76 N. F. DUPUIS ON A MECHANICAL MEANS OF 
The ratio of the length of a sidereal to that of a solar hour is .99726957. 
365.3 
is 
Now this must be nearly the ratio 36,3, Since 365.3 is nearly the number of solar days 
in a year, and 366.3 is nearly the number of sidereal days in a year. 

366.3 365.3 1 
566.5 366.3 

Therefore the meantime hand must be retarded to the extent of 
ofa revolution in each revolution of the sidereal hand. Or, if the sidereal hand be an hour hand, 
the mean time hand must be retarded 10 of a revolution in each sidereal hour. 
v 
663 
10 
520 : il 
But this is equivalent to 35 X 55. 
Hence the arrangement shown in fig. 1, will be approximately true. PP are two 
fixed pins which, catching into the teeth of the wheel 74, shift it through two teeth in each 
revolution of the arm a which is permanently fixed to the arbor s. This, of course, retards 
IP <i 
the motion of m to the extent of 37 X 99 
of a revolution in each revolution of s. 
Inasmuch, however, as 365.3 and 366.3 are both too great, the retardation will be 
insufficient. This must be increased by causing the pins pp, now fixed, to revolve slowly 
backwards, ‘.e., in a direction opposite to the motion of a ; and we must now find the proper 
rapidity of motion for the pins p p, in order to apply the secondary correction. 
Let r the quantity .99726957 
10 : 
366 — retardation by first wheel-work. 
i 
y = no. of sidereal days in a year. 
Then, while s makes 1 revolution 
m makes (1 — w) revolutions. 
But m should make 7 revolutions. 









Fic. 1. Fic. 2. 
‘.m gains (1 — w — r) revolutions in each sidereal hour. 
And m gains 24 y (1 — w — r) revolutions in 1 year. 
