THEORY OF THE REFLECTING EXTENSOMETER. 109 
the very small additive corrections, indicated in Table I. for the 
reading 50 mm., with contact pieces of 30 mm. and 50 mm. 
With the corrected reading the formula (4a), of § 3, becomes 
absolutely exact, hence if Z/Z be 1/250 the extension is 
so that if we add the corrected readings by the two scales we have 
Se Rt Bi ATS 
that is to say, the sum of the corrected readings expresses the 
extension in thousandths of millimetres. Since one-tenth of a 
division can be estimated, the result is given to 0-0001 mm. or 
about 1/250000 inch. Consequently twice the largest correction 
in Table I., shews that the neglect of the exact theory can lead to 
a maximum error of about 08 in 30 or 1 in 375 with the shortest 
contact piece, or of about 1 in 2500 with the longest. Since the 
larger defect would not be likely to occur, we may say generally 
that the error of the approximate theory is after all only of the 
order of about 1 in 1000 at the most. When the corrections are 
applied, I infer from the few opportunities I have had so far of 
judging, that the real error is likely to be about one division of 
the scale or -001 mm. 
é 
Tt ought perhaps here to be added that it is more rigorously 
exact to apply the correction to the mean of the readings. Hence 
if the mean of the differences of the readings of the scales be F,, 
then 1 
= 969 te 
It should not be forgotten that the length #, for which the _ 
extension is measured, is from the knife-edge of the prism to the 
edge of the contact piece. By measuring from the angle of the 
Sroove to the sharp edge of the contact piece, that is from @ to Z 
Fig. 1, EZ can be readily determined. Calling the distance ZG, 
F we have 
H=F- as very approximately......(15) 
The reductions for the five lengths of F# are respectively “343, oe 
