NOVEUBISB 6, 1914] 



SCIENCE 



683 



not seriously interfere ■witt the quantity of 

 water actually transferred; and a little con- 

 sideration will show that the amount of such 

 interference can be calculated with some cer- 

 tainty. 



Nothing has been said as to the nature of 

 a float suitable for indicating the motion in 

 the glass pipe. Somewhat as Forel in his 

 " plemyrameter " used corks weighted to the 

 specific gravity of water, so here a cylinder 

 having a diameter somewhat less than the in- 

 side diameter of the glass pipe, and having the 

 specific gravity of water, could be used. Each 

 of the metal ends of such cylinder should be 

 pierced by a hole, so that the cylinder could 

 be threaded loosely on a fine wire stretched 

 along the axis of the small pipe. However, 

 some other style of float may be preferable to 

 this. The readings should be made at regular 

 hourly or half -hour intervals. 



The amount whereby the observed i, prop- 

 erly corrected for pipe resistance, may fall 

 short of its simple theoretical value, i. e., its 

 value on a perfectly rigid earth devoid of 

 oceans, is an important factor in the deter- 

 mination of the amount of yielding of the 

 earth to the known tidal forces, and so in the 

 determination of the earth's rigidity. The 

 interpretation of such measurements, however, 

 constitutes no part of the present comm.unica- 

 tion. 



E. A. Harris 



Washington, D. C, 

 March 28, 1914 



[Since the above was written, I have seen 

 the surprisingly consistent results obtained by 

 Professor Miehelson and published in the 

 Journal of Geology and in the Astrophysical 

 Journal for March, 1914; also the account 

 published in Science for June 26, 1914. It 

 will be recalled that in these determinations, 

 the vertical oscillation of the water's surface 

 at the two ends of a half -filled horizontal pipe 

 was the quantity measured. E. A. H., Sep- 

 tember 29.] 



APPROXIMATE MEASUREMENT OF TEXTILE FIBERS 



This note is hardly the place for the demon- 

 stration of the following theorem. However, 



it is readily capable of demonstration, and the 

 reader of a mathematical turn of mind wiU at 

 once perceive the line of proof. 



Theorem. If an infinite series consisting of 

 straight parallel linear elements of every pos- 

 sible length, each element arranged perpen- 

 dicularly to and symmetrically to a given 

 straight line, be bisected along that line 

 and the two half-series thus produced be 

 placed with the former outer edges of adja- 

 cent, then if the elements of one of the half- 

 series be systematically rearranged, its longest 

 element matched to the shortest of the other 

 half-series and its next longest to the next 

 shortest of the other half-series and so on, a 

 new parallel-sided uniform series will be pro- 

 duced, each of whose elements has a length 

 equal to the mean length of the elements of 

 the original series. 



If the theorem be changed so that the ele- 

 ments are stated to vary in length within pre- 

 scribed limits,- then for this modified theorem 

 the line of demonstration as well as the final 

 result is the same. 



Fie. 1. Straight elements varying in length 

 within prescribed limits, arranged symmetrically 

 with reference to a given straight line, o-6, in 

 accordance with theorem. 



If the number of elements is limited, say, 

 for example, to a few thousand, the result be- 

 comes approximate; and if the elements in- 

 stead of having their middle points on the 

 given straight line are arranged so that their 

 middle points fall at random on either side of 

 the given straight line a distance less than 

 half the length of the shortest element, then 

 the reconstructed series will have a width ap- 

 proximately equal to the mean length of the 

 original elements; for it will always be pos« 



