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484 SCIENCE PROGRESS. 



This is next converted into a " compound screw " by placing 

 another equal and similar screw of particles inside the first, 

 so that their axes coincide, but not their threads ; and, finally, 

 a number of these compound screws are ranged beside one 

 another in parallel position, so that their axes (supposed 

 vertical) would pass through the knots of a horizontal net 

 whose meshes are all equilateral triangles. This somewhat 

 complicated arrangement is practically identical with that 

 adopted by Wulff (2) and does not differ essentially from 

 one proposed by Mallard. 



Three different authors are therefore in agreement upon 

 a possible grouping of the particles in at least one substance. 



Probable structures have subsequently been suggested 

 for many substances by Mallard, Wulff, Sohncke, Liveing, 

 Fedorow, Lord Kelvin and others, but they need not be 

 quoted since our purpose is only to show at present that 

 the subject is now regarded as something more than a geo- 

 metrical problem, and a few instances will suffice. 



Another step is taken by Muthmann (3), who, in a recent 

 paper on the alkaline phosphates and permanganates, comes 

 to the conclusion that the potassium phosphate KH 2 P0 4 is 

 constructed of "physical molecules," arranged in the follow- 

 ing manner : Space having been divided into equal square 

 prisms, of which the height is represented by the number 

 2*9503, and the horizontal diagonal by 4*4432, a molecule 

 is placed at the centre and at all the corners of each prism ; 

 in the corresponding arsenate the arrangement is supposed 

 to be the same, but the prism has a height of 3*0235, and 

 diagonal 4*5583. These numbers are taken to indicate the 

 comparative molecular intervals along the two corresponding 

 directions in the two salts, a calculation which has never 

 previously been made for any substance. These intervals 

 would be different for the two salts even if they had absolutely 

 the same crystalline form, so it is clear that they are not 

 identical with the usual axial ratios of the crystallogra- 

 phers. 



The author goes even further ; he asserts that each 

 "physical molecule" consists of eight chemical molecules 

 KH0PO4, and he supposes that in this complex cluster 



