38 REPOKTS ON Tllfi S'TAtE OF SCIENCE. — 1916. 



a point P upon it in the neighbourhood required. Taking AM:=1 inch, 

 then PM^' = AM x MB = 1 x 21. 



If next we take AM ^2 inches, then PM2=2x20. One or two 

 points may suffice. 



VIII. Dr. Klotz's Tables. 

 In some convenient tables recently published (' Pub. Dominion 

 Observatory, Ottawa,' vol. iii.. No. 2), Dr. Klotz, who, as above 

 remarked, proposed this method in 1911, has tabulated the values of 

 the above expressions under a slightly different form. "We have written 

 X for the polar distance of the observing station, so that if <^ be the 

 latitude \ = 90° - <^. Dr. Klotz has tabulated 



d= . ^°^» and r= . "° ^ 

 sin <p + cos A sin <j> + cos A 



for a large number of stations (not, however, including Shide, Bidston, 

 Edinburgh, and several other British stations !). He has also given 

 expanded tables for the times of travel of P and S, differing from those 

 used in the Shide Bulletins by the following quantities: — 



A = 10° 20° 30° 40° 50^ 60° 70" 80° 90° 100° 110° 



S. S. S. S. S. S. S. 8. 8. S. S. 



CorrectionP= -5 -4 -1 -5 -4 -3 -8 -13 -14 -17 -12 

 Correction S = -5 -4 -2 -5 -3 -3 -9 -13 -15 -17 -14 



It will be seen that the proposed corrections to the tables in use at 

 Shide (which are the original Zoppritz tables) are small, and are the 

 same for S and P, so that S— P remains unaltered- It is doubtful 

 whether we have as yet sufficient information to be sure of these small 

 quantities. 



Dr. Klotz has very conveniently added tables for PRi, PR2, SEi, and 

 SE2 ; but his table and diagram for PS are apparently erroneous. He 

 seems to have calculated this time by adding times for equal arcs for 

 P and S. 



Thus for A=10,000 km. he gives 



PS - P = lO" 36% P = 13°> 2', .-.PS = 23" 38'. 



Now P for 5,000 km.=8°' 28s S for 5,000 km. = 15" 10^ 



Sum of these last = 23°- 38'. 



By this method he shows PS in his diagram as arriving always 

 before S, whereas it always follows S when properly computed as the 

 maximum time for a combination of P and S. For A = 10,000 km. the 

 correct or maximum time for the combination PS is given (by Klotz's 

 tables) as about 24"" 57", thus: — 



m. s. 111. s. m. s. 

 P tor 2,200 km. and S for 7,800 km. = 4 35 + 20 20 = 24 55 

 P for 2,300 km. and S for 7,700 km. = 4 46 + 20 10 = 24 56 

 P for 2,400 km. and S for 7,600 km. = 4 57 + 20 = 24 57 

 P for 2,500 km. and S for 7,500 km. = 5 7 + 19 50 = 24 57 

 P for 2,600 km. and S for 7,400 km. = 5 18 + 19 39 = 24 57 

 P for 2,700 km. and S for 7,300 km. = 5 28 + 19 28 = 24 56 

 P for 2,800 km. and S for 7,200 km. = 5 38 + 19 17 = 24 55 



This method of adding the two times together and finding the 

 maximum or minimum is a simple and convenient practical way of 



