GEODETICAL STANDARDS WITH THE ENGLISH STANDARD YARD. 
179 
showing that the different series of comparisons are remarkably consistent, and the value 
of the toise most satisfactorily determined ; in fact 
T 0 =C+153-42+0-30. (21) 
Now let T 0 be eliminated between equations (7) and (21), and we get 
®=itM V.-H4-26+0-S7 (22) 
Here Y 55 is supposed at the temperature 61 0, 25. Now the expansion of the yard for 
1° Fahrenheit is 6 ‘51 45 ; therefore if we wish C in terms of Y 55 at 62° we must substi- 
tute in the above equation instead of Y 55 , Y 55 — 4 - 886. Thus it becomes 
C=(2-13151201+0‘0000Q037)Y 55 , (23) 
which is the length of the toise in terms of Y 55 at 62° Fahrenheit. 
The Metre. 
The metre being by definition 443’296 “ lignes ” of the toise of Peru, its true length 
as inferred from the above value of the toise, is 
(1-09362355+ -00000019)Y 5 5. (24) 
The result of the comparisons made in August and December 1864, extending over 
eight days, is that 
M=M 0 +9-98, i (25) 
where M is the length of the platinum metre, both bars being supposed at 61 0, 25 F. 
This equation, combined with (8), gives 
M=MMY 55 - 125-13, 
where Y 55 is at 61°‘25~; but if Y 55 be at 62°, 
* M — ffo h Y s5 — 1 30 -47 (26) 
It would appear from what is stated in the ‘ Base du Systeme Metrique Decimal ’ *, 
that the platinum bars which were to represent the metre at 32° F. were laid off from 
the toise of Peru at 16 0, 25 C. or 61° - 25 F., allowance being made for the contraction of 
the bars according to the rate of expansion ascertained by Borda. At page 326, tom. 
iii. Borda states his results thus, that the expansion of platinum for one degree Reaumur 
is According to this, the correction to the length of the platinum metres at 
61 0, 25 F. would be or 1-5 3 *20 millionths of a yard. lienee the supposed length 
of the Royal Society’s platinum metre at 32° F. would be 
^ im Y 55 - 283-67. 
Finally, according to M. Arago+ this particular metre is too short by 17 '5 9 thousands 
* See tom. iii. p. 681. 
t The only authority on this point is the statement by Captain Rater in the Philosophical Transactions for 
181.8, pp. 103, 104. 
