ON MATHEMATICAL TABLES. 125 
A towards its limiting value is very slow. The formula (v.) was calculated 
for the reason just mentioned—viz. because it is the limiting form of the 
general expression which includes Legendre’s formula. 
If A be determined so that ——“— 
lo A 
on — 
ga 
= lia, then it is found that 
uf 3 13 
A= + 5 
ae logz (log wz)? hs (log x)? * 
&e., 
to which A = 1 + i 1 ig 0 first approximation. It was for this reason 
og @ 
that the formula (iv.) was calculated. For the smaller values of «, the 
deviations are greater than in the case of Legendre’s formula, but there 
is not much difference between them for values of z near 9,000,000. 
When z = 100,000,000, the deviation is less than one-half of that shown 
by Legendre’s formula. 
A portion of the Introduction relates to the calculation of the loga- 
rithm integral liz, which occurs both in Tchebycheft’s and in Riemann’s 
formule. The methods of calculation adopted are explained, and certain 
values of the function Hi(#) are given, and also some corrections to 
Bessel’s values of liz. 
The convergence of Riemann’s formula is very slow, and the con- 
cluding sections of the Introduction are devoted to a discussion of the 
magnitudes of the successive terms. 
Report of the Committee, consisting of Professor Crum Brown 
(Secretary), and Messrs. Mitye-Home, Joun Murray, and 
Bucuan, appointed for the purpose of co-operating with the 
Scottish Meteorological Society in making Meteorological Obser- 
vations on Ben Nevis. 
‘A Grant of 50]. was made to the Committee by the British Association 
in 1882 ‘for the purpose of co-operating with the Scottish Meteorological 
Society in making Meteorological Observations on Ben Nevis.’ 
These observations were on a much more extensive scale than those 
of the summer of 1881. In 1882 six additional stations were established 
at different altitudes between the two principal stations on the top of Ben 
Nevis and at Fort William. These stations were so placed that observa- 
tions could be made at regular intervals of half an hour during the ascent 
and descent; and simultaneously with these, half-hourly observations 
were made at Fort William. The number of observations made daily at 
Fort William was twenty-one, and on the top of Ben Nevis five, the latter 
being from 9 to 11 a.m. 
In addition to the usual instrumental observations, special attention 
was given to noting wind, cloud, and other weather changes, and it may 
be added that these eye observations were carried out by Mr. Wragge 
with an ability and an enthusiasm worthy of the highest praise. 
Owing to the excessive labour in copying these elaborate and volu- 
minous observations from the note-books, the observations only began to 
be received at the Society’s office in June and thereafter from time to 
time in July and August. On this account little more than a beginning 
has been made with their discussion. 
From the half-hourly observations beginning with 5 a.m., the diurnal 
