>. 4-3 



A S'PECIMtN :0 F 



•M 



E_.TI1 O D Oi"F 



By a fimilar fubfutution, if fifty men are-required to make the battery for 

 two pieces, and feventy for that of four pieces, as in Muller's Table j 

 then 30+10 N, is the expreflion for the ,men required for any number N>of 

 pieces in general. 



Instead, therefore, of MtJLLER 9 s Table, the following general one may 

 Be inferted for the number of men, tools, &c. for making a battery for any 

 number of cannon in one night* 



Pwces. 



Lcvgtb of 

 the 



Men 



Battery, j Fafcmes. 





Vala 



nes ,in feet. 











10 | 



8 1 6 



-^ 



K> 



to 



00 







.O 



O 



% 



+ 



+ 



+ 





l_ 



*2 



• NH 





Cr* 



Ot 



"h 



25 



% 



H 



Pickets. Mall, 



Fainil 

 Bills. 



■Plctf, 



Flanks. I Sleepers, j Pickets. 



NO 



3 



1- 

 2 



o 



2 



+ 



1 00 



_ 





co 



+ 



% 



is> 





X 



i 



'In the Tame manner,' from' having a few particular cafes in other kinds of 

 rules, general ones may be found 1 for example if 'N be a number whofe 

 r root is required j and if x r be its neareft complete power j then we know 

 already, that 



,x: N .<» x i,.t x : Nf co x for the 1 root. 



|-x a + |N:'N wx'::x:N{ w x for the fquare root. 



2 X s + N : N w X s : : x : N|- «* x for the cube root. 

 Now the general form of the three laft terms is evident; and to find tliofe 

 of the firft term, let one and two be put for m and n ; and one and three- 

 halves for a and b ..; and by fubftituting in the foregoing expreflion, the gene- 

 ral coefficient of x r Is found to be (r + 1) ; again if we put o and one-half 

 for a and b, we find the coefficient pf N to be (r— r). 



