440 Proceedings of the Royal Irish Academy. 



purpose to be soon mentioned, tliis disk should have on one face a 

 graduation ; to 5° will be sufficient. 



Both the whirling machine and the Ajiemometcr should be pro- 

 vided with electric registration in some form. Por instance, springs 

 of platinum attached to their axles, and making at each revolution 

 contacts actuating small electro-magnets depressing pens to make dots 

 on a cylinder covered with paper and driven by a clock. Either the 

 cylinder or penholder must have a transverse motion, so that the dots 

 may be arranged in helices if the experiment should last for more than 

 one revolution of the cylinder. If the cii'cumference of the cylinder 

 and the time of its revolution be known, these will probably give the 

 time with sufficient accuracy to compute V. It need scarcely be said 

 that time must be allowed for the whirl to become uniform before the 

 register is made to act. 



The most obvious mode of using this apparatus to determine the co- 

 efficients is similar to that used by 31. Dohrandt ; but using the equation 

 (II.), and measuring/, and obtaining corresponding values of Fand v 

 through as wide a range as possible. Then by minimum squares obtain 

 the other co-efficients. I do not like this, because it gives no special in- 

 formation as to the variability of the co-eiflcients, should it exist ; and 

 because since V, except for the very small values of v, is nearly as 7nv, 

 neither minimum squares, nor common elimination, give accurate 

 results without carrying the calculation to a large number of decimals. 



/ 



The co-efS.cient a may be determined without difficulty. It = -^, 



Fo being the velocity which just moves the Anemometer from a state 

 of rest. If we increase the speed till it begin to move, we get F^. 

 This instant may be observed by the dropping of a disk of card, held 

 by friction against a stop, or by employing the electric register of 

 the Anemometer (which is not wanted here), to ring an alarm. One of 

 the cups should be set by means of the graduation on the brake disk 

 to ^ = 0, then to 5, 10, &c., to 90 ; and the mean should be taken 

 through the quadrant to give a. Then the friction should be increased 

 and the a obtained for higher values of Fq. Should these agree with 

 the former, this co-efficient is independent of F; if not, their relation 

 can be found and (II.) modified accordingly.* 



As to the other co-efficients, I have already said that the process of 

 minimum squares is not satisfactory on account of the small variation 

 of m' in a series of ordinary observations. But our apparatus enables 

 us by increasing / to increase m' to any extent. Put (II.) in the form 



am'- - 2/3m' - y - 4" = 0. (VI.) 



* Perfect agreement is not to be expected; for, as ali-eady remarked, the relocity 

 of the -B-hirling uiacHne gives only approximately the action of the air on the 

 rups : and the difference Mill increase M"ith the speed. 



