364 Mr. S. U. Pickering on the Densities 



& 



equality here increased, instead of diminished, the total error 

 by giving higher values for the e% and e s errors. 



In columns C and D are given the results of making 

 drawings which obliterate every alternate one of the true 

 breaks. The errors of such drawings, as will be seen, are far 

 in excess of what they should be, being nearly 19 and 33 

 times greater respectively than the experimental error, and 

 this, too, in spite of the fact that many of the curves for the 

 various sections were much more complicated than those used 

 in the A drawing, the lath having had to be pulled or twisted 

 considerably so as to get even an approximate agreement. 

 This remark applies also, though to a less extent, to the B 

 drawing. 



In three cases the sections composing the A figure are 

 drawn so as not quite to meet, namely at 42, 35, and 4 per 

 cent. The densities must, of course, be a continuous function 

 of the strength, and in every perfect drawing the sections, 

 therefore, must meet ; but apparent discontinuity might 

 be produced if there were two breaks very close together, 

 with an insufficient number of points to show the existence 

 of both. There is strong evidence from an independent 

 source, as will be mentioned below, to show that two such 

 breaks do actually exist in the neighbourhood of 42 per 

 cent., and in the face of such evidence it has been considered 

 safer not to strain the drawing so as to make the sections 

 meet in cases where the lie of the adjacent points seems 

 strongly to favour their not doing so. 



In the case of the break at about 4 per cent., the first 

 section certainly seems inapplicable beyond 3 per cent., 

 while the second section, extending to 12 per cent., does not 

 seem to apply back beyond 4 per cent. ; and in this case the 

 intermediate experimental point at 3*5 per cent, would lie on 

 a short connecting curve, for the drawing of which there are 

 not sufficient data ; it has, therefore, been omitted entirely 

 in the examination of the drawing (column A, Table II.). 



It remains to be seen whether the breaks in the densities, 

 which thus seem to be so well established, correspond or not 

 with the composition of the hydrates of soda which have been 

 isolated in the crystalline condition. The examination of the 

 freezing-points of soda solutions (Chem. Soc. Trans. 1893, 

 p. 890) showed that from solutions up to 20 per cent, strength 

 water crystallized, after which various definite hydrates to the 

 number of eight or nine separated, till a strength corresponding 

 to NaOHH 2 was reached, beyond which the investigations 

 were not extended. 



