186 Le Roy’s Memoir on the best Method 
meter, which would shorten or lengthen it by different tem- 
peratures, as has been practised in the seconds pendulum, ' 
I found presently the insufficiency of this method. Having 
in my machine two regulating springs of about 1S inches 
each, to produce the desired effect, the shortening or length- 
ening would be proportional to this length. By the com- 
putation which I made, four Jines passed over ii the com~ 
pensation pyrometer would barely have sufficed; now three 
feet of copper combined with three feet of steel hardly gives 
a sixth of a line of difference in their lengthening for 30 de- 
grees of ascent in the Jiquor of the thermometer. We see, 
therefore, that I had not the power of obtaining an exact 
compensation, unless by multiplying the effect by very large 
levers, and a great number of metallic bars; but all this 
brings in a play of the parts, and a want of solidity im the 
pieces of the regulator, absolutely incompatible with the 
desired exactness. 
A second consideration determined me against making 
use of these expedients im my machine, and in general all 
those that alter the length of the regulating spring; which 
is, as I have explained, that the isochronism of the vibra- 
tions absolutely depends on a certain Jength of the spiral 
springs: now every method which renders this length varia~ 
ble, not even excepting that of Mr. Harrison, although 
very ingenious, is on this account inadmissible, 
Here, I am sensible, an objection may be made to me which » 
T shall make myself: as a spring loses its elastic force by heat, 
it may be suspected that the place in its length where all its 
vibrations are isochronons cannot be the same in different 
degrees of heat and cold. The following are the experi- 
ments which dispelled my doubts on this subject :—After 
having found by experiment, in a temperate place, the 
Jength of a spring where all its vibrations, long and short, 
were isochronous, I removed the machine tu a cold five de- 
grees below freezing* ; the watch experienced an advance 
proportional to the cold, (for the sake of greater simplicity I 
had not applied any thermometer to it:) then [ made it go 
six hours, the great spring being almost down; and during 
* About 20} of Fahrenheit. : 
SIX 
