2^ PROCEEDINGS OF THE AMERICAN ACADEMY 



soath. liiw?. IS'' IS' in length. The w^uit of uniformitT in the Telocitr 

 of the moon's revolutioo will prodoee an e»steriT and wcsterlj oscilla- 

 lioa in the ' '- " .? the extent of 12~ 36. Nature here 



offers an as: f. on a grtind scale, of two reotau^ilar 



Tibmtio&s of nearly equal amplitude. It is the case of a unison, bat 



a V. ■: exaotlr in tune. For the monthly period which governs 



be: s is not measured in exactly the same way for bo:ii. The 



period oi the first oscillation is the time in which the moon revolves 

 fn>m a node to the same node again. The period of the second 

 oscillation is the time occupied by the moon in going from perigee to 

 perigee again. If the node and the perigee were fixed points, the two 

 periods would be equal. But the node and perigee, in the mean while, 

 are both moving : the former about 1|^^ to the west, and the latter 

 about o' to the east- Hen>."e the periods of the two oscilla::oas will 

 be in the ratio of about o-5-Si^ to 060. or of 79 1 to SOi^. In the course 

 of ei«rhty oiscillations, the north and south one would gain one whole 

 Osscillation upon the other: and once, in about every six years, the 

 earth, as seen from vhe moon, would appear to describe upon the sky 

 all the varieties in lissajous's first group of orbirs. To iUostrate the 

 - ' " ~ " -Tsed the compound per " ~ . ;:p-:>sed to have been 



science twenty-nine ye,. - '"^irds by 6Ia«^bum. 



The total length of the coed was forty inches and that of the single 

 br.. " e inches- ^^ " -ae realized the 



ca? .it fault to the _ .e had the saas- 



facuoo of seeii^ the suspended bob m-^ve over, in the period of eighty 

 vibratioos, the complete series of paths pertaining to all the changes 

 of phase of an imperfect unison. 



In the same year, an elaborate memoir was published by Dr. Na- 

 tbaniel Bowditch.* ~ On the Modon of a Pendulum suspends - - — :: •— ? 

 Points," which be^^r^s with this paragraph- — - The remarks 7 



of morions in a . suspended &om two points, in the car: ~u.s 



experiment in F- -T^^- : 1 -: "-■ - - - — -' r apparent motion or the 

 earth, as viewed from the :o examine the theory of 



s. and I hare : the fondamectal eqoa- 



-. .._ -'- ^--^ - ^ _^... which is the case usually 



considered : - • ^ of the most important results 



of this 



P- 1 _.,_ .. . i the path 



-i by the end of : . ■ case, iran- 



* Mc— ;irs Amer. Acad , lit serie*, vol. iii p. 4ii 



