I7t) PHILOSOPHICAL TRANSACTIONS. [anNO I697. 



China. It is remarked that none of these cruel diseases, the gravel, stone, 

 gout, or sciatica, are known in China. 



Account of a Person tvho had horny Ercresceyices, or exlraordmary large Nails, 

 on his Fingers and Toes. By Mr. Locke. N^ 230, p. 5g4. 

 Mr. Locke saw this young man at Paris, in May, 1678. He was then be- 

 tween 19 and 20. Those horny excrescences, like ill-shaped claws, grew on 

 most of his fingers and toes, instead of nails ; some of them 4 inches in length. 

 There were some also on the back of his hands, but shorter and broad. This 

 disease began about 3 years before, after having had the small-pox, to which he 

 attributes its origin. 



Journal of a Foy age from England l.o Constantinople, made in the Year 1668. 

 ' by T. Smith, D. D. et F. R. S. N° 230, p. 597. 

 This journal contains nothing either useful or curious, not differing from 

 that of a common seaman. It was kept by Dr. Smitli, in accompanying Sir 

 Daniel Harvey, his Majesty's ambassador to the port of the Ottoman emperor 

 at Constantinople. 



A Method of raising an Infinite Multinomial to any given Power, or extracting 

 any given Root of the same. By Mr. Ab. De Moivre. N° 230, p. OJg. 

 About two years since, considering Mr. Newton's theorem for raising a 

 binomial to any given power, or extracting any root of the same ; I inquired 

 whether, what he had done for a binomial could not be done for an infinite 

 multinomial. I soon found the thing was possible, and effected it, as in the 

 following paper ; and I design in a little time to show the uses it may be applied 

 to: in the mean while, those that are already versed in the doctrine of infinite 

 series, and have seen what applications Mr. Newton has made of his theorem, 

 may of themselves derive several uses from this. 



I suppose that the infinite multinomial number is az -f ^"^^ + cz^ + dz* -\- 

 ex" Sec. m is the index of the power, to which this multinomial ought to be 

 raised, or the index of the root which is to be extracted : I say that this power 

 or root of the multinomial is such a series as I have here expressed, viz. 



az + bz- + C2^ + dz" -j- ez* + /z* + gJ + /tz« + iz^ i£c. \ 



r. III r, II 



. m m-I , m + \ , m m—\ m-2 ,., m + 2 , f« . m~l m—'^. m-3 ,3 m + 3 



-j- - a bz + 1 H — " ^'^ + 1 "> 2 " "1 3~ " ^ 



, VI m-\ , m , m— I m-2 , 

 -f - a c + 7 H f- " be 



, m m-l J 



+ -J" a 



