a Loos Hutton’ S Projett, ‘&e. 
by their difference, which divifor or difference will never con 
fift of more than four or five figures, viz. about half the num- 
ber of figures that are in the divifors oo in the: pre- 
ceding article. 
20. Again, As the difference of the cofines : : 
to the fum of the cofines :: 
fo tangent of half their dizerecet 30 
to tangent of half their fam. 
And thus the cotangents will be found by dividing the fum of 
the cofines of two arcs, differing by 2 zp by their esate difference, 
21. Alfo the fecant of an arc is equal to the fum of its tan- 
gent and the tangent of half its complement ; ; and the cofe- 
cant of an arc is equal to the fum of its cotangent and the tan- 
gent of half the arc; or half the fum of the tangent ‘and 
cotangent is equal to the cofecant of the double arc. From 
whence the fecants and cofecants will be eafily made. 7 
22. Thus I have pointed out methods by which the whole 
tables may be readily conftructed, Should any other ufeful 
methods or improvements occur to any perfon, the communi- 
cation of them to me will be thankfully received. ‘I am now 
engaged in making fome of the computations ; and it is hoped, 
that the facility of them, with the defireablenefs of the tables, 
will induce fome ingenious lovers of the mathematics to lend 
their aid in performing fome part of the work. Should ‘any 
fuch be fo inclined, before he begins, I muft requeft he will be 
pleafed to fignify his intention to me, that I may point out to 
him fuch parts of the work as have not before been pei formed 
or undertaken, to prevent the chance of lofing his labour by 
re-computing any parts that may haye been already | executed, 
by myfelf or others, 
Royal Military Academy f POI LL? 
Woolwich, Aug. 12, ree Cuanzes Hurron. : 
