1821.] Phcenomena of Heat, Gases, Gravitation, &^c. 21 S 



friend W. Perry, Esq. of Winterbourne. Without such stimuli, 

 I might never have had sufficient confidence in myself to tread 

 those intricate and almost trackless paths of science. 



An Analytical Inquiry into the Cause of Gravitation, Heat, S^c^ 



Several years ago, namely, in July 1 8 i 1 , while amusing myself 

 with calculating some of the lunar equations from theory, I was 

 induced to try to compute the annual equation to the moon's 

 mean motion, somewhat after the manner in which Newton has 

 '^calculated the magnitude of the variation. The result of this 

 <jalculation, which considerably exceeded the quantity given ia 

 the tables of Halley, the only ones I then had, very much sur- 

 -prised me. At first 1 thought I had committed some error, or 

 made some erroneous assumption ; but on re-examining the 

 calculus, and making every allowance which I thought might 

 have any influence, 1 satisfied myself, that as far as my funda- 

 mental principles were correct, nothing was neglected which 

 could affect the result to any thing hke the magnitude of the 

 difference. At another time it occurred to me, that the quantity 

 of the equation, as given in the tables, might possibly be itself 

 too small. 1, therefore, set myself about correcting it from the 

 observations at the end of Halley's tables ; but so far from solv- 

 ing the difficulty by this means, I found the difference much 

 greater ; for, as far as I remember, the maximum of the equation 

 I found to be, instead of 1 V 49'', only about IT 17'' ; that is, 

 but a few seconds greater than the quantity given in the very- 

 correct tables of Burg. Baffled, therefore, in this attempt to 

 reconcile observation and theory, I conceived that the quantity 

 determined from observation must be the result of two opposite 

 ■equations, one of which had escaped the cognizance of theory. 

 And in this opinion I seemed to be more confirmed by another 

 calculation of this equation, by means of an exponential theorem. 

 I had just before discovered, and by observing that the computa- 

 tion of the same equation by Machin, on the principle of an. 

 equant, came out also much greater than the quantity by obser- 

 vation. It is true I was for a little while staggered in ray opinion 

 by the statement of JYewton, in the scholium to prop. 35, book 3, 

 of the Principia, in which he says, that he had calculated the 

 mean greatest quantity of this equation from the theory of gravi- 

 tation at 11' 49". But as I observed that he simply named the 

 result without even hinting at the method of calculation, though 

 just beneath, in the same scholium, he minutely enough describes 

 his calculus of one or two other equations of considerably less 

 difficulty ; and as I had observed that the quantity I had brought 

 out would coincide with his, if diminished in the ratio of the 

 moon's synodical to her siderial period, I thought it very pro- 

 bable that Newton had pursued the same course that I had ; and 

 that finding his numbers would agree with observation, if dimi- 

 nished in the said ratio of the synodical to the siderial period, 



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