te 
1795] 
Ina fecond memoir, he propofed a me- 
thod of organizing public inftruétion in 
rural c¢conomy, particularly in the vete- 
rinary arts. \ 
TeEYSSIER read two other memoirs 
on the fame fubjeéts. In the fr?, he 
traces the abufes arifing from the ex- 
ceflive encouragement granted to the 
perfons whoclear the forefts, and the in- 
calculable mifchiefs which arife from the” 
extenfion of the practice, affecting the 
foil of the moft ufeful,forefts, mea- 
dows, &c. In the ‘fecond, TEYSSIER 
explained his project of extending the 
{cience of rural ceconomy into other 
-parts of the world, by a general corre- 
fpondence he has eftablifhed, and thus 
contributing to its perfection in France. 
He then entered into a long detail on the 
practice of agriculture in the Canary 
Ifands, and noticed the high degree of 
profperity into which thofe iflands are 
capable of being raifed. —‘TEYSSIER 
is thus employed in tracing a fort of 
grand Agrarian chart, a kind of rural 
map of the world, the execution of which 
has been fo long wanted, and which will 
contribute fo much to the progrefs of the 
firft and moft ufeful of the arts. 
[ Some of the Memoirs will be given at length 
in future Numbers of this Magazine. | 
EEE 
MATHEMATICAL CORRESPONDENCE. 
QuEsTION XIV (No. V).—4x/wered by 
Mr. N. Bofworth, of Peterborough. 
QO duly confidering the nature and cir- 
cumftances of the Queftion, it will 
very plainly appear, that the nail in the 
tire of the wheel will, in every revolution 
of it, defcribe a cyclwoid ; andthat the fum 
of the length ofall the cycloids thus form- 
ed will be in exact proportion to the num- 
ber ef revolutions made by the wheel, and 
to the diftance travelled. ‘Therefore, ac- 
cording to the well-known properties of 
the cycloid, which, I fuppofe, it is unne- 
7, miles 
3.1416 
X 4==8.912656 miles, the fum of the 
lengths of all the curves defcribed by the 
nail, while the coach is going 7 miles, 
which is the mean velocity of the nail 
per hour. 
Tbe fame Queftion was anfwered by 
e ° 

ceflary here to explain, we have 

XV (No. V).—Anfwered by 
Mr. Ff. F——+r. 
If alcohol and water be mixed ‘in any 
proportion, the fpecific gravity of the 
QUESTION 
| Mathematical Corre/pondence. 
797 
compound will be greater than would be 
inferred from the fimple rule of alliga- 
tion, the mafs becoming lefs by meaiure 
after the mixture than the fum of the 
meafures of the two liquors.——The great - 
eft diminution of the whole mafs takes 
place when equal parts by meafure of al- 
coho! and water are mixed; in which cafe 
(the alcohol ufed being extremely de- 
phlegmated and of the {pecific gravity of 
0.8199) the diminution of the mafs after 
the mixture was found to be = 0.0288 
of the whole.—This diminution of the 
mais, and the confeguent increafe of its 
fpecific gravity, takes place in a ratio, the 
relation of which to the proportions of 
the mixture, it has been hitherto found 
diticult to afcertain ; and it has therefore 
long beena defideratum toafcertain the real 
proportion. of alcohol in any weaker fpi- 
rit from its {pecific gravity.—M. Pouget, 
of Montpellier, in a letter to Mr. Kir- 
wan, dated 12th May 1783, and inferted 
in the 3d volume of the Tranfactions of - 
the Royal Irith Academy fer 1789, page 
157, after a great deal of moft ingenious 
reafoning, and a detail of feveral experi- 
ments made with alcohol of the above- 
mentioned {pecitic gravity, gives the fol- 
lowing formula for the folution of this 
problem : 
Put the total volume or meafure of the 
entire mafs or compound =1. The 7ea- 
jure of alcohol contained therein (fuppof- 
ing alcohol of the fpec. gr. of ©.8199 to 
be pure or perfeétly dephlegmated) =z. 
‘The diminution of the volume or bulk of 
a mixture of equal parts of alcohol and 
water found by experiment (equal as be- 
fore ftated to 0.0288) =c. Then, he fays, 
the diminution of the velume of a mix- 
ture containing # meafures of alcohol will 
be =4¢4%—4ca. And putting the fpecific 
gravity of water (==1.0000) =-a, that of 
alcohol (0.8199) =4, that of the un. 
known mixture =y, it will be (as the 
augmentation of denfity does not at all 
change the abfolute weight of the mafs) 
I—# X aby 1 — Acre 40x? X y and 
from hence he deduces the following 
equations : 







a—b cy ey 4 
=0.5——— pea 005 | 
: a ee a 
O.L6OOt . 
0.5— ———- EN Sam eS me POY LT a Hp my et) oY a bt =p 
O.2304y 
Wee! eS aah A 2 cu 
O.T152y 0.2304) eli a 
G—at-+be 10.18 014 
I—4cn-+4cv? 1—0.11 520--0.1 15247. 
Rol 2 Monfieur 


