16 ‘ REPORT—1] 874, 
whence, by dividing the course integrated over into parts each equal to a, 
1 :: 1 a 1 hi 
ee ge) 4 nea) ene ta) 4 o—m@eta) see 
bos (2r+1)rx 
_ 29 a 
Gn 20 “Crflye rt lyn 
e  2an +e 2an 
Now take woe a= ae so that nr= aK? then 
1 1 u 
TU mm * T fa da ca 7 et 
GE 46 2K ax 7H) | aK (w—2K) fe eae aad 
2r+1 ; 
BL ts cos ge 1 ye enn) 
=°K 2] pel 2 
q 
By well-known formule we have 
2r+1 ' 
cos am y= vq 93 Crt ljmu 
kK 1+q7"+! 2K 
dt mu, 46 Sru 
sec am (2, ir’) x 7 _ }s0c OY 1 22 gos SU A eg eee ee 
(% HD = ore ) Pag Te ot Te OK : 
ws 
where =e ' ;- whence 
1 TU TU 
A seg A ela a ok’ Y OK if ae Es 
sec am (2?, i eat a | ap eps (c +e ) @-#+0—....) 
| 2k 4 2k 
~) +(e HH) O—e4e—....)tel 
su _™ 
_@ VE Ma rete eae vier £ | 
PB4+e 2K J4eK jae Tk 
7 1 1 1 
=k! mu _ TU = a Raa 1 mu z _ mu 1 me etre 
e2K' 4 ¢ 2K! te2B' 4-4 e 2K’ te 2K’ 4g eek! 
so that (1) is the identical relation that results from equating the series for cos em 
wand sec am (uz, k’), 
Contributions to the Report on Mathematical Tables, 
By Professor Brrrens pE Haan. 
This important communication, which will form part of a future Report of the 
Committee on Mathematical Tables, consisted of three catalogues—the first and 
second containing descriptions of 128 logarithmic and 105 non-logarithmic tables 
from actual inspection, and the third being a list of 553 logarithmic tables, with 
the date, size, place, author's rame, and number of decimals as far as known, being 
a development of a similar list of 267 tables published by Prof. de Haan in 1862. 
