un the Production of Steam from heated Iron. 75 



almost exactly coincident with an arithmetical progression. Thus the 

 12th series, from the 11th to the 20th experiment, inclusive, may- 

 be regarded as composed of the numbers 8, 9, 10, 11, 12, 13, 14, 

 15, 16, 17, while from the 23rd to the 28th, we have 26, 30, 36, 

 44, 59, 89, yielding the ratios || = 1.153, || = 1.200, || = 1.222, 

 11 = 1.341, and |f = 1.508, and the mean of all these ratios is 1.285. 

 By similar operations applied to the concluding part of every series 

 in this course ex-cept the first and second, we obtain the following 

 mean ratios for the several series respectively, viz. 

 for the 3rd series 1.290 



If we would know the mean of all their mean ratios, we have but 

 to divide their sum by 10, the number of series considered, whence 

 we obtain 1.296 for the general ratio of this part of the several se- 

 ries. It will, however be remarked that the five ratios belonging to 

 the 11th series are themselves in geometrical progression, whose 

 mean ratio is 1.07. 



In order to present to the eye the whole range of experiments in 

 some of the series, I have adopted the method of curvilinear projec- 

 tion, assuming as the unit of vapor, the amount actually employed at 

 each trial, and as the unit of time, the number of seconds taken to 

 vaporize it, at the period of most rapid action. Representing these 

 units by equal vertical and horizontal lines respectively, the relative 

 time of action in each experiment marked on the line a c, is denoted 

 by the dotted lines, a d, eg, &;c. Figs. 1, 2 and 3. Regarding ab 

 as a constant quantity, we have the portions of time above the mini- 

 mum, represented by that part of each vertical which is above the 

 tangent bf. It will be seen by Fig. I. that the arithmetical series 

 exists in the 6th, 7th, and 8th experiments. Fig. 2d. shows the 

 same feature at the 17th 18th, and 19th, while the 12th series, rep- 

 resented by Fig. 3, shows a straight line from No. 11, to No. 20, as 

 already stated. See the plate at p. 71. 



