318 MR. p. W. BARLOW ON THE LAWS WHICH GOVERN 



Deductions from the tabular numbers. 

 The results obtained in Columns 17 and 18 will be seen to differ so much in many^ 

 cases from each other, as to throw an appearance of doubt upon the accuracy of the 

 experiments. These discrepances are attributable, in a great measure, to the result 

 depending upon the square of the difference of two velocities, so that the slightest 

 error in either of the observations is greatly magnified. As the velocity of the wheel 

 is derived from the number of strokes of the engine, the fraction of a stroke makes a 

 very sensible difference in the relative velocities ; and it is to this source that these 

 discrepances may be attributed, for the experiments not having been made with a 

 view to the present investigation, the importance of minute attention to this point was 

 not foreseen. 



There is no doubt, however, with so many experiments, made at different times and 

 under different circumstances, that the means obtained in the Table are sufficiently 

 near the truth for practical purposes. 



As the Table affords us several observations upon vessels of various tonnage and 

 horse power, I have considered it preferable to make a separate class of the larger 

 and smaller ones, because as the proportions of the wheel, and floats, and other cir- 

 cumstances are diflferent, a slight difference in the laws may exist which would be 

 lost sight of by making a general mean. 



The experiments are therefore divided into three classes : — 



1st Class. Vessels having the common wheel of greater diameter than nineteen feet. 



2nd Class. Vessels having the common wheel of a diameter less than nineteen feet. 



3rd Class. Vessels having the new wheels. 



To show what is stated above, that the differences in the results in Columns 17 

 and 18 of the Table may arise from the want of minute attention to the number of 

 strokes of the engine, and the approximation of the general means to the truth, I have 

 calculated what the number of strokes per minute would require to be to give the 

 mean number of each class. And it will be seen how much a fractional part of a 

 stroke per minute affects the numbers, and how little correction is necessary to pro- 

 duce the most accurate agreement in the result. 



1st Class. Mean = -157. 



Number of Number required to 



strokes observed. give the Mean. 



Messenger 20^ 20*5 



Messenger 18 17-8 



Dee 23 21*8 



Rhadamanthus 20 20*5 



Salamander 15 2^.2 



Phoenix 21 222 



19-6 



Monarch 20| 



Monarch 20^ 



Monarch 21 ...... 20*1 



2 



8 19-2 



