1 258 3 
Then S : s — 382 7 : 3827 — 29,51 x 8 (by prob. i.) 
But 3827: 3827 — 29,51 x 8 = 10000: iocoo — 617 =: 10000: 9383. 
Therefore, S : £=: 10000 : 93 83; that is, as one Paris 
toife to one Englifh fathom. Therefore, 
whatever multiple S is of the Paris toife, or 
any part thereof, the fame multiple is £ of 
the Englifh fathom, or its like part. And the 
length of S is expreffed in loooths of a Paris 
S £ toife, by the number which is the modulus of 
the Briggian fyftem (by prob. i.)j therefore, 
the length of £ is expreffed by the fame number, 
in loooths of an Englifh fathom. 
PROBLEM THIRD. 
To find the equation for every degree of bird’s Fah- 
renheit in the mean temperature of the air , above or 
below 39,74. 
C ALL the variation of the length of the fub- 
tangent, correfponding to an increment or de- 
crement of one degree of bird’s Fahrenheit, V ; and 
let S, £, as before, reprefent the fubtangents cor- 
refponding to the temperatures 69,25 and 39,74. 
Now V : S — 8 : 3827 (by prob. 1.) 
And S:2=( 3827 : 3827 — 29,51 x 8=) 3827 13591 very nearly (by prob. 1.) 
Therefore, V : £ — 8 : 3 5 9 1 . 
g 
that is, V=z~ £. (= £ nearly). 
Hence the length of the fubtangent of the atmo- 
fpherical curve, in any temperature, 39,74 ± n is 
to its length in the temperature 39,74 as 359 1 ± 8 x n 
to 3591 i that is, putting B for the fubtangent of 
5 the 
