\QS PHILOSOPHICAL TRANSACTIONS. [aNNO iGjS, 



He then assigns how many toises or fathoms, Parisian measure, answer to a 

 degree of the circumference of the earth; as for instance, the difference of 

 latitude between Malvoisin and Sourdon is found, by observations made in the 



heavens, to be 1° 1 1 ' 57' 



And between Malvoisin and Amiens 1 22 55 



Now the meridian distance between Malvoisin and Sourdon, calculated from 

 measures taken on the earth, as found above, was 604304- toises ; so hence it 

 is concluded, that 57064-l toises, or, in a round number, 57060 toises, are 

 equal to a degree. Hence the whole circumference of the earth, or 360 de- 

 grees, comes out 2054 1600 toises, and its diameter 6538594 toises.* 



* Since this measurement of meridional degrees, by Picard, many others have been made, in different 

 latitudes and countries, and with continual improvements and accuracy, both in the instruments and the ob- 

 servers ; as in America, north and south, Lapland, Germany, Italy, France, and lastly in England, by Major 

 Mudge, of the royal artillery, with an accuracy, both of instruments and labour, perhaps never before at- 

 tempted : Of which we may hereafter have occasion to give a detailed historical account in another part 

 of these abridgements. At present we shall only advert to the probable cause of a newly observed irregu- 

 larity in the measures of the degrees. 



In all the measures of degrees, in different latitudes, when compared with each other, irregularities have 

 occurred, the lengths of any of them appearing to be either too great or too little, in respect of the others, 

 and that by differences which have no uniformity or harmony among themselves. But in the last measure- 

 ment abovementioned, 1 am told there is an aberration in the conclusions which runs in a pretty regular and 

 uniform series, which will probably appear in a paper of Major Mudge, which I have not yet seen, to be in 

 the next volume of the Philosophical Transactions, for this year 1803. Now those irregularities have usually 

 and chiefly been ascribed to errors in the terrestrial measures. But it is our opinion that the deviations prin- 

 cipally arise from the celestial observations, viz. the observed latitudes, resulting from the observed zenith 

 distances of certain stars. These zenith distances are probably all or most of them erroneous, in consequence 

 of the deviations of the plumb line of the zenith sector, produced by the unequal attractions, on the plummet, 

 of the inequalities in the adjacent parts of the earth's surface, sometimes in excess from hills, and sometimes 

 in defect from valleys and seas. And this cause will very well account, not only for the usual irregularities, 

 but particularly for that uniform deviation in Major Mudge's degrees, which are of this nature, that in going 

 from south to north the terrestrial lengths of those degrees become successively shorter and shorter, from 

 beginning to end, instead of measuring longer and longer, as they ought to do, from the oblate spheroidal 

 figure of the earth. Now this aberration appears to be exactly what might be expected from the position of 

 the part of the meridian here measured, which consists of almost 3 degrees, extending from Dunnose at the 

 Isle of Wight, to the north-east corner of Yorkshire, near the mouth of the river Tees. Now by casting an 

 eye on the map of England, or of Europe, we perceive the English channel on the south end of the line, 

 and the still farther extended northern sea at the north end. And these hollows will naturally occasion a de- 

 fect of attraction on the plummet, the one on the south and the other on the north, according as it is near 

 the one or the other of these depressions. Hence then, at Dunnose, or the south end of that meridian line, 

 the plummet, or the lower end of the apparent vertical line, will be drawn toward the north, while at the 

 north end of the meridian line it will hare a deviation to the south, and that in a more considerable degree 

 than the former, on account of the more extensive depression of the northern ocean. In consequence the 

 zenith points of the plumb line will deviate the opposite way, viz. at the southern station the apparent zenith 

 will be too far to the south, while at the northern station it must be directed too far to the north. Hence it 

 must happen that the celestial difference of latitude between these two stations, being the distance between 

 those two apparent zeniths, will be greater than the true or terrestrial difference, by the sum of the said two 

 deviations. From which it follows that, between those two stations, the celestial arcs appearing to be too 

 large, the observed or celestial degrees will change faster than the terrestrial or measured degrees, or will have 

 measures less than the truth, and that always more and more in defect, in receding from the south, and ap- 

 proaching to the noith, on account of the greater defect of matter at this latter. Thus then we have a pro- 



