On Water- Pressure Engines. 129 
ing you the lengths of strings, vibrations and beats, of the 
‘irregular douzeave system of the Rev. William Hawke, 
which has been treated of, or referred to, in four places in 
your Magazine (viz. vol. xxvi. pv171, vol. xxvill. p. 304, 
vol. xxx. p. 5, and vol. xxxvi, p. 47), without these impor- 
tant particulars having been published ; the last of which, the 
beats, are particularly useful in showing the proportionate 
effect or aunoyance which the ear will receive from every 
false concord in the scale; at the same time that they 
furnish an almost infinite number of ways of tuning this 
system, or of checking the tuning as it proceeds, 
I am, sir, 
; Your obedient servant, 
London, Feb. 9, 111. J.B. 
TABLE OF Beats. 
us { Z. 3. 45 a 6. 7 | 8. 9, 
er [oo || a F f : 
Cj +5000-000) 480. fi 
Bj :5333°333) 450. $:377|36-S91| 4-478| 39:350) 8933 16-833 
SB | *5597+118| 428-7929 || 54-049} 5-333] —— | 3-199/63:712|10-680 
_Ay | -5970-259) 400-9925 |! 11-956] 5-000} 4-000] 2993) 7-981 110-012 
%*G | -6352:475) 377-8055 || 16-853 |30-972 | —— |*10-029/14-981 |$5-748 
G *B6885950) 359-1066 || 10-680| 4-466] 3'573| 2-674|14-240| 8-944 
&F | -7128-801) 336.6625 || 10'012|31.856| 3-350] 2-506 6-683 (31-856 
E. | -7481:390| 320-7960 || 35-748} 3-990] 3-192] 2.388!47-664| 7-990 
E_ | -7980-149| 300-7463 || 8-944] 7-491| 2993 2:289| 5:970| 7-491 
bE 4 .8395:679| 285°8614 || 31.856} 7-120|b10-029| —— |56-891 |10-693 
_D } -8933-168] 268-6623 || 7-990) 3-341] 25674] 2:000) 5'933| 6-669 
®C | -9528:710! 251:8704 || 7-491-|23-832] 2-506] ——] 5-000 27-024 
1c 1000-00) 240: 10-693 | 2-985] 2388} 1-787/30-972| 5+97% 
4 | Lengths | Vibra- [] usd. fy tlld. | aath. | bVth. | beth. ja Vith. 
= ef tion in || ey —— 
% | Strings. Is Beats made in one Second. 
_ The beatings are all flat or sherp, as expressed in the titles 
at thebottom of each column, except the 4th on bE, and the 
Vth on *G, which are otherwise expressed. 
XXIV. Communication on ‘Water-Pressure Engines. By 
Mr. Joun Taytor. 
To Mr. Tilloch. 
Sir, Tix your Magazine for January, I have just seen the 
remark of Mr. John Farey on a passage in a former Numbet 
relative to an improvement of mine in Water- pressure En- 
gines. He conceives that he has discovered a mistake in 
Vol. 37. No. 154. Feb. 1811. I the 
