Michelson and Stration — New Harmonic Analyzer. 13 



tersections with the ordinates midway between the heavier 

 ordinates, give the coefficients of the sine and cosine series 

 respectively. The sums of the first twenty terms are repre- 

 sented by the curves D and E, and finally the sum of these two 

 curves produces the curve F, which agrees sufficiently well 

 with the original to be easily recognizable. 



It appears, therefore, that the machine is capable of effect- 

 ing the integration / <p(x) cos kx dx with an accuracy compara- 

 ble with that of other integrating machines ; and while it is 

 scarcely hoped that it will be used for this purpose where great 

 accuracy is required, it certainly saves an enormous amount of 

 labor in cases where an error of one or two per cent is unim- 

 portant. 



The experience gained in the construction of the present 

 machine shows that it would be quite feasible to increase the 

 number of elements to several hundred or even to a thousand 

 with a proportional increase in the accuracy of the integra- 

 tions. 



Finally it is well to note that the principle of summation 

 here employed is so general that it may be used for series of 

 any function by giving to the points \p) the motions corre- 

 sponding to the required functions, instead of the simple har- 

 monic motion furnished by the excentrics. A simple method 

 of effecting this change would be to cut metal templates of the 

 required forms, mounting them on a common axis. In fact 

 the harmonic motion of the original machine was thus pro- 

 duced. 



Eyerson Physical Laboratory, University of Chicago. 



