%NSWER Td REMARKS ON MR. VINTt'S PAMPHLET. 345 



the words in the latter sense, as it would have destroyed it 

 as a general proposition here proposed for investigation, 

 and reduced it to a particular case, besides, the two first 

 terms of the whole as forming one series would not have 

 had a definite meaning ; for we might write down all the 

 first terms of each series, and then all the second terms, in 

 their order: or, we might write down the first and second 

 terms of the first series, and then the first and second terms 

 of the second series, and so on. As the terms of each 

 series are the alternate terms of the binomial theorem, 

 the first terms only of the first three series were put down, 

 with -J-, &c. showing that the other terms were to be under- 

 stood. Two terms only of each series were proposed to 

 be taken, to show, even upon that supposition, that as 

 different powers of a must then enter into the two first 

 terms of each series. The whole could not constitute a 



quantity which should vary as — . But Mr. D. seems to have 



paid no attention to the words, u taking only the two first 

 terms of the series," nor to have considered that the word 

 series is used in both numbers; and hence, instead of 

 taking the first and second terms of each series, he has 

 taken the first terms of the two first series, leaving out the 

 second terms which it was proposed to take in, and thus 

 (to use his own expression) u committed so palpable a 

 blunder," as totally to do away the whole force of his 

 objection. 



But Mr. D. goes on thus : cc on this point the professor's Another mis- 

 whole demonstration rests." This is another most un- take P omtfed 



out. 

 fortunate mistake, and contains a further proof, how little 



Mr. D. attended to the subject. What is here assumed, is 

 only a very near approximation to the force, but still suf- 

 ficient for our purpose; the correct law of the force is 

 obtained by taking in all the terins of each of the series, 

 instead of the two first only. And the proof of my pro- 

 position further rests upon this, that the density of the 

 planet enters into the expression for the force; on which 

 account it was not necessary for me to have gone any fur- 

 ther in the investigation than the 13th article; here I have 

 fully established my proposition: but the subject being 



new, 



