r 2 57 ] 
fcale, above or below this given temperature ; and a de- 
gree of M. de luc’s fcale is to a degree of bird’s Fah- 
renheit as 178 to 80. Therefore, the fubtangent varies 
by __ 8 tt of the fame quantity, for every degree of 
bird’s Fahrenheit, above or below the given tempera- 
ture. Hence, if n denote the difference of the tem- 
perature of the air, or, in the cafe of unequal tem- 
peratures, the difference of the mean of the tem- 
peratures of the two ftations, above or below 69,25 
in degrees of bird’s Fahrenheit; then, B=t B 
is the length of the fubtangent in ioooths of a 
Paris toife : that is, the fubtangent of the atmofphe- 
rical curve, in the temperature 69,25 ± n, is to fo 
many ioooths of a Paris toife, as are expreffed by 
the modulus of the Briggian fyflem, as 3827 ~t iTxg 
to 3827. 
PROBLEM SECOND. 
To determine the temperature , in which the length 
of the fubtangent of the atmofpherical curve is ex- 
preffed in thoufandths of an Englifh fathom, by the 
fubtangent of the Brlggian fyflem, 
F ROM the number 69,25 fubtracl the 8th part 
of the number, to which 3827 bears the pro- 
portion of 10000 to 617 ; that is, from 69,25 fub- 
traft 29,51 ; the remainder 39,74 expreffes the re- 
quired temperature, in degrees of bird’s Fahrenheit. 
For, let S, £ reprefent the fubtangents, of the 
atmofpherical curves in the temperatures 69,25 and 
69,25 — 29,51, refpe&ively. 
Vol. LX IV. L 1 
Then 
