126 



SCIENCE 



[N. S. Vol. XLII. No. 1073 



now abandoned, wliicli lie made concerning my 

 earlier paper, says: 



This assumption was supported by uncertainty 

 as to meaning and by lack of homogeneity of his 

 expression for the potential function introduced on 

 page 342 of Ms first paper; and still more by his 

 identification of astronomic with geocentric latitude 

 (on p. 339, same paper) by means of the loose 

 phrase "with sufficient approximation." A sim- 

 ilar lack of ' ' accuracy and precision ' ' will be 

 found in several parts of his latest paper cited 

 above. See, for example, his equations (j), wherein 

 he confounds geocentric with reduced latitude; 

 also p. 199, where he identifies his equations (38) 

 and (41) with my equation (26) and makes with 

 respect to them the surprising statement, ' ' it is, of 

 course, evident that this function corresponds to 

 some distribution of revolution" in the earth's 

 mass. 



I shall reply first to tte criticism concern- 

 ing the " identification of astronomic with 

 geocentric latitude." After having derived (in 

 my first paper) a general formula for the 

 meridional deviation of a falling body, I as- 

 signed various particular forms to the poten- 

 tial function and thus obtained the formulae 

 for the meridional deviations corresponding to 

 these particular potential functions. Some of 

 these potential functions were expressed in 

 terms of astronomic latitude, and others in 

 terms of geocentric. Consequently, the same 

 thing was true of the corresponding formulae 

 for the meridional deviation. For instance, 

 the formula of Gauss was expressed in terms 

 of astronomic latitude and several others were 

 expressed in terms of geocentric latitude. In 

 order to compare the magnitudes given by the 

 special formula I replaced, in the formula of 

 Gauss, the symbol representing astronomic 

 latitude by that representing geocentric, and 

 in so doing I used the expression " with suffi- 

 cient approximation " for which I am now 

 criticized. It is of course evident that by this 

 procedure a slight error was made in the 

 formula of Gauss after its rigorous form had 

 been derived. But none of the other work was 

 thereby affected, the derivation of the general 

 formula as well as that of each of the special 

 formula being strictly rigorous. Concerning 

 the criticism about my equations (/) I wish to 



say that the parameter ij/ may be regarded as a 

 geocentric latitude, since it is measured at the 

 center of the spheroid and from the equatorial 

 plane. I did not say that it was the geo- 

 centric latitude of the point (r, cr). How- 

 ever, it would have been well to mention that 

 it is called the reduced latitude of the point 

 (t, cr). But even if the reader interprets it as 

 the geocentric latitude of the point (r, a), the 

 argument in which it is used will not thereby 

 be vitiated. For, as I pointed out, the rela- 

 tion (l) in which it is used is approximate, 

 the relation (n) being the exact relation ap- 

 proximated. Now, the error made in using rela- 

 tion (Z) instead of relation (n) is twice as great 

 as the error made in relation (I) by calling 

 ij/ the geocentric instead of the reduced lati- 

 tude of the point (r, o-) . As regards the " sur- 

 prising statement," I should like to point out 

 that on page 192'^'* I defined a distribution of 

 revolution as one for which dV/dx, ^ 0, and 

 surely my function (38) satisfies this condition 

 since it does not contain the longitude A. 

 Then I was very particular to say — in the last 

 foot-note on page 199 — that for the assumption 

 B = A made by Dr. Woodward in his rela- 

 tions (31), his potential function (26) is the 

 same as my potential function (38). Con- 

 cerning the potential function introduced on 

 page 342 of my first paper, I stated that it had 

 been taken from Poincare, " Figures d'Equi- 

 libre d'une Masse Fluide " (1902), Chapt. V. 

 Following Poincare, I used the symbol M where 

 Dr. Woodward used the symbol Mk. In other 

 words, I suppressed the gravitation constant. 

 But it was easy to see from the expressions and 

 values of the constants that no error had been 

 made in so doing. Wm. H. Eoever 



Washington University, 

 St. Louis 



vegetative regeneration of alfalfa 

 When growing alfalfa plants in the green- 

 house, for infection experiments with the 

 crown-gall of alfalfa (Urophlyctis alfalfce), 

 the writer found it desirable to clip the shoots 

 at intervals in order to secure a multiplication 

 of the adventitious buds from the crown. 

 14 Astronomical Journal, Nos. 670-72. 



