44 Compendious Logarithmic Tables. [No. 121. 



the body of the table, the successive differences will be found in the 

 corresponding part of the same vertical columns throughout the table. 

 The proportional parts are found exactly in the same way ; and thus, for 

 finding the whole of the common differences and proportional parts, 

 only ten calculations are needed ; the remaining labour being merely to 

 transcribe from the columns in the body of the table, taking care to 

 keep the numbers always true in the last figure. 



The whole of the differences and proportional parts, after being written 

 in, have been carefully re-examined, and I hope it will be found that 

 these precautions have not been misapplied, so as to have failed as to 

 the object intended. 



These tables are of the minimum size, at least I do not see the possi- 

 bility of making them any smaller without rendering them useless. 

 Lalande " after 50 years' experience," at page 6, of the preface to his 

 Tables, makes the following remarks on the advantage of smallness : — 



" La plupart des calculs n'exigent que les minutes : les astronomes, 

 ' les navigateurs, les militaires, les geographes, les arpenteurs, les archi- 

 ' tectes, ont un besoin continuel de petites tables, bien plus rarement des 

 ' grandes. Si Ton cherche les minutes dans un gros volume qui con- 

 1 tient les secondes, on perd du terns. Le format de celui-ici n'exige 

 ' rigoreusement que le terns necessaire a l'operation : d'ailleurs les vues 

 ' basses ont de la peine avec les grandes tables ; enfin plus le volume est 

 ' mince, plus il est commode a l'usage ordinaire. Ainsi j'ai reduit 

 ' celui-ci au pur necessaire.". 





