Changes of Curvature by Means of a Flexible Lath. 437 



(2) that the evidence as to the existence and position of the 

 breaks obtained by this method is certainly not dependent on 

 the taste of the draughtsman ; and (3) that the splitting-up of 

 the figure into different sections is due to the special nature of 

 the figure, and not to the fact that any figure, whatever may 

 be its nature, will split up into sections of any defined 

 character provided the sections taken are sufficiently small. 



Mr. Hayes has recently shown (Phil. Mag. vol. xxxii. p. 99) 

 that the mathematical basis of the graphic method is sound ; 

 that continuity is the essential feature of a curve formed by a 

 lath when bent by forces applied near its extremities ; and 

 that the curve is of a high degree of generality, and superior 

 in this respect to the parabolic equations ordinarily employed. 

 The practical results, moreover, which have so far been 

 obtained by the method argue strongly in favour of its 

 validity : various properties of the same solutions, though 

 forming figures of totally different general appearance, all 

 indicate consistently changes at the same strengths ; these 

 strengths correspond, moreover, to solutions of definite com- 

 position ; and one of the hydrates thus indicated has been 

 subsequently isolated in the solid condition. 



Experimental and Graphic Errors. 



The known magnitude of the experimental error is the 

 chief criterion by which the legitimacy of any particular 

 representation of a series of points can be determined ; and 

 no representation should be accepted if it attributes to those 

 points an apparent error, either greatly in excess of, or greatly 

 inferior to, the known experimental error. If, moreover, as 

 occasionally happens, two different drawings show the same 

 value for the apparent errors of the points which they are 

 supposed to represent, we are bound to accept the simplest of 

 the two, unless any independent evidence in favour of the 

 other be forthcoming. 



The experimental error may generally be determined satis- 

 factorily by a repetition of the individual determinations. In 

 the present case various series of freezing-point determinations 

 were taken as instances for investigation ; each series was 

 performed in duplicate, fresh solutions being made for the 

 duplicates, and if any exceptionally large difference appeared 

 in the results, further repetitions were made. The solutions 

 used in the repetitions were all of the same strength*, and 

 the arithmetical mean of the various observations gave the 

 mean result at this strength ; each of these mean results gives 



* Slight errors in composition doubtless exist, but the total error may. 

 for convenience sake, be regarded as being entirely due to the readings oi* 

 the thermometer. 



