b 



. [ 371 ] 



vacuum to be made under the elevated pifton, and that no 

 external air intrudes ; fo that when either of thefe takes place, 



the 



difference of their exponents. But when the rec'' is large, and many flrokes will be 

 requifite to exhauft it; the operator who muft calulate what fhould be the power of 

 his machine, may avail himfelf of the help provided for him by the noble inventor 

 of the table of logarithms : for as in thefe the fum or difference of any two logar' 

 is the log" of the product or quotient of tlie correfponding natural N''' ; and that 

 the produift or quotient of a log'" (multiplied or divided by any Nf) is the log"' of that 

 power or root of the correfponding natural W, whofe exponent is the multiplicator 

 or divifor of the log" : fo whatever is effefted by multiplication, divifion, involution 

 or evolution of natural N'"% may be performed by addition, fubtra£lion, multiplica- 

 tion and divifion of their log'. And thus the quotient above-mentioned may be found 

 by fubtraBing the log"" of the recr from that of the aggregate of the rec'' and cyl', 

 and then multiplying the remainder by the N'" of flrokes of the pifton ; for the pro- 

 duel will be the log™ of that Nr which exprefles the rarefadlion ; alfo to find what Nr 

 of ftrokes will produce any required rarefadlion ; take the log'" of the N'' expreflnvj- 

 this rarefadlion ; it is plain from what has been faid, that this log™ mud belong to 

 that natural N'', which is fuch a power of the aforefaid quotient as would be pro- 

 duced by the fame N'' of involutions, as there fhould be flrokes of the pifton em- 

 ployed to produce the rarefadlion ; and that if this log"" were evolved as many times 

 as we mull fuppofe its root to have been involved ; that root would be found which 

 belongs to the original quotient by whofe involution it was produced ; and that if the 

 log" of ^he power be divided by the log"" of the root, the quotient will be (from the 

 nature of log"") the N'' cxpreffing how often it had been involved : there is nothing 

 then to be done fince we know the log"" of the above-mentioned quotient, which 

 is the root, but to divide by it the log™ of the defigned rarefadlion, and the quo- 

 tient will be the N^ of flrokes of the piflon required. 



I infert this and many other things for the eafe of thofe who may be more con- 

 verfant in experimental chemiftry than calculation, and to enable fuch (without 

 recurring to other books) to fubjedl the air-pump to a rigorous trial ; thefe will alfo 

 be the perfons mod likely to make the belt ufe of this machine, on which account 



3 A 2 and 



