1888 - 89 .] Dr E. Sang on Fundamental Tables. 
253 
number tt, we measure the areas of the segments not in parts of the 
square of the radius, but in parts of the surface of the circle ; a 
superficial degree being the sector standiug on a degree of arc. 
For the construction of such a table, it was necessary to compute 
the canon of sines measured in parts of the quadrant. The sines 
for the single degrees were therefore computed by simple multi- 
plication of the ordinary sines, to serve as verifications of the 
subsequent work. Afterwards those for each quarter degree were 
obtained by using the previous multiples of 2 ver. 25' for second 
differences ; these two operations completely checked each other. 
Again the sines for each fifth minute were got by help of the 
multiples of 2 ver. 5'. But, as the computations were carried only 
to the tenth decimal of the quadrant, the products by 2 ver. V were 
not needed. 
Sines Measured in Degrees. 
In this way the “ Canon of Sines measured in degrees ” now 
presented was completed, the actual volume contains the whole 
details of the work, and it is hoped without any error exceeding 
two units in the tenth place. 
Canon of Circular Segments. 
Since the number which expresses the area of a segment in 
degrees of surface is the difference between those which express the 
arc and its sine, it follows that the second differences in the table 
of circular segments are identic with those of the sines ; and there- 
fore the canon of segments was constructed directly from those 
second differences. In the present volume it is extended to the 
entire circumference, that is to forty thousand minutes, and shows 
the value of each segment true to within two or three units in the 
ten-thousandth parts of the centesimal second. Its accuracy, thus, 
is very far beyond any requirement in actual astronomy. This work 
furnished another check on that for the canon of sines measured in 
degrees. 
This table of circular segments enables us very easily to discover 
the mean anomaly when the angle of position is known. The con- 
verse problem, “ to find the angle of position from the mean anomaly, ^ 
has to be solved by approximation ; which is sufficiently rapid if 
the first assumption be not very wide of the mark. When, for the 
