Febeuaby 21, 1902.] 



SCIENCE. 



291 



served the northeastern sky from the same 

 line. The count was as follows: 



Nov. 14. 1:^:15 to 13:40. Miss Post and Miss 

 Greenough, 38; Miss Post — northeastern sky, 31; 

 Miss Greenough — southeastern sky, 31. 13:40 to 

 14:20. Messrs. Post and Kees looking out of the 

 opening in the roof of the Observatory toward 

 the radiant, 20. 14:20 to 15:00. Miss Post- 

 northeastern sky, 10; Miss Greenough, southeast- 

 ern sky, 16. 15:50 to 17:55. The Misses Post 

 and Greenough counted being assisted from 16:30 

 to 17:55 by Post and Rees. The total count of 

 the four observers was 273. Total for the even- 

 ing, 418. 



Nov. 15. Post and Pees assisted by Mr. Post's 

 'handy man' counted, while engaged on the photo- 

 graphic work and looking out of the observatory 

 opening, as follows: 11:45 to 13:00. 25, several 

 of which were non-Leonids. 14:35 to 15:45. 3 

 of which 1 non-Leonid. 16:01 to 17:00. 23, sev- 

 eral non-Leonids. 



Nov. 16. 12:00 to 17:00. Looked out frequent- 

 ly but saw so few that no record was kept. 



3. Individual Meteors. 



Nov. 14. 11:30. Two bright Leonids — trails 

 yellow-red 10° long — width very distinct. 

 11:51. Leonid from Proeyon to 6 Orionis — blue 

 streak. 12:07. From star above Proeyon to 

 'yardstick' — trail 25° long — lasted several sec- 

 onds — ^yellow — Leonid. 12:10. Leonid through 

 Ursa Major — bright trail. 12:15. Leonid 

 through Ursa Major. 12:17. Leonid through 

 Auriga. 13:18. Brilliant Leonid, near radiant — 

 very small trail — orange color — bright as Mars at 

 best. 13:27. Fine Leonid from Leo to zenith — 

 trail 30° long — yellow-red. 13:30. Leonid 

 through Ursa Major — fine. 13:40. Meteor near 

 Proeyon — from zenith down-^short trail. 13:44. 

 Fine Leonid through bowl of dipper — trail 5°. 

 13:51. Leonid under Proeyon — 8° trail — ^yellow- 

 red. 15:58. Brilliant Leonid — trail 5° — lasted 

 twenty seconds — ^blue- white — 1st magnitude. 

 16:04. Leonid under Proeyon — blue-white — 10° 

 trail. 17:28. Two brilliant meteors visible at 

 same time — trails crossed — bright heads. One 

 came from radiant and passed near a and /3 Can. 

 Ven. — trail 30° long and lasted several seconds. 

 The second seemed to come from below /3 Leonis 

 and cut the trail of the first under Canes Venatici 

 — ^trail 30°. Magnitude of each — 2. 



Nov. 15. 14:52. Bright Leonid under Leo 

 Minor. 15:37. Leonid bright as Jupiter — in 

 sickle-^blue and red trail. About 15:55. Fire 



ball below Leo came from Orion. 16:10. From 

 zenith through Leo Minor ( 1 and /i ) — long train 

 40°. About 17:00. The zodiacal light showed 

 itself in a grandly beautiful manner. 



A Theorem concerning the Method of 

 Least Squares: Harold Jacoby. 

 The following theorem and conclusion 

 are doubtless Avell known to many astron- 

 omers, but the writer has not found an ex- 

 plicit statement of them in print. Let 

 there be given two series of observation 

 equations as follows: 



a^x -\- b.^y -\- c^z -\ 1- m^ = 



(1) 



"i^; + 6i2/ -(- c,z -I -f PiW H 1- «! = 01 



OjZ -f 62J/ + Cg2 4 \-p-iV>-\ h «-i = I- (2) 



the equations being identical in the two 

 series except for the addition of one or 

 nxore new unknowns, iv, . . . in (2). Let 

 each series of equations be solved by the 

 method of least squares, and let [t'v]i be 

 the sum of the squares of the residuals re- 

 sulting from the solution of equations (1), 

 [vv]o be the sum of the squares of the 

 residuals resulting from the solution of 

 equations (2) ; then, no matter what may 

 be the law of the coefficients p^, Pa? ■ • • j 

 and even if these coefficients are assigned 

 at random, [vvl^^ is always larger than 

 [vv]^. 



Corollary.— The theorem can be ex- 

 tended easily to an additional case of 

 equal importance. Instead of introducing 

 the new unknowns w, . . . , by adding them 

 to those already occurring in equations (1), 

 we may select out certain equations from 

 the series (1), and simply substitute new 

 unknowns, like iv, for old ones, like z, leav- 

 ing the coefficients unchanged. 



Conclusion. — The method of least 

 squares is used ordinarily to adjust series 

 of observation equations so as to obtain the 

 most probable values of the unknowns. But 



