190 Proceedings of the Royal Society of Edinburgh. [Sess. 
of business this occasionally gives rise to mistakes. On the other hand, 
with 400° on the azimuth circle, we should only have to add or subtract 
200 c , thus almost obviating the chance of a mistake. Hence the surveyor 
would be greatly benefited by the immediate publication of a five-place 
trigonometrical canon, arranged in the decimal way.” 
List of Logarithmic, Trigonometrical, and Astronomical Calcula- 
tions, in Manuscript, by Edward Sang. 
JS T os. 1 and 2. Logarithms /., II. Construction. 
These two volumes contain a complete record of the articulate steps of 
the calculations for the logarithms, to 28 places, of all prime numbers up to 
10,000, with those of other large primes which happen in the course of 
the work. 
No. 3. Logarithms III. Revision. 
This third volume contains the calculation, in revision, for all those 
primes whose logarithms had not been computed thrice. This record is 
accompanied by an Index of all the Divisors used in the work, and of the 
primes themselves and the divisors with which they have been connected. 
In this revision no deviation exceeding 10 units in the 28th place was 
allowed to pass. 
By this registration, a future computer is enabled to lessen his labour 
when he happens to have to do with a divisor which had occurred before, 
or when any easy multiple or sub-multiple may occur. 
No. 4. Logarithms. Primes. 
This is a list of the first 10,000 Prime Numbers (up to 104,759), with 
the logarithms, to 28 places, of those which have been computed (con- 
tinuously up to 10,037, with occasional ones beyond), and with references 
to the pages of the construction in which they have been given. (The 
logarithms of the remaining primes are given to 15 places.) 
No. 5. Logarithms 0. 
Contains the logarithms, to 28 places, of all numbers up to 10,000 ; 
those of the composites having been got by the addition of those contained 
in No. 4. 
No. 6. Logarithms I. 
Contains the logarithms, to 28 places, of all composite numbers from 
10,000 to 20,000, with those of primes incidentally found. 
