70 Prof. S. P. Thompson on Formulae 



speed at which each motor was wound to work at. Mr. 

 Clifford's results are arranged in tables which would be of 

 considerable practical value were it not that the essential 

 condition for making such tests has been absolutely dis- 

 regarded. Hence Mr. Clifford's tables are not only valueless 

 but are most misleading. We are able to speak definitely on 

 the subject, because the results of the tests made on a motor of 

 ours, which are quoted, are made with the motor running at 

 less than half its normal speed, and supplied with less than 

 one quarter of its normal power. As well might incandescent 

 lamps intended to be run with very different P.Ds. be com- 

 pared when run with totally wrong P.Ds., and a 100-volt lamp 

 condemned as useless because when supplied with only 50 

 volts it emitted but little light. 



IX. On the Formulae of Bernoulli and of Haecker for the 

 Lifting -poiver of Magnets. By Professor Silvanus P. 

 Thompson*. 



EOKMULiE for the lifting-power of magnets have been 

 given by D. Bernoulli and by Haecker, and more re- 

 cently by Van der Willigen. 



Bernoulli's empirical rule f is that the lifting-power varies 

 as the cube root of the square of the magnet's weight, or 



P a ^W 2 , 



where P is the lifting power or pull exerted by the magnet 

 in contact with its keeper, and W the mass of the magnet. 



Haecker \ gave precision to the rule by introducing a co- 

 efficient, the numerical value of which varies with the qualities 

 of steel employed. Writing 



Prrav'W 2 , 



he found that (when the unit of mass taken was the German 

 pound) a had values between 8 and 10 for bar-magnets, and 

 double these values for horseshoe-magnets. That is to say, 

 according to Haecker a steel horseshoe-magnet weighing 

 1 pound could lift between 16 and 20 pounds, according to the 

 quality of the steel and the intensity of its magnetization. 

 The formula was found to be reasonably valid for magnets 

 between y^ pound up to 40 pounds in weight. 



Van der Willigen §, repeating the investigation partly with 



* Communicated by the Physical Society ; read May 26, 1888. 

 t Acta Helvetica, iii. p. 233 (1758). 

 % Pogg. Ann. lvii. p. 321 (1842). 



§ Sur le magnetisme des aimants artijiciels, par V. S. M. Van der 

 Willigen (Haarlem, 1878). 



