420 



NA TURE 



[March i, 1894 



The first of the three parts into which the paper is divided 

 contains a summary of the attempts which have been made, 

 more particularly t>y Poiseuille, Graham, Rellstab, Guerout, 

 Pribram and Handl, and Gartenmeister, to elucidate this 

 question. Although it is evident from the investigations of 

 these physicists that relationships of the kind under considera- 

 tion do exist, it must be admitted that they are as yet not very 

 precisely defined mainly for the reason that the conditions by 

 which truly comparable results can alone be obtained have 

 received but scant consideration. 



For example, it seems futile to expect that any definite 

 "toichiouietric relations would become evident by comparing 

 obbtrvations taken at one and the same temperature. Practic- 

 ally, nothing is known of a quantitative character concerning 

 the influence of temperature on viscosity. 



From the time which a liquid takes to flow through a capillary 

 tube under certain conditions, which are set out at length in the 

 paper, a measure of the viscosity of the liquid can be obtained. 



An apparatus was, therefore, designed on this principle which 

 admitted of the determination in absolute measure of the vis- 

 cosity, and for a temperature range extending from o° up to the 

 ordinary boiling point of the liquid examined. 



Full details ot the conditions determining the dimensions of 

 the apparatus and of the modes of estimating these dimensions, 

 together with the methods of conducting the observations, are 

 given in the paper, and the corrections to be applied to the direct 

 results are discussed. 



The question of the mathematical expression of the relation 

 of viscosity of liquids to temperature is considered, and reasons 

 are given for preferring the formula of Slotte — 



»/ = <:/( I + bt)"' 



T] is here the coefficient of viscosity in dynes per square centi- 

 metre, and c, b, and n are constants varying with the liquid. 



With a view of testing the conclusions set out at length in the 

 historical section of the paper, and, in particular, of tracing the 

 influence of homology, substitution, isomerism, and, generally 

 speaking, of changes in the composition and constitution of 

 chemical compounds upon viscosity, a scheme of work was 

 arranged which involved the determination, in absolute measure, 

 of the viscosity of some seventy liquids, at all temperatures 

 between o° (except where the liquid solidified at that tempera- 

 ture) and their respective boiling points. 



Part ii. of the memoir is concerned with the origin and modes 

 of establishing the purity of the several liquids ; it contains the 

 details of the measurements of the viscosity coefficients, together 

 with the data required to express the relation of viscosity co- 

 efficients to temperature by means of Slotte's formula, and tables 

 are given showing the agreement between the observed and 

 calculated values. 



In Part iii. the results are discussed. In the outset the 

 factors upon which the magnitude of the viscosity probably 

 depends are dealt with. The influence of possible molecular 

 aggregations, as indicated by observations of vapour densities, 

 boiling points, and critical densities, and, more especially, by 

 measurements of surface energy, made by Eotvos in 1886, and 

 more recently by Ramsay and Shields, are taken note of. 



The deductions which may be made by considering the 

 graphical representation of the results, showing the variations 

 of viscosity coefficients with temperature, are then set forth. 



For liquids which probably contain simple molecules, or for 

 which there is little evidence of association of molecules at any 

 temperature, the following conclusions may be drawn : — 



(i) In homologous series the coefficient of viscosity is greater, 

 the greater the molecular weight. 



(2) An iso-compound has always a smaller viscosity co- 

 efficient than the corresponding normal compound. 



(3) An allyl compound has, in general, a coefficient which is 

 greater than that of the corresponding isopropyl compound, but 

 less than that of the normal propyl compound. 



(4) Substitution of halogen for hydrogen raises the viscosity 

 coeflicient by an amount which is greater, the greater the atomic 

 weight of the halogen ; successive substitutions of hydrogen by 

 chlorine in the same molecule bring about different increments 

 in the viscosity coefficients. 



(5) In some cases, as in those of the dichlorethanes, substitu- 

 tion exerts a marked influence on the viscosity, and in the case 

 of the dibromides and benzene, it may be so large that the com- 

 pound of higher molecular weight has the smaller viscosity. 



