342 Mr. G. F. Becker on some 



V. Conclusion. 

 § 17. We were already led by our first investigations to 

 the opinion that the further one was able to penetrate into 

 the infra-red, the simpler the relations would become. While 

 we had to limit ourselves in 1893 to the region 



2 <&'/*.< 75, 



the results in the present communication cover the interval 



0-08 < Vj\ < 2 ; 



if we consider the measurements for \ = 100 /jl carried out 

 with an angle of inclination £=60°, b'/X even becomes equal 

 to zero. 



The problem which we set ourselves in the beginning may 

 therefore be considered as solved. Indeed, the general result 

 throughout corresponds to expectation, in that a practically 

 complete Hertzian polarization finally occurred with all 

 gratings (§ 10). 



Our final result, which assumes quite a simple form, is 

 throughout in unison with the principles of the electro- 

 magnetic theory of radiation. The special theories mentioned 

 in the introduction also show the same final result, provided 

 that b/\ or dj\ be only sufficiently small. The theories are 

 still unsatisfactory with regard to the extended interval 

 between; the relations there are much more complicated 

 even, although they again simplify themselves in the first- 

 mentioned optical region. 



We are much indebted to Mr. Morris Ow T en for help in 

 preparing this paper. 



XXXIII. Some Aeiv Mechanical Quadratures. 

 By George F. Becker *. 



MECHANICAL quadratures are in some circumstances 

 unavoidable, but they are usually shunned as clumsy 

 and troublesome. Were the formulas neater and their 

 applicability better defined, they might be of great use in 

 experimental physics and might compete with other in- 

 tegrations by series in the computation of functions. This 

 paper is intended as a contribution to that end. 



There are three distinct systems of mechanical quadrature, 

 each depending upon the integration of a general formula 

 for interpolation. By integrating Newton's interpolation 

 formula, Simpson's rule, Weddle's rule and some others can 



* Communicated hv the Author. 



