Royal Society. 459 



the least ; red cloth being intermediate between them. Cottons and 

 silks gave, on trial, precisely the same results, which were further 

 confirmed by the different weights acquired by these substances from 

 the deposition of camphor upon them. 



6. " Researches on the Arseniates, Phosphates, and Modifications 

 of Phosphoric Acid." By Thomas Graham, Esq., M.A, F.R.S. E., 

 Lecturer on Chemistry 'in the Andersonian Institution at Glasgow; 

 Communicated by Dr. Turner, F.R.S. • 



This paper, which forms the sequel to the one on the same subject 

 which was read at the preceding meeting, continues the inquiry into 

 the combinations of phosphoric acid with different bases, and more 

 particularly with soda. The crystallized salt of phosphate of soda was 

 found to contain 37 1 of the phosphate, and 629 of water ; so that 

 the author infers its composition to be three atoms base, namely, two 

 of soda and one of water. The pyrophosphate of soda, on the other 

 hand, contains only two atoms soda as base, and gives accordingly 

 bibasic precipitates. The biphosphate of soda was found to admit of 

 so great a number of changes in its composition and properties, as to 

 render it an object of great interest. Of the four atoms of water 

 which the crystals contain, they lose two atoms at the temperature of 

 212°, and not a particle more till the heat is raised to about 375°. 

 There is every reason to believe that the two atoms of water retained 

 are essential to the constitution of the biphosphate of soda j and that 

 it contains three atoms of base, namely, one atom soda to two atoms 

 water, united to a double atom of phosphoric acid. Other varieties- 

 of this salt are also met with ; the first of which may be called a bi-. 

 pyrophosphate, containing only one atom of basic water ; the second 

 being anhydrous, though soluble in water, and neutral in its reaction 

 on litmus, but of which the exact composition is not well determined ; 

 the third being an insoluble variety ; and a fourth being a metaphos- 

 phate of soda,— the author designating, by the term Metaphosphoric 

 acid, a peculiar hypothetical state of composition of the elements of 

 phosphoric acid in conjunction with water. This new acid enters into 

 combination with barytes and with lime, forming with these bases 

 other metaphosphates. The author concludes by a general review of: 

 the several modifications of phosphoric acid which have resulted from 

 these inquiries. » 



7. " On the Development of the Disturbing Function upon which, 

 depend the Inequalities of the Motions of the Planets, caused by their 

 Mutual Attraction." By James Ivory, Esq., K.H., M.A., F.R.S. 



The progress of physical astronomy has been retarded by the ex- 

 cessive labour requisite for the arithmetical computation of the in- 

 equalities in the motions of the planets, arising from the perturba- 

 tions produced by their mutual attractions. If an inequality depended 

 solely on the quantity of the coefficient of its argument in the ex- , 

 panded algebraic function, the difficulty of computation would not be 

 great, since, from the smallness of the elements on which it depends, 

 namely, the eccentricities and the inclinations of the orbits to the 

 ecliptic, the resulting series decreases, in every case, with great ra- 

 pidity : but as its magnitude depends also upon the length of its pe- 



3N2 



