596 
PHILOSOPHICAL SOCIETY OP WASHINGTON. 
No. 26 for those near 0 h , and No. 27 near 12 h of right ascension. These 
apply to Bessel’s reduction, unaffected by a correction derived from Brad¬ 
ley’s observations of the sun and introduced by Bessel between -f 14° and 
— 14°; the value of which correction, smoothed by repeatedly taking 
means of successive values, gives column 28. It is of the same sign as the 
Boss correction, and agrees more nearly with column 26 than with a mean 
of Nos. 26 and 27. 
It may be worth while to summarize the reasons for believing that Brad¬ 
ley’s observations, even in the elaborate and skillful reduction of them 
made by Dr. Auwers, are open to a large correction in the direction of the 
Boss system, the first of which is furnished by that system itself, which 
is for 1820-30 practically a mean of Bessel’s, Struve’s, and Argelander’s 
independent and carefully determined places. (2) The evidence of 
Piazzi’s results (see columns 21, 22). (3) Evidence of the same kind from 
contemporary work by Mayer in Gottinger and La Caille in Paris, both 
of whom put their southern stars considerably northward of Bradley. 
(4) The similarity of Boss’ correction to that adopted by Bessel, repre¬ 
sented in column 28. For a correction to Bradley of opposite sign 
there is one reason: that the Boss system requires us to adopt for 
Greenwich in 1755 a latitude considerably higher than is now used. 
Auwers adopts a latitude for Bradley’s epoch 0 // .88 smaller than Bessel’s 
value, though 0 /7 .56 larger than the one suiting recent observations, while 
Boss is satisfied with Bessel’s latitude. Though the change of a second or 
more is quite possible, and agrees with observations elsewhere, there is no 
independent reason for suspecting it, and the series of catalogues under 
Airy’s long direction of this observatory shows no sign of its continuance. 
This consideration, together with the uncontested high superiority of 
Bradley over Mayer or Piazzi as an observer, may be held sufficient to 
keep the question for the present doubtful. 
Professor W. A. Rogers (Memoirs Amer. Acad., n. s. vol. 10) has already 
made a comparison between these two declination systems, and has paid 
attention to the important difference of proper motions used in their for¬ 
mation. The present paper is, however, entirely independent of the re¬ 
searches of Professor Rogers. 
Mr. M. H. Doolittle presented a communication on Means 
and Averages, of which the following is an abstract: 
[Abstract.] * 
Such problems as require the determination of the average value of a 
variable may be divided into two classes. 
In the first class there is a locus within which points, lines, or surfaces 
are equally distributed. In the solution the equicrescent variable grows 
but is otherwise stationary, and its definite integral is the locus of equal 
distribution. For illustration, let it be required to determine the average 
value of a right triangle inscribed in a given semicircle, the vertices of the 
