state, and M- / //,/" r<ttnr> <>f //<> t'ormntini, of in from solutions is lower 

 tli:tn O . I-'urther. both the diminution of vapour tension and the 

 lowering of tin- freexing point proceed, at lea-t in dilute solutions, 

 alnm-i in proportion to the amount of a substance dis.-olved. ls Thus, 

 if ]ier 1 I.H Drains of water there lie in solution 1 . ">. 1 (J grains of common 

 salt (Na('l), then at 100 the vapour tension of the solutions decreases 

 li\" 1. L' 1 , -1.) mm. ot the baromet ne eohimn. a^atn.-t 7'iO mm., or the 

 vapour tension of water, whilst the free/in^ point.- are U'">> . '_M'l . 

 and t'rl'J respectively. The above figures '' are almost proportional 



temperature-,, than the ten-ion of water and of formic acid itself. Tim-, in thi- case the 

 ten-ion of a solution i- never equal to the sum of the tension of the di--ol\ in-- liquid-, us 

 Kt jnaiili already showed when he dist in^ui-hed thi- ca-e from that in which a mixture 

 of liquids, which arc insoluble in cadi other, evaporates. I-'IMHI this it is evident that a. 

 mutual action occurs in solution, which diiniui>lie- the \apoiir ten-ion- pi-oper to the 

 indi\idual substances, as would lie expected mi the suppo-itioii of the fonnatiou of com- 

 pounds ,,(' the di>-ol\iiiL: >ul)-tance- in -olutioii-. l)ecau-e the ela-ticity then alway- 



'" Thi- amount i- u-ually exprt-ssed liy the wei-ht of the -ul.-tance dissolved per l*u 

 pai't- liy weight of water. 1 'rohalily it would le lietter to expre-s it \>\ the (|uantity of 

 the -nli-taiice in a definite volume of the-olution for instance, in a litre. 1 -peak in 

 detail of t lie different method- of expres-in^- the competition of solutions in the work 

 mentioned in note lit. p. f, J. 



' The vai'iatiou of the \apour tension of solutions ha- lieen inve-ti^ated liy many. 

 Thebe>t kniiwn researches aiv those of Wiillner . ls:,s-isf,e and of Tamilian ilHHTi. Tin- 

 re>earclie- on the temperature of the formation of ice from various solutions ai'i' ulso 

 very numerous; Bla^den i_17wi, Kiidorfl i lsf.1 .. and \^<- L'oppet 1 1*71 1 e-tal>lislied the 

 1 H"j inn i ]r_ r . lint thi- kind of m\'e-ti^'at ion takes its chief inteie>t fi'oin the woi'k ot 

 Itaoult. lie_ r un in l^-i> on aijiieous -olution-. and afterward- continued tor -olutions in 

 \ariou- ot hei- eii~ii\-lro/.en licpiid- - for in-tance. lien/eiie. (', 1 1. 'inch- at I'lU'i I. acetic 

 acid. ('.,}!,(.)., i It'rT'i . and other-. An especially important intei'ot is attached to these 

 investigations of llaoult on the lowering of the free/in^ point, l.ecau-e he took >olut ion- 

 of nmiiv well-kn..wn carlxi 



mpolllHls ana discovered a -mi] 

 molecular weight of the Mili^tances and the temperature of cr\ -talli-at ion of the 

 solvent, which enaliled this kind of research to he applied to the m\ e-t i-at ion of the 

 nature of stil>Mtance>. \Ve >hall meet with the ajiplication of Kaoult's reMilts Inter on, 

 and at pic-enl will only cite the deduction arrived at from the-e re-lilt -. The solution 

 o! one - liundreilt h part of t hat molecular i: ram u ei- lit \\ Inch corre-pond- \\ ith the formula 

 of a -ul'-taiice diolved I for example, Na('l :.s-:,. ( ' .1 1, ( ) ir,. ,\ ,-. in ]oiipart> of a 

 solvent lower- the free/in^ ]ioint of it - -olution in u a t er if 1 s.'i . iii lien /cue ()' I'.i . and in 

 acetic acid H-o'.i .or twice an much as with water. And a- in weak >olut ion- t he fall of free/in- 

 point i- proportional to the amount of the -uli-taiice di--ol\ed. it follow- that the fall of 

 free/in^' point for all other -olution- may lie calculated from tin- rule. So. for in-tance, 



the weight which corre-pond- with the formula of acetone, ( '-H, <>. i- ," ; a -oluti 'on- 



t a mi i ix !' \:i. i - i"J-J. .11 id 1 !".',:> ^ram- of acet pel- loo ^ram- o] water lorin- ice ' according 



to the determination- of heckmaiim at tt'TTd . r:t:;ii . and :) -_!o . ;( iid the.-e ti^ure- -how 

 that uiih a Milulion containing o-;,> -ram- of acetone per loo ,,| water the fall of the 

 temperature ,,| the formation ,,f ice will lie d'ls.") , If 1 -o . and d'17'.H. It mu-t lie 

 remarked that the la\s of projiort iomtlity I.etween the fall of temperature of tlie forma- 

 tion of ice, and the composition of a solution.i> in general oul\ approximate, and i- only 



applicable to ueak -ollll ion-. 



We will here remark that the theoretical intere-t o! tlii- Mibjecl was -t ren^t hened 

 on the disco\er\ of tin connection existili" between the tall o! teli-i ui. the fall of the 



