S83 
A TRONOMICAL OBSERVATIONS OF THE ANCIENTS. 
or 20°. It exceeds this quantity a very little ; 
the reason ot wliich may be, tliat ihe bulb 
of (lie ihei mometer being at the bottom of 
the vessel wheie the Siili actually (liss^olyed, 
probably the lemneratuie in that spot inight 
iiave been lather higher than at the sutlace ol 
the liquid. 
The specific gravity of anhydrous carbonate 
of soda is 2'640. 
Tlie S| ecific gravity of a saturated solution 
of carbonate of soda at 80® is r2291. 
It is composed of water 1000 
Anhydious salt 292’3 
1292*3 
The mean specific gravity of such a mixture 
is 1*1647. But the specific giavity of the so* 
iuiion i.s 1*2291. It is, tlieietoie, a good deal 
tlensei than tlie means. 'J’hiswill explain in 
paittlie reason why the temperature isgieater 
than it ought to be from iheory. 
2. 300 grains of ciystallized sulphate of 
soda in powder, were thiown into ICOO grains 
of water ot the teui[)erature 57®*5, and the 
liquid was stifled about w ith a thermometer 
till the whole salt was dissolved. A longer 
time elapsed leiore the sulpiiate dissolved 
than was itquisite for the solution of tiie car* 
boiiate of soda. The thermometer sunk to 
45° 5 or 12°. 
300 giaiiis of anhydious sulphate of soda in 
fine [)Ou<lef, weie ihiown into )000 grains of 
Water ot me tempeiaiure 61®*5, tlie mixture 
was stirred about with a tliei mometer. 1 he 
tempeiature rose to 65°*5. or 4°. 1 his lein- 
perature continued unalleied fur nearly half 
ail hour, showing that the salt \\ as giving out 
heat during the whole of that time. 
The quantity of salt di^solved was 165*8 
grains. The quantity remaining solid was 
therefore 134*2 grains. 
'i he specific giavity of anhydrous sulphate 
of soda IS 2*640. 
'I'iie Sj ecific gravity of a saturated solution 
ofsul| haieol soda at 6l°'5 is 1*1549. 
Now the mean specific gravity ofa mixture 
of 1000 giainsof waier oi 6i°*fj and 165*8 giains 
of anhydrous sulphate ot soda is 1*0959. The 
solution, iheiefore, is a good deal denser than 
the mean. 
3. 300 grains of crystallized sulphate of 
magnesia in powder were thrown into 1000 
grains of water of the temperature 56° 5, and 
stirred with a thermometer ; the solution was 
rapid but incomplete. The thermometer sunk 
from 56°*5 to 51° or 5°2. 
4. 300 grains of crystallized proto-sulphate 
of iron in pow'der, were thi own into lOOO 
giains of water of the temperature 58°, and 
Ihe mixture was stirred till the salt dissolved. 
'J he thermometer sunk Irom 58° to 53°'5 or 
6°§. So that the cold evolved by the solution 
of sulpiiate of magnesia and proto-sulphate 
of iron is sensibly the same. 
The quantities of water of crystallization in 
300 grams of each of these salts ate as follows : 
giains. 
Carbonate of soda 187*50 
Su Iphate of soda 166 66 
Sulphate of magnesia 153 65 
PiOto*sulphate of iron 135 95 
Now, Ihe ratios of these numbers to each 
other aie very nearly as the numbers 37§, 
33 30|, 27^. 
While the cold produced by the solution 
of eadi salt was 16°, 12°, 5°j, 5°f. 
We see t!iattiie«e two ratios are not the 
same or even analogous to each other. It is 
obvious from this that the mere knowledge of 
the water of cry-tailization, and the solubility 
of a salt, is not suffirdent to enable us to 
foreiell the degree of cold that will he induced 
by its solution in water. A great deal 
depends upon the rapidity of the solution. 
Hence, it hapfiens that more cold is produced 
hy dissolving sn Its in dilute acids; because 
by this method tlie rapidity of the solution is 
veiy much increased . — Records of Science. 
ON SOME ASTRONOMICAL ME- 
THODS OF OBSERVAITON. 
By William GALunAirii, A. IM., 
Teacher of Mathematics, Edinburgh. 
ON THE OBLIQUITY Of THE ECLIPTIC. 
To trace the various methods of astronomi- 
cal observation used by the ancients, would 
be a task too laborious ami iiksome for our 
present purpose. It vvouM not, however, he 
uninteresting to notice a few of their pioces- 
ses and instruments which they most generally 
employed. Among the latter tiie g/moroo con- 
structed in various ways appearetl to be that 
in w'hich mo.-t confidence was placed. 
The rudest example of the gnomon was an 
upright pole, placed perpemliculai ly to the 
lioiizoiilal plane by means ofa plumb line, 
though there aie instances of some of them 
constructed of masonry of considerable 
heights, but these could not propeily be cal- 
led instruments. The altitudes ot liie heavenly 
liodies were fiom these calculated hy com- 
paiing the length of their shadows with their 
height*. In modern mathematical language, 
the height of the gnomon divided by the 
length of its shadow, gives tlie natural tan- 
gent of the allilmle of the celestial body, such 
as the sun, whence hy means of a ubie of 
natural tangents tlie angular measure of that 
altitude I ecomesknown in some conventional 
measnie, such as degrees. 'I hus let the 
height of the gnomon be 5 feet, and tiie length 
of its slradow 10 feet, then or 0*5 being 
found in a lalrle of natural tangents will give 
the angle equal to about 26® 30', the aliituda 
of the sun at that time. 
'1 his method was found to be inconvenient, 
because the lengili of the shadow w'as required 
to be mea'ured each lime an observation was 
made. It, therefore, occm red to the ancient 
asiionomers to foi m a n insfi ument of moderate 
dimensions on similar principles, like the 
artizin’s square, having the horizontal side 
divided into equal parts as it was at first, and 
afterwards into the natural tangents called by 
the Arabians .s/rrtdows, to the radius, ami by 
this means the angle of elevation hecatno 
known in degrees and parts ofa degiee by 
iuspection, though not to any great accuracy. 
