8 Mr. Ivory on the Ellipticiti) of the Earth 



and this equation being subtracted from the second, we get, 

 •0020296 = '610844 M — -941311 N. 



And in like manner by combining the first equation with each 

 of the remaining four, the following results will be obtained, viz. 



•0027395 = -798000 M — '632307 N 

 •0029932 = -888457 M — -382506 N 

 •0031170 = -926974 M - -256266 N 

 •0031716 = -966884 M — -112945 N. 

 These are the equations from which we are to find M and N ; 

 but it may be proper to inquire previously, what degree of 

 exactness we ought to assign to the results. All the numbers 

 in the equations may be considered as exact, except the quo- 

 tients of the pendulums, the exactness of which will depend 

 upon the accuracy of the experiments. Now it may be af- 

 firmed that, when the pendulum is expressed in English inches, 

 there is no one instance in which we are quite sure of the 

 figure in the fourth decimal place, and all the following figures 

 are uncertain. 



In the Phil. Trans, for 1818, the length of the pendulum in 

 London is found equal to 39*13860; but there is a necessary 

 correction of -00079 to be added, on account of an omission 

 in estimating the specific gravity of the pendulum, which makes 

 the length 39-13939 (Phil. Trans, for 1819, p. 415). It is 

 then said, the allowance of '00031 for the height above the level 

 of the sea, should, according to Dr. Young, be only -00021 ; and 

 this brings the pendulum to 39-13929. There is thus a unit 

 of uncertainty in the fourth place of figures, arising from a 

 difference of opinion about a necessary reduction; and we 

 should be warranted in concluding that the length of the pen- 

 dulum cannot possibly, from the nature of the case, be ascer- 

 tained beyond the degree of exactness we have assigned, what- 

 ever be the skill and care of the experimenter. In the Journal 

 of Science, No. 39, p. 102, the length of the pendulum is 

 stated at a mean equal to 39*13910, which is the number we 

 have adopted. 



The length of the decimal pendulum at Paris, determined by 

 Borda, when all reductions are made, is, in parts of a metre, 

 0*741904* ; and the same length, according to the later expe- 

 riments of MM. Biot, Mathieu, and Bouvard, is 0*741 91 749 f. 

 The difference is '00001349 of a metre, or *00053 of an inch. 

 The later determination is no doubt the more exact ; yet it 

 cannot be said that this instance forms an exception to what 

 we have affirmed. 



* Conn, des Terns. 1816, p. 321 . -f Supp. Encycl. Brit. vol. vi. p. 134. 



We 



