ON THE REPETITION OF ANGLES. 
By H. G. Fourcape. 
(READ 26TH APRIL, 1892.) 
THE method of repetition admits of an almost unlimited accuracy 
whenever the quantity to be measured can be added to itself, without 
any error in the juxtaposition, until some multiple is found to coincide 
very nearly with a multiple of the unit employed. Some of the 
results obtained by the use of the method, such as the ratio of the 
mean solar day to the mean sidereal, or that of the mean motions 
of the sun and moon are known, in consequence, with a precision 
probably never equalled in direct measurements, few of which are 
correct to more than six significant figures. The pendulum, likewise, 
is an instance of a measuring instrument which owes its high 
perfection to the fact that it admits of indefinite repetition without 
introducing error in the adding up of the separate beats. 
The application of this principle to the measurement of angles 
first proposed by Tobias Mayer in 1752, was embodied by Borda in 
the repeating circle, an instrument which soon became extensively 
adopted in Continental Europe whenever precise measurements were. 
aimed at. 
Theoretically, the advantages of the method are unquestionable. 
when use is made of badly divided instruments that cannot be read: 
with the requisite accuracy. For it may be shown that the probable: 
error « of an angle obtained by m repetitions and the two end 
readings is, calling a the probable error of a bisection and 6 that 
of a reading, 
e= Re ae + 2/3" 
1 n? 
while the probable error of an angle obtained by m independent 
fies Se _— + OP 
j n ait ©. 
/ 
( 
observations is 
