GEODETICAL STANDARDS WITH THE ENGLISH STANDARD YARD. 
175 
toise of Peru and has found them “perfectly equal” in length. The authority of 
Bessel’s toise is stated in a certificate signed by MM. Arago and Zahrtmann*, who 
assert that they have compared the toise constructed for M. Bessel with the toise of 
Peru, and have found it too short by tzTw °f a “ligne” (the toise =864 lignes). If, 
therefore, we put F s and F A for the length of these two toises at 16°-25 C., and C for the 
length of The Toise 
F S =C (9) 
F 4 =C— CF0008Q (10) 
In Russia the standard to which all their geodetical measures are referred is a bar 
two toises in length, designated Nf. Its length was determined from F s : the com- 
parisons are given in M. Struve’s ‘ Account of the Russian Meridional Arc of 25° 20',’ 
the deduced length of N being, at 16°-25 C., 
N=2F.+0 , -01249±0-00070 (11) 
The Russian double toise P, which has been compared at Southampton with two 
lengths of T 0 , is a copy of N ; the difference of the two bars at 16°-25 C. being 
P=N — 0-01809 ±0-00019 (12) 
This bar P has been very extensively used in Russian geodesy. In 1850 it was used 
as the Standard in the Measurement of the Base of Alten, in Finmark, and the next 
year in the measurement of the Base of Ofver-Tornea, in Lapland. In 1852 it was used 
at the measurement of the Base at Taschbunar at the southern extremity of the Russian 
Arc in Bessarabia, and in various other bases for geodetical operations undertaken by the 
Topographical Depot. Subsequently it was used in Eastern Russia. 
M. Struve also compared the Prussian toise T ]0 described above, with his normal bar 
N, the result being, at 16 0, 25 C., 
2T 10 =N— 0-01421 ±0-00020 (13) 
The Prussian and Belgian toises T 10 , T n were compared in 1852 by General Baeyer 
with Bessel’s toise. The comparisons will be found in the work entitled. “ Compte 
rendu des Operations de la Commission institute par M. le Ministre de la Guerre , pour 
etalonner les regies qui ont dte employees a la mesure des bases geodesiques beiges ,” 
Bruxelles, 1855. The results are J, at 16°-25 C., 
T 10 =F A -(F00019±0-00011, (14) 
T n =F A -0'-00020±0-00012 (15) 
The difference of these two toises, according to these comparisons, is a very minute 
and inappreciable quantity. It appears, then, that although the very valuable standards 
T 10 , T u , P, which have been compared at Southampton with T 0 , have not been themselves 
immediately compared with the toise of Peru, yet the connexion with that standard is 
*. See ‘ TJ nter suchungen iiber die Lange des einfachen Secundenpendels,’ von E. W. Bessel, Berlin, 1828, p. 126. 
t See ‘ Arc du Meridien de 25° 20' . . . .’ Introduction, pp. xl, lxxiii-lxxvi, also pp. 36-38. Tlie results 
of M. Struve’s comparisons among different bars are collected in the Table, pp. lxxiii, lxxiv. 
X See pages 36-52 of the work named. 
