[ 225 ] 
Now M. de luc hath found, that whatever 
be the value of y ; 
■rAm ] °g- y — a~T. 
But log. y — log. v + log. b. 
and log. v — log. x 4- log. d — log. c. 
and log. x — log. z -f log. E — log. F. 
Therefore log. y ~ log. z + log. E + log. d + log. b. — log. F — log. c. 
and ^-s-o- 4 -oo log- * + 4-5- o"o- l®g* F. + log. d-\- log. b — log. F — log. c — a = T. 
But ^-o4-4-o- 5- log- F + log .d+ log. b. — log. F — log. c — a = —4171,55. 
the French foot being to the Englifh as 2,1315 to 2 j vide Phil. Tranf. vol. LVIIL 
Therefore -^ 44 -<ro log. z — 4171,55 = T. 
9 9 'p 
And ^-00-0-0-0-0-0 log. z — 41,7155 = — — _ t} ie height 
100 0 
of the thermometer, plunged in boiling water, above 
melting ice, in degrees of M. de lug’s fcale, when 
the height of the barometer, in tenths of an Englifh 
inch, is 2;. 
T 
Now for z write 300. Then — — 80,902. 
which therefore is the height of the thermometer, in 
boiling water, above melting ice, in degrees of 
de luc’s fcale, when the barometer is at 30 inches 
Englifh. And in the fame Fate of the barometer, 
the height of the thermometer plunged in boiling 
water, above melting ice, in degrees of bird’s 
Fahrenheit, or, — , is i‘8o. Hence the numbers 
100 
T and 0 are in the confhnt proportion of 809 
and 1800, whatever be the value of z. For the 
change produced in the heat of boiling water, 
by any change of z 9 being always the fame for 
both thermometers, the temperature expreffed 
by T in parts of one fcale, is always the 
Vol, LXIV, G g fame, 
