2 E. D. Preston —Measurement of the Peruvian Arc. 



of to-day, but more than a hundred miles north of it in 

 Equador. When the results of these two expeditions were 

 made known, the scientific world accepted Newton's theory, 

 and all later measures have only served to confirm it. 



Let us pause just for an instant to examine the triangulation 

 by Cassini, and the time determination by Richer. Looking 

 at the data with our present knowledge of the accuracy attain- 

 able in the two kinds of measurement, it seems strange that 

 the former could for a moment have cast doubt on the latter. 

 In the first place, Cassini's results do not agree among them- 

 selves. He gives the following statement of the length of one 

 degree in toises : 



(j) T 



49° 56' 56970 



49 22 57060 



47 57 57098 



Even were there no other reason for distrusting the observa- 

 tions, their disagreement would almost condemn them. We 

 now know that the length of one degree in latitude 49° 

 changes about ten toises per degree, so that the change of 

 more*than one hundred and thirty toises in a space of as many 

 miles, indicates either some large error or a value for the earth's 

 radii entirely incompatible with even the rudest observations. 

 Besides, if the first difference were accepted, it would require 

 the place of observation to be in a latitude very different 

 from that known to have been the case. Therefore the 

 triangulation in itself is not very trustworthy. Moreover any 

 assumption in regard to the ellipticity of the meridian derived 

 from measures not extending beyond two degrees, is extremely 

 hazardous. 



On the other hand, when we consider that Richer's clock 

 lost two minutes daily, and that it must have been a compara- 

 tively easy matter, even at that time, to get differential time 

 within a second, it is plain that the only source of error worth 

 examining is that due to the change of the length of the pendu- 

 lum. Barring accidents, and leaving to one side the effect of 

 temperature, which must have been well understood and taken 

 account of by the observer, the length could not have changed 

 by nearly so much as its one-thousandth part, and as the time 

 varies as the square root of the length of the pendulum, the 

 time of one oscillation could not have been in error more than 

 one-half this amount. Hence no error can be admitted that 

 would materially change the result, and the pendulum work 

 might have been accepted as demonstrating the oblateness of 

 the figure. But the Academy resolved upon an independent 

 determination, and the two expeditions were equipped. 



