358 Mr. E. B. Elliott, On the Interchange of the [June 20, 



In the case of liquids a quadrant electrometer was immersed in the 

 liquid in question, and the deflection observed at different tempera- 

 tures. The liquid was heated in a water-bath, and the needle and 

 quadrants were attached to insulating supports above the bath. The 

 electromotive force was obtained from a Ruhmkorff coil without the 

 condenser, and with a high resistance between the terminals by which 

 to control the E.M.F. The poles of a second electrometer in air were 

 connected to the poles of the liquid electrometer, and the ratio of the 

 readings of these two gave a measure of the specific inductive capa- 

 city independent of variations of E.M.F. The results are shown in 

 the following table ; and in the last column are inserted for com- 

 parison the rate of change of refractive index for the four of the 

 liquids for which Messrs. Dale and Gladstone have determined it. 

 Mean values are given except for these four. For glycerine there is 

 no similarity between the two effects ; but for the other three tbe 

 effects are of the same order of magnitude, although not exactly in 

 the ratio 1 : 2 indicated by the electromagnetic theory of light. 



Turpentine 



jj 



Carbon bisulphide, 

 Glycerine 



55 i 



BenzoKne 



J5 



Benzine 



Olive oil 



Paraffin oil 



Rate of decrease of specific 

 inductive ' capacity per 

 degi-ee. 



between 20° and 36° 



0-0012 



y> 



„ 49 



0011 



5» 



„ 62 



0-0009 



') 



15 and 43 



0-004 



)> 



18 and 41 



0-006 



>> 



„ 61 

 19 and 41 



0-0053 



)) 



00006 





52 



o-oon 



') 



63 



0-0015 



JJ 



15 and 39 



00014 



55 



585 



0-0012 





17 and 68 



0-0024 

 increase 



J> 



18 and 54 



0-0023 



Rate of decrease of refrac- 

 tive index per degree for 

 A line in solar spectrum. 



between 10° and 47° 0*00035 



between 20° and 4S° 0-0001S 

 between 25° and 39° 00037 



between 10° and 39° 0*0004 



XII. "On the Interchange of the Variables in certain Linear 

 Differential Operators." By E. B. Elliott, M.A., Fellow 

 of Queen's College, Oxford. Communicated by Professor 

 Sylvester, F.R.S. Keceived June 5, 1889. 



(Abstract.) 



Recent theories of functional differential invariants, reciprocants, 

 cyclicants, &c, have brought into notice a considerable number of 



