﻿49$ APPENDIX. 



" that seven can be opened ; and lastly, one is the 

 " number of times the whole may be opened together j 

 " and the sum of all the different times is 255." 



The demonstration is evident to mathematicians ; 

 for as the second term's coefficient in a general equa- 

 tion shews the sum of the roots, therefore, in the 

 n power of 1 + 1 where every root is unity, the co- 

 efficient shews the different dries that can be taken in 

 ti things : also, because the third term's coefficient is 

 the sum of the products of all the different twos 

 of the roots, therefore when each root is unity the 

 products of each two roots will be unity, and there- 

 fore the number of units, or the coefficient itself, shews 

 the number of different fOaos that can be taken in n 

 things. Again, because the fourth term is the sum of 

 the products of the different threes that can be taken 

 among the roots, therefore, when each root is unity, 

 the product of each three will be unity, and therefore 

 every unit in the fourth will shew a product of three 

 different roots, and consequently the coefficient itself 

 shews all the different threes that can be taken in ;/. 

 things ; and so for the rest. 1 should not have added 

 this, but that I do not know well where to refer to it. 



P. S. There is an observation, perhaps worth re- 

 marking, with respect to the change of the poles; name.- 

 ly, that the small rock-oyflers are generally all dead 

 within about a foot above high water-mark ; now pos- 

 sibly naturalists may be able to tell the age of such shells 

 nearly by their appearance ; and if so, a pretty good 

 eftimate may be formed of the rate of alteration ot the 

 level of the sea in such places where they are ; for 1 made 

 some astronomical observations on a rock in the sea near 

 an ifland about seven miles to the south of the island 

 of Cheduba^ on xheAracan coast, whose top was eigh- 

 teen feet above high water-mark, and the whole rock 

 covered with those shells fast grown to it, but all -of 



