STABILITY, PROPULSIONj AND SEA-GOING QUALITIES OF SHIPS. 41 



deviation from the mean line ; but they evidently would not disclose any 

 steady inclination to which the rolling might be superadded. 



The gyroscope or top will, of course, have its own proper oscillatory revo- 

 lution, which, however, soon spins out, on the same principle that a peg-top 

 " sleeps." 



On the whole, there does not seem to be much room for improvement in 

 Admiral Paris's instrument, unless, perhaps, in diminishing the atmospheric 

 resistance. Possibly also provision might be made for adjusting the point of 

 support to the centre of gravity. 



Recommendation of Experiments on Moiling. 



* 



The mathematical theory of rolling is very far from easy, and leads to equa- 

 tions of which there is no known solution. The time of a common pendulum, 

 for instance, depends upon an elliptic integral, and, beyond the degree of 

 complexity involved in such a function, mathematics are in the condition of 

 uncleared ground. Accordingly, while it is possible to give a rational 

 account of the immediate gross results of a compound oscillation, these 

 results cannot be expressed or measured with the requisite combination of 

 generality and accurac3^ In order to treat them, we are obliged to intro- 

 duce simplifying suppositions, which do not necessarily belong to our pro- 

 blem — as, for instance, isochronism, or the neglect of certain elements of 

 resistance, or the grouping of others. 



Now, Avhen this occurs with any branch of practical knowledge, the proper 

 mode of applying mathematical investigation is to start, not from the known 

 principles of general mechanics, but from an advanced base of observations 

 peculiar to the science itself. In hydrodj-namics, between minuteness and 

 number, the ultimate molecular unit escapes our notice, and we are only 

 able to observe effects in the gross ; being thereby driven to a certain want 

 of detail, both of observation and of reasoning, which allows us to trust our 

 conclusions only when they have been made to rest on a broad experimental 

 foundation. Whether we regard the theory of the propulsion of ships, or 

 that of their rolling, our analysis has assuredly been pushed quite to the 

 extreme verge to which general reasoning can be trusted ; and a largely in- 

 creased extent of exact observation ought to precede further attempts at 

 inductive reasoning on these subjects. We have many exact experiments on 

 propulsion, although, from the complicated character of the phenomena in- 

 volved, it is difficult to separate the issues ; and this wiU probably not be set 

 right without further special investigation. With regard to rolling, how- 

 ever, we have much vague observation, and but little exact knowledge de- 

 rived from experiment. 



We are not aware of any one published experiment on the rolling of ships 

 in waves in which the details necessary to make any mathematical use of 

 the results are supplied. The data required are, as a minimum for each 

 case, — 



1. A draught of the ship, and her calculated elements. 



2. The position of her centre of gravity. 



3. Her periodic time in still water. 



4. The condition of her wet surface. 



5. The extent and period of her roll. 



6. Was the rolling simple, or mixed with pitching ? 



7. The height, length, and period of the waves in which she was rolHng. 



8. Were these waves simple ? 



9. What alterations have been made in her displacement, her trim, and 



