FHILOSOPHICAL TRANSACTIONS. 505 



2. The infinite powers of the first two ranks are = -f. 



Those of the first three are := ^, 

 Those of the first four are = 4-. 

 Those of the first five are = -f. 

 &c. in infinitum. 



3. All the powers of all the infinite ranks, except the first, are = -^. 



all, except the first two, are = -^. 

 all, except the first three, are = 4-. 

 all, except the first four, are = -J-. 

 < &c. in infinitum. 



These later corollaries may all appear by simple addition and subduction, and 

 so may many more. 



Experiments made with the Liquid and Solid Phosphorus. Communicated to the 

 Collector, by Dr. Frederick Slare, F. R. S. and one of the College of Physicians. 

 Philos. Collect. N° 3, p. 48. 



The experiments that I showed the Royal Society the last summer were, some 

 with a liquid, and some with the solid phosphorus. These two do not materially 

 diflfer, being made both out of substances taken from the human body. The 

 liquid is a substance mixed with a liquor, which though it burns a person when in 

 a solid mass, will not offend the most tender hand, or even heat, when washed 

 in it. This phosphorus retains not its light very long, if close stopped; yet in 

 one sort I have observed a kind of flashing six or seven times successively, 

 though the glass was close stopped. The other phosphorus, which is solid, 

 differs not, as was said, materially from the fluid, being made for the most part 

 from urine ; but I am satisfied that it may be as well made of blood, if it could 

 be as easily obtained as urine in great quantities, since the latter is only the se- 

 rum of the blood strained through the kidneys. In this preparation, we have 

 not only the common analysis into phlegm, spirits, volatile salts, sulphurs, or oils ; 

 but divers other extraordinary appearances before this grand product comes. 



The substance of this phosphorus may be made as transparent as any resinous 

 body, and will melt like wax in warm water: and when cold, it is exceedingly tough, 

 and cuts like luna cornea, or rather somewhat harder. When it is all under the 

 water, it ceases to shine; but whenever any part of it chances to emerge, or get 

 up into the air, though the glass be hermetically sealed, or perfectly shut, yet 

 it will shine. I have kept it in a large glass without water for several days, and 

 yet continually shining with little or no diminution of its light or weight. 



VOL. II. 3 T 



