Time or Expence to make, and therefore might be 
fupplied by new ones, as often as they happen'd to 
break. 
Thefe Moulds feem to have been burnt or baked 
fufficiently to make them hard, but not fo as to ren- 
der them porous like Bricks, whereby they would have 
loft their fmooth and even Surface 5 which in thefe 
is plainly fo clofe, that whatever Metal fhould be 
formed in them would have no Appearances like the 
Sand-Holes, by which counterfeit Coins or Medals 
are ufually dete&ed. 
London , May 20. 
*747- 
XXVI. An extraSi of a letter from William 
Jones Efq\ F. R. S. to Martin Folkes Efq- y 
P ref dent of the Royal Society ; containing 
a commodious difpoftion of equations for ex- 
hibiting the relations of goniometrical lines . 
THEOREM. 
Fre/ented July 4 - JN a circle whofe radius is r, let there 
*747- 1 y e two arcSj a the greater, a the lefs , 
each in the firfi quadrant $ put s, t, f, and v, for 
the fine, tangent, fee ant , and verfed fine of an arc s 
s', t', f', the fine , tangent, fecant of the complement , 
and v- , th e njer fed fin e of t he fupplement of that arc 5 . 
let z = iA-|- 3 ,x = iA' — a 5 or if z and x be put for 
the arcs, it will be A = z-f-x,a = z — x. 
Then will the terms in any column of the follow- 
ing table, be proportional to their correjponding ones 
in any other column. 
From 
