Illumination of a Plane due to Small Source of Light. 463 



From the foregoing numbers we see that the value of 

 / always decreases with increase of temperature, both for 

 associating and non-associating bodies. The only exception 

 is the value of/ for carbon bisulphide at —10°. The oscilla- 

 tions of/ for oxygen and ethylene are simply due to diffi- 

 culties in executing the experiments at such low temperatures. 

 The difference between the highest and the lowest value for 

 oxygen is, however, not so great — it does not reach 2 per 

 cent. ; whilst the mean values for ether, from Prof. Battelli's 

 and Profs. Ramsay and Young's determinations, differ by 

 3 3 per cent.* 



From the numbers above and the equations (2) and (3) it 

 follows that the disagreement of / with its normal value is a 

 measure of the disagreement of specific pressures it at corre- 

 sponding temperatures, and vice versa. The association of 

 the molecules of the liquid has an influence on/, but is not 

 the only reason of its increasing. In such a case/ would, for 

 instance, become smaller with the increase of the molecular 

 weight in the series of alcohols, for Messrs. Ramsay and 

 Shields have proved that the association decreases with the 

 increase of the molecular weight. Besides, of ten esters 

 for which Prof. Guye has calculated/, six have /much higher 

 than 3*06, so that they would appear to be associated ; from 

 the paper of Messrs. Ramsay and Shields it follows that they 

 are not associated. That shows that the association, but 

 not it alone, exerts an influence on / It would therefore 

 be necessary to find out the relation between /and the nature 

 of the substance ; perhaps there is some relation with the 

 molecular weight, for we see that the heaviest of the alcohols 

 examined, isobntyl alcohol, has the highest /; but to get 

 more knowledge on this point we shall have to obtain more 

 information on the critical constants and vapour-pressures 

 of different bodies, those of homologous chemical structure 

 being best for the purpose. 



XL. On a Simple Geometrical Construction for finding the 

 Intensity of Illumination at any Point of a Plane due to a 

 Small Source of Light symmetrical about an Axis perpendi- 

 cular to that Plane. By Charles H. Lees, D.Sc.\ 



I^HE following geometrical construction for finding the 

 illumination of a plane due to a given source of light of 



* Cf. Guye, Arch. d. Sc. ph. et nat. Geneve, xxxi. p. 471. 

 t Communicated bv the Author. 



2 K 2 



