In January of 1878, there was laid on the Society's table the Canon of Sines to each fifth minute of the decimal division of the quadrant, computed to thirty-three for thirty places; along with a detailed record of every step in the process. During the years 1880–81, this work was continued for each single minute, but only to eighteen- for fifteen places, and the record thereof to fifteen places is now submitted. When the rejected figures were from 497 to 503 a mark of interrogation is recorded, and it is believed that not a single error exists in the work. The arrangement of the sines with their first and second differences in position enables us instantly to detect an error.