 1 2 -|- m : in the elements of 

 perfect tune, it is =C + 2 : in diatonic elements, T — t, 

 as before observed: in chromatic elements, 3 — 6 : 

 nd in concordant, or tunable elements, it is 2 3 ds + 

 III — ■ '' vherej on such an instrument as Mr Lis- 



ton's organ, it may be correctly tuned, as it may more Comnaa. 

 readily, and indeed is, in numerous instances on that """"V"' 

 organ, by 6 V — VIII — VI, by the help of perfect in- 

 tervals only. 



The following equations exhibit the value of the 

 major comma, in terms of all the several intervals in the 

 Table, Plate XXX. of Vol. II. viz. 



c=ll2+m 



= €+2 

 = R+/c 



c=T — t 

 =d —2 

 =£ — € 

 =S — L 

 =§ — iS 



=P — s 



=s — s 



=rf -/ 



=/ -6 

 =/ -D 

 =D — x 



=*■ -ie 



=3 — x 

 =111 — 2t 



c=102 + 3f+d 

 = 102+ f+F 

 = 52+ f+R 

 = 32+ r+R 

 = 22+ £+R 



c=232 + 2m — ct 

 =21 2 + 2m— € 

 = 2+ /— * 



= ,r+ f_2 



= R+ *■-_€ 



= £+ t— / 



= 2+ <p— f 

 — R+ R_f 

 = £+ f_,j> 

 = F+ <p — m 

 = P+ S— T 

 = €+ fc-r 

 = <* + r— x 

 = lld + 33f— 10m 

 = T+ €— 2S 

 3= 23 + 111— 24 



c= t— 2rf— € 



= /- r_d 

 = f- x-R 



= D— f— 32 



= *•_ f_42 

 = «r — X — 2 

 = 2S— /— R 



By the help of this Table, the major comma can 

 readily be expressed hi any notation of three intervals, 

 or of two when practicable. This interval is called the 

 greater, syntonic, or elementary comma of various 

 writers. It is also called a schism, or schisma, by Des 

 Cartes, Holder, and others. It is the minor comma of 

 Kollmann ; and it is the enharmonious interval of 

 Wood and Gregory. Intervals which are increased, 

 sharpened, or made more acute by this interval (c), are 

 said to be acute, and are marked with the icute accent 

 ('),-as an acute major third IIP, by Overend, Maxwell, 

 Liston, Farey, &c. ; and intervals that are decreased, 

 flattened, or made more grave by this interval (c), are 

 said to be grave, and are marked with the grave 

 accent (*), as a grave minor third 3". These same 

 marks, when affixed to letters of the scale, imply also 

 the same thing, as A', B" are read A acute, B grave, 

 &c. Chambers marks the acute and grave of inter- 

 vals, or letters, by a dot placed over or under them, 

 thus III, III, A, B, but which is far inferior in conve« 

 nience to the above. By the same author, our grave 

 or acute intervals are said to be deficient or redundant 

 intervals. In our nomenclature, after Mr Overend, 

 such are said to be comma-deficient, or comma-redun- 

 dant intervals. M. Henfling calls our grave or acute 

 intervals inconcinnous ones. 



In his Harmonics, prop. 8. cor. 4. Dr Robert Smith 

 wives a rule for finding a numerical ratio, extremely 



near to any fraction of the major comma, as ' c, viz. 



161 p—q J_ _ 161 XJ 1—1 __ 1_770 _ £85 



161/;+ 5 ; 11 C ' ~ 161 X 11+-1 ~" 1772 ~ H&&' 



is extremely near to T ' T th of a comma, being 1.0007020 S-, 



and -t^-c is 1.00071476 2, 



the difference of which is 



