284 Mr. T. E. Thorpe on the [Feb. 17, 



The common value of P, As, and Sb would appear to be about 27 ; that 

 of Si, Ti, and Sn about 35. But on examining the details of the observa- 

 tions, it becomes evident that this conclusion is not strictly borne out by 

 the results; the numbers obtained for the individual members of the 

 group differ in many cases considerably from the common value, the 

 divergences being far wider than could arise from errors of observation, 

 either in the determination of the physical constants or in the estimation 

 of the atomic weights of the constituent bodies. In fact the order of 

 the divergences would seem to render it probable that the specific volumes 

 of the several members of a family of elements increase with their atomic 

 weights. 



In a former communication to the Eoyal Society I have given the results 

 of a series of observations on the specific gravities, boiling-points, and 

 rate of expansion of certain liquid chlorides of phosphorus*. Since Roscoe 

 has shown that vanadium is a member of the phosphorus group of ele- 

 ments, it has appeared to me that a comparison of the specific volumes 

 of the analogously constituted phosphoryl and vanadyl trichlorides might 

 serve to throw additional light on this question of the relation of the 

 specific volumes of the members of a family of elements to their atomic 

 weights. 



Methods of observation. — A detailed account of the methods of observa- 

 tion and of reduction and calculation employed in this series of researches 

 is reserved for a subsequent communication ; but in order to render certain 

 of the data given in this paper more intelligible, it may be desirable to 

 state that the rates of expansion of the various liquids have been deter- 

 mined in thermometer-shaped vessels (dilatometers), graduated and 

 accurately calibrated. The readings were made with a telescope provided 

 with a micrometer eyepiece. Three series of thermometers were em- 

 ployed, two of which were obtained from Mr. Casella, and the third from 

 Dr. G-eissler, of Bonn ; for a description of these instruments I refer to 

 the paper by Prof. Eiicker and myself on the " Expansion of Sea- water 

 by Heat "f. 



All observations of temperature, unless otherwise stated, are converted 

 into air-thermometer degrees by means of Kegnault's and Recknagel's 

 Tables +. In the determination of the boiling-points the bulb of the 

 thermometer was placed in the vapour of the liquid. I mention this fact 

 as serving to account for the discrepancy in the numbers given by Pierre 

 and myself, Pierre's observations being made with the bulb in the liquid. 



probable number 122'3 (Dexter, Kessler) be adopted, the specific volume is found to 

 approximate more nearly to that of phosphorus and arsenic ; at least the variation from 

 the mean value for the two last-named elements is less than the difference between the 

 specific volumes of tin and titanium, which are regarded by Kopp as practically identical. 



* Proc. Roy. Soc. vol. xxiii. p. 364. Ber. Deut. Chem. Gesell. 1875, p. 326. 



t Ante, p. 159. 



\ WiiUnei*'s Lehrbuch der Physik. Pogg, Ann. cxxiii. p. 115. 



