VOL. XXXIII.] PHILOSOPHICAL TKANSACTIONS. 65 



what is more, we must tuke this angle with an instrument of 39 inches radius, 

 because the 10-foot sector was only used at the ends of the two parts of the 

 meridian. 



To disprove M. Cassini's hypothesis, we need only observe whether a plumb 

 line makes an angle of 5 minutes with a perpendicular to the surface of stagnant 

 waters, or lines of level. 



To prove M. Cassini's opinion, the height of a great many mountains must 

 be accurately measured by trigonometry, which mathematicians have always 

 found very difficult. 



To prove Sir Isaac Newton's opinion, we are only to measure, to about one- 

 tenth'of an inch in a rod of 39.129 inches; and to know what to allow for the 

 lengthening of the same rod by the summer heat, when it is shut up in a case, 

 and carried towards the equator. For though the experiments on pendulums, 

 made by several persons that travelled southward, differ among themselves, )et 

 they all agree in this, that the observers were obliged to shorten their pen- 

 dulums, in order to make them swing seconds, as they went towards the 

 equator. And when we come to compare them together, in order to have the 

 exact proportion of length in different latitudes, we must rely on the most 

 exact experimentor, which we may very well do on M. Richer; because when 

 he found a difference, he was so careful to find out how much it was, that he 

 caused a simple pendulum to swing, and compared it with a good pendulum 

 clock, which he did several times every week for 10 months together; and 

 when he returned to France, he compared it with the length of the pendulum 

 at Paris, which is of 3 feet Sf lines, or 39.129 English inches, and found it to 

 be shorter by IJ- line. 



Dr. D. in another N° resumes the discourse as follows: Since his paper con- 

 cerning the figure of the earth was read before the Royal Society, M. Mairan, 

 in the Memoirs of the Royal Academy of Paris, for the year 1/20, has a dis- 

 sertation, where he has taken a great deal of pains to reconcile the observations 

 made on pendulums, found to be shorter at the equator tlian at Paris, when 

 they swing seconds, with the oblong spheroidical figure of the earth, deduced 

 from M. Cassini's measures. And though on a strict examination of his con- 

 jectures, and what he gives for demonstrations, there is no reason to alter the 

 opinion concerning the oblate or flatted spheroid, which Sir Isaac Newton has 

 shown to be the figure of the earth; yet since it might be thought by some, 

 who have read M. Mairan's treatise, and afterwards may read the Doctor's, that 

 he had not considered all the circumstances, he shows where he thinks M. 

 Mairan is mistaken, and gives other additional proofs of his assertions. 



First tlien, M. Mairan says, " th.it it is as reasonable to suppose the earth, 

 VOL. VII. K 



