185 
1907-8.] Dr Edward Sang’s Tables. 
preparative. Laplace had, in anticipation, reduced all his data in the 
Mecanique Celeste to the new system, and instruments had been graduated 
suitably. 
“We can hardly doubt but that if this new canon had then been 
published, the decimal graduation of the quadrant would have been very 
generally adopted even at the beginning of the present century ; by the 
end of the first decade of this century it might indeed have been univer- 
sally adopted. But the new trigonometrical tables, though magniloquently 
described, never made their appearance ; and thus for something like 
seventy years the progress of the sciences thereon depending has been 
impeded. 
“Very few are old enough to remember the disappointment felt 
throughout the scientific world. About 1815, in our school, the boys were 
exercised in computing short tables of logarithms and of sines and tangents, 
in order to gain the right to use Hutton’s seven-place tables ; and well do 
I recollect the almost awe with which we listened to descriptions of the 
extent and value of the renowned Cadastre Tables. 
“In 1819 the British Government, at the instigation of Gilbert Davies, 
M.P., approached the French Government with a proposal to share the 
expense of publishing the Cadastre Tables, and a commission was appointed 
to consider the matter. The negotiations, however, fell through, for reasons 
which were never very publicly made known — but in the session 1820-21 
the rumour was current amongst us students of mathematics in the Uni- 
versity of Edinburgh, that the English Commissioners were dissatisfied of 
the soundness of the calculations — and so it was that the idea of an entire 
recalculation came into my mind. 
“ In the year 1848, encouraged by the acquisition of a copy of that 
admirable work, Burckhardt’s Table des Diviseurs up to three million, the 
idea took a concrete shape in my mind, and I resolved to systematise the 
work which before I had carried on in a desultory way. Necessarily the 
first step was to construct a table of logarithms sufficiently extensive to 
satisfy all the wants of computers in trigonometry and astronomy; and 
having many times felt the inconvenience of the loss of the details of the 
calculations made on separate papers, I resolved to record from the very 
beginning every important step. This plan of operation has many con- 
veniences — it enables us to retrace and examine every case of doubt, and 
also to take advantage, in new calculations, of anything in the previous 
work which may happen to be applicable. 
“For all the ordinary operations of surveying and practical astronomy 
five-place logarithms, as M. Lalande has stated, are perfectly sufficient ; and 
