Mabch 23, 1906.] 



SCIENCE. 



463 



4. With a three-and-one-lialf-inch Goerz 

 doublet of thirty-three and one half inches 

 focus (used during the previous expedi- 

 tions of 1896, 1900 and 1901), attached to 

 one of the automatic movements, sixty-three 

 fine pictures of the corona were secured 

 during the 186 seconds of totality. Some 

 of these show the coronal streamers to ex- 

 ceptional length. 



5. Sketches of the corona, were made 

 with the usual results. 



6. Observations of the shadow bands 

 were begun at least ten minutes prior to 

 totality. The bands were wavering and 

 narrow, moving faster than one could walk 

 and at right angles to the wind, their 

 length with it. They were observed to 

 wax and wane five times during the in- 

 terval of observation preceding totality. 

 These observations have been communi- 

 cated in detail to Mr. Lawrence Rotch, of 

 Blue Hill and embodied in his exhaustive 

 study of this phenomenon. 



Computed Traces and Totality -Durations 

 of the Total Solar Eclipses of the 

 Ttventieth Century: Professor David 

 Todd and E. H. Bakee, Amherst College, 

 Amherst, Mass. Read by title. 

 A Possible Extension of the Theory of 

 Envelopes: Professor L. G. Weld, State 

 University of Iowa, Iowa City, la. 

 '{a) In the equation f{x,y,a) =0, rep- 

 resenting a family of loci, by giving to a, 

 first an increment aud then a corresponding 

 decrement, each of magnitude Aa, solving 

 the resulting equations for the coordinates 

 of the point of intersection and, finally, 

 letting Aa = 0, there will be obtained 



a;' = 0(a), y' = yf>{a). 



These equations define a point of the en- 

 velope of the given family of loci and 

 eliminating a between them gives 



F(x',y')=0, 

 the equation of the envelope. 



The point {x',y'), determined as above, 



may be called the tracing point of the locus, 

 that is, the point which, for the moment, 

 is tracing the envelope. It was shown in 

 the paper, by way of illustration, that the 

 tracing point for the envelope of the family 

 of ellipses, 



is the Fagnag-ni point. 



(6) The inverse of the above notion was 

 nest developed with reference to the right 

 line, viz. : A point on the line 



;+ 



:1, 



being assigned at will, to find the func- 

 tional relation between the intercepts, 



*{a,|8) =0 



{i. e., the law governing the motion of the 

 line), in order that the given point may 

 trace an envelope and, finally, to obtain 

 the equation of the envelope. The re- 

 quired relation is given by either of the 

 differential equations, 



/32 



a/ = 0(a, /3). 



2/' = *(a, /3): 



/J — a 



dl3' 



„da^ 

 "-^dlS - -da 



In general both equations will be needed 

 in order to determine the constants of in- 

 tegration. Having thus obtained the func- 

 tion #, which is, in effect, the tangential 

 equation of the envelope, the equation in 

 rectangular coordinates readily follows. 



Several examples applying the principles 

 were presented and its application to other 

 families of loci was suggested as a prom- 

 ising field of investigation for the amateur 

 mathematician. 



Laenas Giffoed Weld, 



Secretary. 



SCIENTIFIC BOOKS. 

 Die Schule der Chemie. Erste Einfiihrung 

 m die Chemie fiir Jedermann. Von Wil- 

 HELM Oswald. Zweiter Teil. Die Chemie 

 der wichtigsten Elements und Verbind- 

 ungen. Braunschweig, Friedrich Vieweg 

 und Sohn. 1904. Price, bound, 8 Marks. 



