of Edinburgh, Session 1883-84. 
601 
lacobiana sara 1’ imagine della curva di contatto della superficie col 
cono circoscritto. La lacobiana d’ una rete di Kg e dell’ ordine 3 ’5 
e passa con 3 ‘2 — 1 = 5 rami per ciascuno de’ punti dati. Ma di essa 
h evidentemente parte la H ^2 ^ dunque la curva residua e una cubica 
coi punti seniplici 123456 ; e siccome due curve analogbe si segano 
in altri tre punti, cosi la superficie e della terza classe. 
Si vede cosi che la superficie e la reciproca della superficie gene- 
rale di terzo ordine. 
Monday, ^th May 1884. 
ROBEET GRAY, Esq., Vice-President, in the Chair. 
The following Communications were read : — 
1. On the Construction of the Canon of Logarithmic Sines. 
By Edward Sang, LL.D. 
In setting about the construction of the Canon of Logarithmic 
Sines, we naturally look for any means of lessening the heavy 
labour of the undertaking. 
The very first table of logarithms, that given by Repair in his 
Canon Mirificus, was one of logarithmic sines, and was made by 
the actual computation of the logarithms as given in Reinhold’s 
table of sines (see Constructio, section 39). But, in the modern 
text-books on trigonometry, we are told that the logarithms may be 
computed independently of the sines themselves. If this computa- 
tion be less laborious than, and as trustworthy as, the operation 
from the already computed sines, it must be adopted. Our canons 
of sines, and of logarithms to fifteen places, then only serve for 
occasional verifications. 
In the introduction to Callet’s admirable collection of Tables 
Portatives, the investigation of the formulae and the series for the 
logarithmic sines are given. According to the rule strictly followed 
in the preceding works, each of our steps must be made indej^end- 
