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A Specimen of a Method of reducing Practical Tables and 

 Calculations into more general and compendious forms. 



HOUGH practices ufuaf in one fcience may often be transferred with 

 advantage to another, yet the general clafs of writers are fo much 

 intent upon making books than improvements, that it very feldorm 

 happens to be the cafe ; and therefore, though the following hints can have 

 little claim to ingenuity, they are certainly valuable on account of their ufe„ 



It is common in Aftronomy, when there are two feries of quantities, 

 whofe refpective terms depend on each other, to find a general expreffion 

 for an intermediate term, by what is called the method of interpolation ; 

 that is applied by Newton to Comets, and by De La Caille to 

 Ecliffes j and I fhall here, as afpecimen, apply it to fome few examples in 

 artillery and fortification. 



Let g + hx be an expreffion by which the quantity a is derived from m, 

 and b from n; then if N is any term in the feries m, n, the term derived 

 from it in the feries a, b, will be (an-bm) s (n-m) -j- N (b-a) : (n-m). 



In p, 174 of Muller's artillery,, the length of a battery for two pieces of 

 cannon is forty feet ; and for four nieces fifty-eight feet : now if N be the 

 number of cannon, a general expreilion for the length of the battery, may 

 be found by fubftituting two for m, and four for n> forty for a and fifty-eight 

 forb, in the foregoing form, which then becomes 22 + 9 Nj and therefore 

 for twenty pieces of cannon, the length of the battery is 202 feet* 



