1873.] in determining the best Course for a Ship. 267 



It seems strange that so useful and definite a conception as that of the 

 contour we have been considering should not long since have acquired a 

 name. The idea in its general application is not unfamiliar to us, 

 because we are all accustomed to reflect how far we can travel in an 

 hour's walk, ride, or drive from our house, in various directions, and we 

 know that the distances in different directions vary according to the good- 

 ness or straightness of the road. Nevertheless our vocabulary does not 

 admit of an expression of the idea upon which this memoir is based, with- 

 out a tedious paraphrase including references to (1) equal and specified 

 times, (2) direct geographical distance, (3) universality of directions, and 

 (4) a bounding line. I therefore propose to employ the word isochrone 

 (equality of time) in a special sense in this memoir, meaning thereby all 

 that is expressed by the contour just described, which I should call the 

 " isochrone from A," the unit of measurement being understood to be a 

 single day's sail, unless otherwise specified. The isochrone towards A will 

 be the same figure reversed and inverted. 



The lines of swiftest passage from one port to another can only be de- 

 termined after computation of the isochrones for a sufficient number of 

 ocean districts within the region of inquiry to enable those at any par- 

 ticular spot, or as much of them as is needed, to be found by interpola- 

 tion. It seems to me perfectly impossible to draw any portion of an 

 isochrone, except in a rudely approximative way, without previous com- 

 putation. Calculation to 8 or 16 points takes so long to perform, and small 

 differences in the mean force of the winds have so large an influence, 

 that no human brain is competent to deduce correct results after a mere 

 inspection of the data. As an example, I may be allowed to mention 

 that I asked a naval officer of unusually large experience in the construc- 

 tion of weather charts, and who was familiar with the sailing qualities of 

 a " Beaufort standard ship," to estimate portions of isochrones in certain 

 cases ; and I found the mean error of his estimates to exceed 15 per cent. 

 The guesses of ordinary navigators would necessarily be much more wide 

 of the truth. Now we must recollect that a very small saving on the 

 average length of voyages would amount to an enormous aggregate of 

 commercial gain, and that, where precision is practicable, we should never 

 rest satisfied with the rule of thumb. Our meteorological statistics afford 

 the best information attainable at the present moment, and they exceed 

 by some hundredfold the experiences of any one navigator ; their pro- 

 bable errors may nevertheless be large, but that is no reason for need- 

 lessly associating them with additional subjects of doubt. The probable 

 error of a navigator's estimate of an isochrone, and consequently of the 

 data which he must use, whether consciously or not, whenever he. attempts 

 to calculate his best track, is due at the present time to no less than three 

 distinct sets of uncertainties : — a, the average weather ; b, the performance 

 of his ship on different courses with winds of different force (which I under- 

 stand to be hardly ever ascertained with much precision) ; c, the computa- 



