196 
Proceedings of the Poyal Society of Edinburgh. [Sess. 
Although more convenient in some respects than Captain Weir’s 
diagram, it has the disadvantage of throwing the scale-readings both of c 
and C, which are near 0 C or 180°, too far away from the centre,* whereas 
Weir’s does this only for the variable c. If we wish to have all values 
of c on the diagram, we could transform d’Ocagne’s nomogram so that the 
oscale goes to infinity and is replaced by a c-circle about the new origin. 
The required transformation is analogous to the one just given. 
D’Ocagne has also published*!* a straight-line nomogram for the case 
(3.1) formula (1). It consists of two scales a;= — 1, 7/= — cosa; cc=+l, 
u ir 
y—— cos A, together with the network made up of the two identical 
families of ellipses, 
(x— l) 2 = (x-\- 1) 2 cosec 2 b + iy 2 sec 2 6 ) ,, 9 s 
(x— 1) 2 = (z-j-1) 2 cosec 2 c + 4?/ 2 sec 2 c ) ' ' ' 
The intersection of a 6-ellipse and a c one determine a point (6, c) on the 
diagram which is collinear with the point a on the ct-scale and the point 
A on the A-scale, provided the four variables b, A, c, a satisfy the equation 
(1). It is reproduced in fig. 4. 
* This was subsequently partially remedied by Perret by an additional construction. 
See Assoc, franpaise pour Vavancement des sciences , 1905, p. 93. 
T Bulletin Astr ., t. xi (1894), p. 5 ; Soc. Mach. France Bull. (1904), p. 196. 
