on some of the leading Doctrines of Caloric, c. 89 
-By the/same equation we find the 20th term or for 290° to be 
124:28; while experiment gives 120-15, showing a difference of: 
4:13.inches. Ata higher point the error becomes greater. We 
here see that a geometrical series may coincide apparently through 
a considerable range with experiment, and yet be inaccurate when 
further extended. 
Dissatisfied, therefore, with this approximation, I prosecuted » 
thesinquiry, and had.the happiness to discover-a very simple and 
beautiful ratio, which will actually apply through an extensive: 
scale of temperature, and is incomparably easier in practice than 
the preceding rule. The elastic force at 212° =30 inches being 
divided»by 1+23, will give the force for 10° below; this quotient 
divided by 1-24, will give that for 10° lower; and so on pro- 
gressively. To obtain the forces above 212°, we have merely to 
multiply 30 by the ratio 1:23, for the force at 222°; this pro-_ 
duct»by 1°22 -for that:at 232°, and thus for each successive in- 
terval of 10° above the boiling point. 
Thus 30x 1:23=F 55, 30123 x1'22=Fo354 using F 
to denote the force at any temperature 7, according to the nota- 
tion of Laplace. 
By departing from the point of 210° F., we shal! obtain re- 
sults equally accurate, but more convenient for comparison with 
the experimental table. The following numbers exhibit the cor - 
respondence of this ratio with actual observation, 
TaBLE II. 
Observed Elasticity of aqueous Vapour compared with the Ratios. 
Calcul. 
ae 
[) 
& |!\Darton |BETANC.|ROBISON. 
Force. a 
210° | 28°9 | 28:9 210°, 289 | 28-9 ||) 2884 | 288 28°65 
200 |23°5 }23°6 220°) 35°54! 35°54|| 34.99 35:80 
199 }190 |190 230°| 43°36] 43.10} 41:75 | 45°5 4470 
180 |15°2 {15°16 || 240 | 52:46| 51°70|| 4967 5490 
170 |1207 |12:05 |} 250 | 6295} 61-°90') 58-21 66 80 
160) | 9°50'| 960)|| 260 | 7491] 72:30] 67°73 | 80°17 | 80:30 
150 | 7:42 | 758 || 270 | 88°S9| 86:30.) 7785 94:10 
140 | 5.75 | 5°77 |} 280 |103-41|101°90 | 88-75 | 105:12 | 10590 
130 | 442 | 436 |] 290 1119 95}120°15)|| 10012 
120 | 3°37 | 3°33 || $00 187°94 139-70 | 111-81 
110 | 255 | 2°45 || 310 |157-25/161-30 | 123°53 
~» 
S 
= 
re) 
Lo) 
= 
200 22°5() 22 62 
100 | 192] 1°86 || 320 \177-70 ‘| 135°00 
90 1-43 | 1°36 | | as seb 
‘06 | Temp, |Berane. |Rosison, 
70 | 0°77 | 0°726) eae pt mitted 
60.| 056 | O'51G 32° oo--| 00 
50 | 0-40 | 0°36 | | 50 o'12 
40|° 0284 0°25 | 80 081 082 
30 | 0'20;}. O19 | | 100 165 1 60 
20 | 014| 0714 / 120 295 3.00 
10 | 0-098 140 5:00 515 
0 | 0-068 | 160 900 | 865 
| 180 14:00 14-05 
