LIEUT. -COL. A. E, CLAEKE ON STANDAEDS OF LENGTH. 
467 
If P were placed in contact with other bars having terminal cylinders of the same 
diameter and same radius of curvature for the spherical surfaces, but free from the 
peculiar defect of P, the correction would be, supposing the axes adjusted into the same 
line, or the touching cylinders at the same height, 
4 = 4 - 34 . 
If the contacts at the two ends of P were made with very small cylinders, the radius 
of curvature of whose spherical contact surfaces were exceedingly small, then, supposing 
the axes of these cylinders to be coincident with the axes of the corresponding cylinders 
of P, the correction to the length of P would be 
S=8'«8J 
and this quantity is equal to the difference between the maximum length of P and the 
distance between the centres of its terminal disks. 
The comparisons of P in 1865 were commenced, as stated at page 258 of the ‘ Com- 
parisons of Standards,’ in ignorance of the peculiarity of these terminal surfaces. It was 
attempted to make contacts at the centres of the disks, while at the same time the axes 
of the cylinder of P and of the contact-apparatus were in one line. It may be assumed 
that the result would be less than the maximum length of the bar by some quantity 
intermediate to the two corrections (Case 1 and Case 2) which we have just computed, 
viz. 6-31 and 11-83. A reduction of the forty observations so made shows the length 
obtained to have been 10 - 15 shorter than that which resulted afterwards, when the 
contacts were made so as to give the maximum length. So far this is perfectly satis- 
factory. 
The new comparisons of P extend over five days in March 1868 and one day in April, 
the temperature being about 45°; over nine days in August and one in September 1869, 
temperatures ranging from 61° to 65°. In these comparisons the contacts were so 
adjusted that the axes of the cylinders of P and of the contact-apparatus were in the 
same line (Case 1). 
The result of the forty comparisons is this, both bars being at 61°-25, 
P=2T 0 — 323-90 + 0-29. 
If we correct the observations of 1868-69 for the position of the point of contact, so 
as to give the maximum length of the bar, we get, by adding 6-31, 
P = 2T 0 — 317-59. 
This differs sensibly from the length determined in 1865, which was 
P=2T 0 — 320-48. 
If from the maximum length we would determine the length of the bar measured 
between the centres of the terminal disks, we have to subtract 8-68; this gives 
P=2T 0 — 326-27. 
