APPENDIX. 



Formula and Tables in the Metric System (dated October, 1902).* 



It is easy to convert the formulae and tables of the preceding memoir from Eng- 

 lish into metric measures by using the following relations : 



mile „ , ,» „„^ meter 



Velocity, 1 r = 0.447 032 , . 



•' ' hour second 



mile meter 



Acceleration of velocity, 1 r 2 = 0.000 124 175 5 ,-, . 



■' hour second^ 



^. , . mile^ „,„ ,,, meter^ 



Circulation, 1 r = 719.415 3- . 



hour second 



mile' meter^ 

 Acceleration of circulation, 1 -. ^ — 0.199 837 5 -tj . 



The formulae of this memoir thus become converted respectively into the follow- 

 ing, where the units are the meter, the second of mean solar time and the degree 



centigrade : 



(2) g = ff,{l - 0.000 000 314(2 - z,)). 



(3) 5, = ^„(1 + 0.000 000 196(2„-s)). 



(4) F„ = ^„^„(l + 0.000 000 098g. 



(5) F= V^ + ^„2,(1 - 0-000 000 1 572,). 



(6) g^ = 9.80604(1 - 0.00259 cos 2\) (1 - 0.000 000 I962J. 



_ 0.760 X 9.80604 x 13.59593 p dp 

 ^^'> '"'~ 0.001293052x273 X, P ' 



(18) EJi= 660.9 (< + 273°)f/(log^). 



(19) n ^j = j3 ^„ ( 1 - 1 ««»•«-' Po '+"») . 



m\ t i 0-377'/(< + 273) 



* In order to meet any possible question of priority or responsibility it is proper to say that this memoir by J. W. 

 Sandstrom was received by Professor Cleveland Abbe in April, 1902, -with permission to translate and publish : the appen- 

 dix in metric measures vpas received in October, 1902. The translation by Dr. Cleveland Abbe, junior, was finished during 

 1903, and was read by Professor Abbe at the annual meeting of the American Philosophical Society, April, 1905. — C. A. 



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