GEODETICAL STANDARDS WITH THE ENGLISH STANDARD YARD. 
177 
as possible to the curved edge. Next, let the two semicircles be placed in contact, the 
plates being in the same horizontal plane and their lengths parallel in direction ; the 
semicircles being kept in contact by pressure of a spring. In this position the lines 
drawn on the semicircles will be parallel and very close to one another. If we now, by 
the transverse movement only, slightly alter the position of one of the plates, the 
distance of these parallel lines will vary, and there is obviously a certain position in 
which their distance is a maximum ; this occurs when the (vertical) tangent plane to the 
curved surfaces at their point of contact is parallel to the lines. This distance, when 
measured, is that by which the length of the toise is increased when the contact pieces 
are adjusted to its extremities. 
In the actual apparatus, this distance <r, from very numerous observations, repeated on 
various occasions, is found = 565 - 85+0T08 millionths ofa yard. The toise (Prussian 
or Belgian) has been invariably supported on four points 2P5 inches apart. For the 
comparisons at Southampton a stout bar of iron, rather more than a toise in length, was 
prepared, carrying on its upper surface four rollers fitted with the necessary adjustments 
for strict alignment ; at each of its extremities it carried a horizontal brass plate to 
which the contact apparatus was attached. The iron bar itself Was held at one-fourth 
and three-fourths of its length ; either support being capable of vertical movement for 
focus or levelling. The four rollers on which the toise lay were adjusted to a horizontal 
plane by means of a spirit-level. The contact pieces were held in contact with the 
ends of the toise by spring pressure. To prevent any constant error in the comparisons, 
the contacts were renewed after each comparison, and all the adjustments thrown out 
and re-made as often as possible. 
The number of comparisons between the Prussian toise and T 0 is very large ; they 
extend over twenty-five days, involving 2340 micrometer and 520 thermometer readings. 
The resulting difference of length of the two bars at 61 0, 25 F. is 
T 10 ==Tp— 154-52 ±0T5 (16) 
In the case of the Belgian toise, the comparisons extend over eight days, and with 
the following result : — - 
T n =T 0 -156-33±0-27 (17) 
From these comparisons it would appear that there is a sensible difference between 
the Prussian and Belgian toises, amounting to 1-81 millionth of a yard ; whereas General 
Baeyer found the difference only 0-02 + 0‘40. 
The comparisons of the Bussian double toise extend over 14 days, involving 960 
micrometer and 480 thermometer readings. Its length in terms of T 0 is found to be, at 
61°-25 F., 
P=2T 0 — 321-52+0-31 (18) 
The ten equations (9) ... (18) trace the connexion between the Ordnance toise and 
the toise of Peru through the intervention of six other bars. If we make the unit for 
mdccclxvii. 2 B 
