286 Mr. W. D. Niven on the Calculation 



Table (continued). 





0. 



1. 



2. 



3. 



4. 



5. 



6. 



7. 



8. 



9. 



146... 



•7910 



•7870 



•7830 



•7790 



•7750 



•7710 



•7669 



•7629 



•7589 



•7549 



147... 



•7509 



•7470 



•7430 



•7391 



•7352 



•7312 



•7273 



•7234 



•7194 



•7155 



148... 



•7115 



•7077 



•7038 



•6999 



•6961 



•6922 



•6884 



•6845 



•6806 



•6768 



149... 



•6729 



■6691 



•6654 



•6616 



•6578 



•6540 



•6502 



•6465 



•6427 



•6389 



150... 



•6351 



•6314 



•6277 



•6239 



•6202 



•6165 



•6128 



•6091 



•6053 



•6016 



151... 



•5979 



•5943 



•5906 



•5870 



•5833 



•5797 



•5760 



•5724 



•5687 



•5651 



152... 



•5614 



•5578 



•5542 



•5506 



•5470 



•5435 



•5399 



•5363 



•5327 



•5291 



153... 



•5255 



•5220 



•5185 



•5149 



•5114 



•5079 



•5044 



•5009 



•4973 



•4938 



154... 



•4903 



•4868 



•4834 



•4799 



•4765 



•4730 



•4695 



•4661 



•4626 



•4592 



155... 



•4557 



•4523 



•4489 



•4455 



•4421 



•4387 



•4352 



•4318 



•4284 



•4250 



156... 



•4216 



•4183 



•4149 



•4116 



•4082 



•4049 



•4015 



•3982 



•3948 



•3915 



157... 



•3881 



•3848 



•4815 



•3782 



•3749 



•3716 



•3684 



•3651 



•3618 



•3585 



158... 



•3552 



•3520 



•3487 



•3455 



•3422 



•3390 



•3357 



•3325 



•3292 



•3260 



159... 



•3227 



•3195 



•3163 



•3132 



•3100 



•3068 



•3036 



•3004 



•2973 



•2941 



160... 



•2909 



•2877 



•2846 



•2814 



•2783 



•2751 



•2719 



•2688 



•2656 



•2625 



161... 



•2593 



•2562 



•2531 



•2500 



•2469 



•2439 



•2408 



•2377 



•2346 



•2315 



162... 



•2284 



•2254 



•2223 



•2193 



•2162 



•2132 



•2102 



•2071 



•2041 



•2010 



163... 



•1980 



•1950 



•1920 



•1890 



•1860 



•1831 



•1801 



•1771 



•1741 



•1711 



164... 



•1681 



•1652 



•1622 



•1593 



•1563 



•1534 



•1505 



•1475 



•1446 



•1416 



165... 



•1387 



•1358 



•1329 



•1300 



•1271 



•1243 



•1214 



•1185 



•1156 



•1127 



166... 



•1098 



•1070 



•1042 



•1013 



•0985 



•0957 



•0929 



•0900 



•0872 



•0844 



167... 



•0816 



•0788 



•0760 



•0732 



•0705 



•0677 



•0649 



•0621 



•0594 



•0566 



168... 



•0538 



•0511 



•0484 



•0456 



•0429 



•0402 



•0375 



•0347 



•0320 



•0293 



169... 



•0266 



•0239 



•0213 



•0186 



•0159 



•0133 



•0106 



•0080 



•0053 



•0027 



An example of the use of these Tables was given in the abstract which 

 was printed in the ' Proceedings ' of the Society, vol. xxv. p. 18. 



Postscript. 



Professor J. Couch Adams, to whom this paper was shown before 

 publication, has obtained a solution of the equations employed in the 

 second method, which is of a more complete and satisfactory character 

 than the one given aboye. The results he has arrived at are contained 

 in the following note, which he has kindly allowed me to subjoin :— 



" Employing the notation of the paper, and supposing the resistance to 

 vary as the nth power of the velocity, the horizontal velocity q is given 

 by the equation 



1 =^( S ee^J +, («-/5){H-^(n+l) [(«+2> ( se c^)"'-(« +!)](„ 



where a-/3 is expressed in the circular measure. 

 " The inclination of the chord AB is given by 



$ = £+£ + J J£? (« - /3) 4- 1 (tan a -+^)(« ~0f, 



where a— $ is supposed to be expressed as before in the circular measure. 

 If a— /3 be expressed in minutes, the last term must be multiplied by 

 sin 1'. 



