2 Michelson and Stratton — New Harmonic Analyzer. 



The principle upon which the use of springs depends may be 

 demonstrated as follows : 



Let a (Fig. l)=lever arm of small springs, s. (but one of which 



is shown in the fig.) 



#=lever arm of large counter-spring, S. 



/ o =natural length of small springs. 



Z =natural length of large springs. 



£-)^r=stretched length of small springs. 



X-j-y=stretched length of large springs. 



e=constant of small springs. 



i£=constant of large springs. 



??=number of small springs. 



jp=force due to one ot the small springs. 



/ > =force due to the large spring. 



e ,. . a v 



then p= -{lJ rX --y) 



P=|jL+y) 



a%p=bP. 



whence %x 



y= 



n 



(i+i) 



From this it follows that the resultant motion is proportional 

 to the algebraic sum of the components, at least to the same 

 order of accuracy as the increment of force of every spring is 

 proportional to the increment of length. 



To obtain the greatest amplitude for a given number of ele- 

 ments, the ratios y- an d -r should be as small as possible, but 



of course a limit is soon reached, when other considerations 

 enter. 



About a year ago a machine was constructed on this princi- 

 ple with twenty elements and the results obtained* were so 

 encouraging that it was decided to apply to the Bache Fund 

 for assistance in building the present machine of eighty ele- 

 ments. 



Fig. 1 shows the essential parts of a single element, s is 

 one of eighty small springs attached side by side to the lever 

 0, which for greater rigidity has the form of a hollow cylinder, 

 pivoted on knife edges at its axis. S is the large counter- 

 spring. The harmonic motion produced by the excentric A, 

 is communicated to x by the rod R and lever B, the amplitude 

 of the motion at x depending on the adjustable distance d. 



* Paper read before the National Academy of Science, April, 1897. 



