B I L 



505 



B I N 



Milliards, tlie striker should hit the ball, and hole his own ball, 

 r~ or force it over the table, or on a fort or cushion, 

 or into either of hi3 own forts, or into either of his 

 adversary's forts, which has been taken, or is out 

 of the angle, (See 21. and 22.) he loses two points. 

 SO. If either of the adversary's balls should lie be- 

 fore either of the striker's forts which has not been 

 taken, and (the said bah> being out of sight) the 

 striker wishes to strike the cushion hirst, and hit the 

 said ball backwards, to make a prisoner of his ad- 

 versary's ball, by saying, / do not see, if he hits the 

 ball, he wins two points, and if he makes a prisoner 

 of his adversary's ball, he wins six pc :uid 



his adversary's ball must return to its proper spot. 



40. When the striker gives warning, saying I do not 

 see, his adversary, or the company, have a right to 

 be judges, or the marker, in case of any dispute. 



41. If the striker holes, or, &c. either of his ad- 

 versary's defending balls, it i3 at his adversary's op- 

 tion to place the said bail oa either of the pr. 

 spots, if they are both vacant. 42. Whoever touches 

 both balls with mace or cue, makes a foul stroke. 

 He cannot therefore reckon any points made by the 

 *aid stroke, if it is discovered by the opponent, and 

 proved to be so by the company and the marker ; 

 but if it is not discovered, rlie marker is obliged to 

 reckon all the points made by the stroke. But if 

 the said stroke is proved to be foul, then it is at his 

 enemy's opiion either to break the balls, or to r 

 him return to his proper spot. 43. If the striker 

 makes a foul stroke, and holes his own ball, or forces 

 it over the table, &c. he loses two points fur each 

 of his own balls so holed or forced over the table ; 

 and it is at his adversary's option to part the balls. 



44. If the striker moves the ball, it must be put 

 back to the proper place it was moved from. 



45. Blowing on any of the balls when running is 

 deemed foul, (See art. 42.) 46. -If the striker, by 

 blowing on his own ball, should put it out of its 

 proper course, especially when running near a hole, 

 he loses two points ; and it is deemed foul, (See art. 

 42.) 47. Stopping a ball with stick or otherwise 

 after the stroke, is deemed foul, (See art. 42.) 

 48. Playing with both feet off the floor, without 

 permission from his adversary, is deemed foul, (See art. 

 42.) 49, Flaying upon a ball when running, is deem- 

 ed foul, (See art. 12.) 50. Whoever retains his 

 adversary's cue or mace, when playing, loses two 

 points; besides it is foul, (See art. 42. ) 51. 



gets the first twenty points, each fort being regular- 

 ly taken is four points, wins the game. 'si. When 

 four parties play a double match, he who plays be- 

 fore his turn loses two points. N. B. The rest of 

 the necessary rules are the same as the rules, &c. of 

 the White Winning Game. See Hoyle's Games, 

 and the Dictfonnture des Jcux in the Encyclopedia 

 Met Sume account of the principles of the 



"aards may be seen in the Dictionnaire 

 ties Jcux Malhentatifue* ; Journal de Physique, 

 xlv. 45; Observations par Rozier, xl. 1!); and Dr 

 Young's Natural Philosophy, vol. i. p. 81. 



BIL3TON, a large village of England, in Staf- 

 fordshire, between Wolverhampton and Birmingham, 

 ibout a mile and a quarter long, and contains 

 numerous manufactures of japanned and enamelled 

 in. part in. 



goods. The buckle chafes manufactured here are 

 particularly celebrated. The country about the 

 town is covered with smelting furnaces for iron ore, 

 forges, and slitting mills, and abounds with mines 

 of coal and ironstone. An orange coloured sand, 

 which is in great request among founders, is also 

 found here ; besides a quarry, consisting of twelve ho- 

 rizontal strata of remarkable stones, gradually increa- 

 sing in thickness downwards. These stones are prin- 

 cipally employed in the formation of cisterns, troughs, 

 &.c. By means of numerous canals, Bilston commu- 

 nicates with the rivers Dee, Mersey, Ribble, Ouse, 

 :;t, Trent, Severn, Humber, Thames, and 

 Avon. Number of houses in 1801, 1246. Popula- 

 tion 6914, of whom 2414 were returned as employed 

 in trade and manufactures. See Shaw's History of 

 'fdshire. (j) 



BINARY Arithmetic. See Arithmetic Index. 



BINARY Logarithms, are a species of logar- 

 ithms contrived and calculated by M. Euler, ( Ten- 

 tamen Novas Theorice Musicce, chap. vii. ) for facilita- 

 ting musical calculations ; wherein 2 is made the unit, 

 or modulus, instead of 10, as in the common logar- 

 ithms, or 1 in the hyperbolic logarithms. 



In these logarithms, the powers of 2 have succes- 

 sively 1, 2, 3, 4, &c. for their logarithms, as in the 

 following table, for the first 10 numbers, viz. 

 Numbers. Binary Logarithms. 



1 o^oooooo 



2 1.000000 



3 1.58496.3 



4 2.000000 



5 2.321928 



6 2.584963 



7 2.807356 



8 3.000000 



9 3169925 



10 3.321928 



The great ease with which musical calculations are- 

 performed by the binary logarithms, owing to the 

 same representing the decimal values of the intervals, 

 in terms of the octave as unity, induces us to give 

 here another table of these logarithms, answering to 

 the several elementary intervals, which are represent- 

 ed in Plate XXX, on which there was not room for 

 this column. 



Binary. 



Charac- 

 ters. 



m 

 f 

 d 

 F 



X 

 r 



% 



it 



h 



R 

 It 

 

 9 



Namc9 of Intervals. 



Reciprocals 

 of the Bina 

 ry Logar- 

 ithms. 



Minute 



Lesser Fraction . . . 

 Medius Fraction . . 

 Greater Fraction . . 



Sckisma 



Minor Residual . . . 

 Medius Residual . . 

 Semi-comma major . 

 Semi-comma maxime 

 Greater Residual . . 

 Major Residual . . . 

 Minor Comma . . . . 

 Prisma ....... 



3s 



0.000045 

 0.000259 

 0.000893 

 0.001411 

 0.001625 

 0.003508 

 0.005134 

 0.006759 

 0.008384 

 0.008643 

 0.009536 

 0.016295 

 0.016554 



