7 
of a new Pendulum. 
of the rod EG by heat, then likewise upon the rod GB ex- 
panding, it will carry the point B, and consequently the point 
C, as much higher than the point E, as it would have been if 
the materials connecting G and E had been incapable of being 
expanded by heat, and therefore ED will always continue of 
the same length. The same reasoning will hold in cases of 
contraction from cold. 
Therefore, if materials be employed in the rod GB, which 
contract considerably more than those which compose the rod 
CD, then the fixed point G is to be taken at a distance from 
B, in an inverse ratio to the inferior expansile power of the 
materials of which the rod CD consists, and in a direct ratio 
of the expansile power of the materials which connect E and 
G. That is, supposing that it was taken in the inverse ratio of 
the inferior expansile power of CD, then it would be at G ; 
but to counteract the expansile power of the materials GE, it 
must be somewhat lower at I. 
If then the proportion of the expansion of the materials of 
the rod AB, or GB, the rod CD and the materials which con- 
nected AE or GE were known, and the length of a pendulum 
swinging any proportion of time, in that case the distance and 
perpendicular height between GE and IE might be taken at 
once, and a pendulum might be always made which would 
always be of the same length, therefore swing equal arches in 
equal times. But these not being perfectly known, and it be- 
ing extremely difficult, if not impossible, to measure off length 
perfectly, it is necessary to have the power of varying the dis- 
tances and perpendicular height between I and E, A and E, or 
H and E, so that it may be found from trial whether these 
fixed points I, A, or H, be properly taken. For if, on construct- 
