and the Mode of its Communication. 87 
perpendiculars GH and LM be drawn, representing the dif- 
ference of the temperatures after the times EG and GL have 
elapsed, a curved line PQ, drawn through the points D, F, H, M, 
will be the logarithmic curve ; or, if it vary from that curve, its 
variation, within the limits answering to a change of tempera- 
ture amounting to a few degrees, (especially if they be taken 
when the temperature of the hot body is about 40 or 50 degrees 
above that of the medium,) will be so very small, that no sen- 
sible error will result from a supposition that it is the logarithmic 
curve, in supplying, by computation, any intermediate observa- 
tions, which happen to have been neglected in making an 
experiment. 
These computations are very easily made, with the assistance 
of a table of logarithms, in the following manner. 
Supposing CD, CG, and GH, to have been determined by 
actual observation; and that it were required to ascertain, by 
computation, the absciss CE, corresponding to any given inter- 
mediate ordinate EF, or, (which is the same thing,) to determine 
at what time the cooling body was at any given intermediate 
temperature (= EF) between that (= CD) which it was found 
by observation to have at the point C, and that (=GH) which 
it was found to have after the time represented by the line CG 
had elapsed ; 
It is log. CD — log. GH, is to CG as 1 tom; (= modulus 
= the subtangent of the curve at the point D.)* And CE m 
x log. CD — log. EF. 
* The subtangent shows in what time the instrument would cool down to the tem- 
perature of the air -in which it is placed, were its velocity of cooling at the point D to 
be continued uniformly from that point ; and, as the subtange;it of the logarithmic 
curve is constant , if PQjvere the logarithmic curve, it would follow, that the velocity 