(6) Certain liquids, which probably contain molecular com- 



NO. 1270, VOL. 49] 



plexes, do not obey these rules. Formic and acetic acids are 

 exceptions to Rule i. The alcohols at some temperatures, but 

 not at all, are exceptions to Rule 2 ; at no temperatures do they 

 conform to Rule 3. 



(7) Liquids containing molecular complexes have, in general, 

 large values of dr\ldt. 



(8) In both classes of liquids the behaviour of the initial 

 members of homologous series, such as formic acid and benzene, 

 is in some cases exceptional when compared with that of higher 

 homologues. 



As regards the influence of temperature on viscosity, it is 

 found that the best results given by Slotte's formula are incases 

 where the slope of the curve varies but little with the tempera- 

 ture. From the mode in which the values of the constants n 

 and b are derived, it cannot be expected that their magnitudes 

 will be related in any simple manner to chemical nature. With 

 the exception of certain liquids, such as water and the alcohols, 

 which are characterised by large temperature coefficients, and in 

 which there is reason to expect the existence of molecular 

 aggregates, the formula 



7j = <r/(l + ^/ -j- 7^:2), 



obtained from Slotte's expression by neglecting terms in the 

 denominator involving higher powers of/ than /'-, gives a close 

 agreement with the observed results, and in this formula the 

 magnitude of ^ and 7 are definitely related to the chemical 

 nature of the substances. 



In order to obtain quantitative relationships between viscosity 

 and chemical nature, and to compare one group of substances 

 with another, it is necessary to fix upon particular temperatures 

 at which the liquids may be taken as being in comparable con- 

 ditions as regards viscosity, and to compare the values of the 

 viscosities at those temperatures. 



The first comparable temperature which suggested itself was 

 the boiling point. 



A second comparable temperature was obtained by calculat- 

 ing values of corresponding temperatures by the method of van 

 der Waals with such data as could be obtained. 



The third basis of comparison consisted in using temperatures 

 of equal slope, i.e. temperatures at which the rate of change of 

 the viscosity coefficient is the same for ail liquids. 



At each of the different conditions of comparisons, the experi- 

 mental results have been expressed according to the same system, 

 in order to show at a glance relationships between the magni- 

 tudes of the viscosity constants and the chemical nature of the 

 substances. The liquids are arranged so that chemically related 

 substances are grouped together. Tables are constructed which 

 give the values of the three different magnitudes derivable from 

 measurements of the viscosity of the substances. 



(i) Values of viscosity coefficients (77). 



(2) Values of 7j x molecular area, i.e. molecular viscosity. 



(3) Values of 77 x molecular volume, i.e. molecular viscosity 

 luork. 



The coefficient -q is the force in dynes which has to be exerted 

 per unit-area of a liquid surface in order to maintain its velocity 

 relative to that of another parallel surface at unit distance equal 

 to unity. It seemed, however, that relations between viscosity 

 and chemical nature would best be brought to light if, instead 

 of adopting merely unit-areas, areas were selected upon which 

 there might be assumed to be the same number of molecules. 

 The 7noleci<lar viscosity is proportional to the force exerted on a 

 liquid molecule in order to maintain its velocity equal to unity 

 under the unit conditions above defined. With the units chosen 

 it is the force in dynes exerted on the molecular area in square 

 centimetres under unit conditions. The 7noUcular viscosity work 

 may be regarded as proportional to the work spent in moving a 

 molecule through the average distance between two adjacent 

 molecules under unit conditions. In ordinary units it is the work 

 in ergs required to move a surlace equal to the molecular area 

 in square centimetres through the molecular length in centi- 

 metres. 



In the case of the comparison of the viscosity coefficients at 

 the boiling point, it is found : 



(1) As an homologous series is ascended, in a few cases the 

 viscosity coefficient remains practically the same, but in the 

 greater number of series the coefficients diminish. In one 



I series the coefficients increase ; in the case of the alcohols the 

 coefficients vary irregularly with ascent of the series. 



(2) Of corresponding compounds, the one having the highest 

 molecular weight has in general the highest coefficient (the 



