62 I'HILUSOPHICAL TRANSACTIONS. [aNNO]725. 



built on a mathematical certainty, his premises may be called in question, and 

 his conclusion, though mathematically drawn from these premises, is only pro- 

 bable. But Dr. D. first endeavours to show, from undoubted phaenomena, 

 that as his conclusion will lead to an absurdity, his measures must be false, 

 because his reasoning from them is just; which therefore disproves his figure of 

 the earth. And he afterwards points out some of the errors which he supposes 

 to have occasioned the mistake in the measures. 



M. Cassini, as well as the English astronomers, believes that the earth makes 

 one revolution about its axis once in 23^ 36"". Let h be taken in any parallel 

 of latitude, fig. ]5, pi. 1, as for example, that of 51° 46'; a plumb line, lh, 

 will be perpendicular to the curve bh, at h, and produced pass through the 

 zenith of the point h, if the earth had no diurnal rotation ; but since the 

 earth moves round its axis, all bodies on its surface endeavour to fly from the 

 axis of their motion, with a force proportionable to their distance from it, in a 

 direction along the plane of their parallel. Let that force, explained by M. 

 Huygens, and called a centrifugal force, be represented by the line h1, or its 

 equal and parallel Lh; now a plummet placed at l, if the earth stood still, 

 would descend in the line lh; but as it is at the same time acted on by the force 

 h1 in the direction Lh, it will move in the direction l1, the diagonal of the paral- 

 lelogram h1, according to the known laws of mechanics ; and the plumb line 

 LH, instead of being perpendicular to the curve at h, will in the latitude 51° 

 46' make an angle of 5' with hl. This angle will be less towards the poles, till 

 at the very pole it quite vanishes, as it also does at the equator. Now since 

 there is no such angle observed, but in all water levels we find the plumb line 

 always perpendicular to the line of level, the surface of the earth must be de- 

 pressed towards g, and rise farther from the axis towards i, in order to become 

 perpendicular, that is, to have its tangent perpendicular to the line l1, in which 

 the plumb line must descend. 



But to say, that those gentlemen could observe the latitude so nicely, as to 

 find a difference in the length of the terrestrial degrees, and that only of 12 

 toises, when they made it the least, or of 31 toises when they made it the 

 most, is attributing to them an exactness so far beyond the nature of the instru- 

 ments which they made use of, that it would be rather a dispraise than a com- 

 mendation to insist upon it. 



For in the first place, the instrument with which they took observations for 

 the latitude at tiie two ends of their meridian, was a 10-foot sector, where the 

 '200th part of an inch answers to 8 seconds of a degree: now the 200th part of 

 an inch being one of the least visible parts we can see in a divided line; they 

 could not take an angle nearer than that; and their instrument was divided only 



