396 Reports on Special Researches 



Suppose that a rod of length x be imagined supported at one end on a universal joint 

 at the element ds, so that the other end of the rod may be slid along the inner surface of the 

 cylinder. Let w be the solid angle subtended between the tangent plane to the cylinder at 

 ds, and the cone traced out by the rod as it rotates around a normal to this plane, with its 

 free end touching the inner wall of the cyUnder. Then, knowing the radius of the cyUnder, 

 it will obviously be possible to graphically determine co as a function of x. Again, if R is 

 the range of the a-particle, the loss of ionization due to the annihilation of the portion of 

 the path from x to J? is a function of {R-x) of the same fomi for a-particles from all types of 

 substances.^ The form of the function can be determuied from the ionization curve for 

 the a-particles. Calling this function f (R-x), we thus see that it is possible to plot f{R — x) 

 as a function of x, and so of w; and, as regards the a-particles emitted from the element ds, 

 the total loss of ionization as a result of the above action is, 



Pds[f{R-x)do} 

 where il is the value of co for .r = /?. Thus 



/ = 2irrPds - Pds CfiR - x)dw 



and observmg that ///o = l//i, we have, using (18), 



11 1 r" 



Ti=2~4^r\f(^-^^^^ (19) 



Jo 



With the ionization chamber used it was found that the second member on the right-hand 

 side of (19) constituted a correction of about 18 per cent on /. 



In view of the large amount of labor involved in analyzing the cui-ves, and of the 

 fact that the amount of emanation when calculated was extremely small, it was considered 

 sufficient to combine the curves for the separate days mto groups of about 10. The mean 

 cm-ve for each group was then drawn and the corresponding amount of emanation was 

 deduced according to the above scheme. For the purposes of a statement of the results, 

 in a more detailed but less absolute manner, the values of the quantity t; corresponding to 

 the time 3 minutes after the termination of the deposit have also been shown in Tables 79-83, 

 for each of the days on which observations were taken. 



RADIOACTIVE CONTENT OF THE SEA-WATER. 

 Attempts were first made to estimate this quantity by evaporating to dryness about 

 one liter of sea-water and testing the residue. The chief difficulty associated with this 

 method lies in the absorption, by the residue itself, of a large amount of the a-ray radiation. 

 Some observations have been made by this method, but it is now felt more satisfactory not 

 to attempt any actual determination of the radioactive content of the sea-water aboard the 

 vessel, but to forward the complete residues to Washington. Here they can be redissolved, 

 and their radium content may then be determmed by the charcoal method. Owing to the 

 desirability of making all such determinations at one time, this work has been postponed 

 until the completion of the Carnegie's fourth cruise. Thus, no data for the radium-emana- 

 tion content of the sea-water are record ed in this report. 



'Since, if the number of ions produced per unit length of path be plotted against the distance from the end of the range, 

 the curve so obtained is the same for all substances. 



