( 142 ) 



In order to find the composition of the solid phases which can 

 be in equilibrium with definite solutions I have acted in the same 

 manner as I did previously with ternary systems; I have applied 

 the "residue-method". 



If the solution is in equilibrium with one solid substance the 

 conjugation line solulion-residue must pass through the point indicating 

 this solid substance; if it is in equilibrium with two solid substances 

 the conjugation line solution-residue intersects the communication line 

 of the two solid substances and if it is in equilibrium with three 

 solid substances it intersects the triangle which has those three solid 

 substances as its angular points. 



These constructions are much facilitated by taking a rectangular 

 tetrahedron instead of an equilateral one and projecting the whole 

 on two of the side planes. 



Astronomy. — "The investigation 0/ the weights in equations accord- 

 ing to the principle of the least squares". By J. Weeder. 

 (Communicated by Prof. H. G. van de Sande Bakhuyzen). 



When results of measurement deduced from different modes of 

 measuring or originating from different observers are equated mutually, 

 it is generally advisable to test the weights assigned to these results, 

 before equating, with the apparent errors produced by the equation 

 in order to be able to judge whether it is necessary to correct them 

 and to distinguish in what direction correction is obtained. Let the 

 material of observation break up according to its origin into groups 

 and let out of the apparent errors of each group separately the mean 

 error of the unity of weight be deduced, then it is a necessity for 

 the differences of those values to be small, at least they may not 

 overstep the limits which can be fixed taking into account the num- 

 bers of apparent errors in each group. 



Already at the outset of such investigations the problem thus 

 appears how the mean error of the unity of weight can be calculated, 

 if one wishes to use but a part of the apparent errors. 



When equating determinations of errors of division of the Leyden 

 meridian circle I have applied the following formula: 



-k ■ 



Here 

 H = the mean error of unity of weight, 

 g = the weight of a result of observation, 



-1/3 



