164 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1914. 
of a degree is in error by about 2,000 toises. Though his triangles 
were solved as plane triangles, neglecting spherical excess, the 
labor involved in their solution will be realized when we remember 
that at that time logarithms had not been invented. 
The first attempt at degree measurement in England was made 
by Norwood about 1635. He measured with a chain the distance 
from London to York, occasionally, however, resorting to pacing, 
and determined his latitudes by observing altitudes of the sun on 
the same day, June 11, in the years 1633 and 1635. His adoption 
of Fernel’s method instead of following in the path marked out by 
Sneliius, is to be regarded as a retrograde step, in spite of the fact 
that his value of a degree, 367,176 feet, or 57,420 toises, is so near 
the truth. Its accuracy, however, must have been the result of a 
compensation of errors. 
Another improvement was now introduced by Picard, who used, 
in 1669, telescope sights on his angle-measuring instrument. He 
measured a base line with wooden rods of 5,663 toises, and a base 
of verification of length 3,902 toises, and his triangulation extended 
from Malvoisine, near Paris, to Sourdon, near Amiens. His result 
for the length of 1° was 57,060 toises. 
Picard’s work was rendered famous in another way, in that it 
furnished Newton with data by which he was enabled to establish 
the law of universal gravitation. About 1665, when he had retired 
from Cambridge to his home at Woolsthorpe on account of the 
ereat plague, his thoughts were first turned to the subject of gravity. 
Reasoning from Kepler’s laws he readily proved that the planets 
are kept in their orbits by an attractive force directed to the sun 
whose intensity varies inversely as the square of the distance. It 
at once occurred to him that if this law is universal it must be in 
virtue of it that the moon is retained in her orbit about the earth; 
that the distance through which the moon falls toward the earth, 
or is deflected from a tangent to her orbit, in a unit of time stands 
in a simple relation to that through which a body falls in the same 
time near the earth’s surface. 
To be more explicit, the distance through which a body falls 
in a given time varies directly as the attractive force and the square 
of the time. The moon’s distance is 60 radii of the earth; therefore 
the force of the earth’s attraction acting upon it is only 1/3,600 of its 
value at the earth’s surface, so that the moon falls in ene second 
only 1/3,600 as far as a body at the earth’s surface. In one minute, 
or 60 seconds, it will fall 3,600 times as far as in one second; there- 
fore the moon should fall as far in one minute as a body near the 
earth’s surface falls in one second, or 16 feet. 
Newton, however, by assuming 60 miles to a degree, the value 
used by navigators at that time, found only 14 feet for that quantity. 
