184 PROCEEDINGS OF SECTION A. 
dimensions arrived at by different authorities, the following are 
tabulated :— 
Date. Authority. Ellipticity. meh 
MSO eh. \yvenlloyselie: “Susaanesoossuasonc 1 : 302'8 10,000,268 
JS RIO) saaco oboe Schmidt eee eeeeeeeee 1 : 297°5 10,000,075 
NESW ssooosnonae (MIB Yoo wonnteuiee aso eeene ace 1 : 299°3 10,000,976 
NS oes senses IBGSSel nan ean eo eteaasne 299-2 10,000,856 
ISIS sooanseouce Clarkersineierwenn cass ] : 298°1 10,001,515 
UfSlOe souoonanne ce Piraittinns wscoscoeeeeeenece 1 : 295°3 10,001,924 
NWS 6Gs-cre oct: Clarke Ran. nee aces 1 : 295 10,001,888 
USGS ee IMBC? cadoo cousonoedccddac 1 : 288°5 10,001,714 
WS Zeeanecsce: JOTERETINE Bq. cesugnoacodunenooc 1 : 289 10,000,218 
NS Wuihasctedecaees Schottrent teeter eactiente 1 : 305°5 10,002,232 
ihe aooogntosane Oran Beene sence cases 28655 10,000,681 
SSOP eye. Clarkes avoir 1 : 293°5 10,001,869 
For the four principal of these the following further details are 
added :— . 
Element. 
Bessel, 1841. 
Clarke, 1866. 
Coast Survey, 
1877. 
Clarke, 1880. 
Equatorial radius, a 
6377397°2 M 
6378206°4M 
6378054°3M 
| 6278248°5 M 
Polar semi-axis, ¢ .... 6356079 M) 6356583°8M | 6357175 M | 6356514:‘7M 
Compression a= 1] ; 299-15 1 ; 294-98 1 :305°48 1 : 293°5 
Mean length of ade-) 111120°6M| 1111382-1M| 111135°9 111131°8 
gree. 
For the elements adopted, various functions much used in the 
calculations have been tabulated ; these include, of course, the 
logarithms of the radius of meridian curvature and of the normal 
or radius of curvature in a plane at right angles to the meridian, 
which are respectively represented by 
2 GA Nees) aks. a 
= (1 —e? sin® ¢)! : (1 —e? sin® )# 
in which @ is the equatorial radius, e the eccentricity of the 
elliptic meridian section, and ¢ is the latitude. Among other 
functions tabulated was the logarithm of the quantity ==-,5——~ ,, 
5 | Y INR sin1 
which was required in the reduction of the spherical excess by 
ab sin C , ; ' 
SA | mm which @ and 6 are sides of a 
2 N BR sin’ ] 
riangle, C is the angle included between them, an and R ar 
triangle, C is tl el luded bet them, and N and R are 
as above. The following more convenient expressions, however, 
the formula, « = 
