484 



which make the specific gravities too low. The following is a list of 

 the strengths tried, and of the corresponding specific gravities ob- 

 served : — 



The constant error supposed to pervade Dr Ure's determinations 

 of specific gravities for the higher strengths, was accounted for by 

 supposing that Dr Ure must have operated with two or more differ- 

 ent specimens of acid ; the error arising in his determination by 

 chemical analysis of the strength of each, and different acids being 

 used for high and low strengths. As an instance of this, taking 

 strength 90 as our standard, the proportional condensations for 

 strengths 68, 67, 63, 65, are respectively -0426, -0429, -0410, 

 •0411; that for strength 66 being very much less than that for 

 strength 67. This is indicated by an abrupt fall in the curve at that 

 point, after which it goes on slowly rising, just as before its fall. 



These experiments confirmed a maximum point corresponding to 

 the hydrate HO, SO3 + 15 HO, and showed a minimum point corre- 

 sponding to the hydrate HO, SO3 + 6 HO. 



Allusion was made to Professor Langberg, who, in a report to 

 the British Association for 1847, has described a method of research 

 somewhat similar, but giving negative results. Professor Langberg 

 expresses the specific gravity of an acid, in terms of its strength, by 

 means of an empirical formula, the constants of which he derives 

 from Dr Ure's experiments, and, by means of this formula, he is 

 enabled to exhibit the proportional condensation of any strength (for 

 a given standard) as a function of that strength, so that, equating 

 the first differential coefficient of this function to zero, the resulting 

 equation gives the position of maximum condensation. The points 



