192 Transactions. 



specimens having the dorsal surface almost wholly covered with brown 

 markings. 



Length, 5 mm. ; breadth, 2 mm. 



Hah. — New Plymouth and Mount Egmont, in nests of Amhlyopone 

 cephalotes and Huheria striata (W. W. Smith) ; Rai Valley, in nests of ants 

 (J. MacMahon). Probably widely distributed in the North Island and in 

 the north-western portion of the South Island. 



The specimens from Greymouth collected by Mr. R. Helms, which I had 

 previously referred with hesitation to T. otakensis* belong to the present 

 species. I have specimens also from Swanson, Auckland (H. Suter), and 

 one from Kapiti Island (E. A. Newson). The last specimen is much browner 

 than those actually taken in ants' nests by Mr. Smith and Mr. MacMahon, 

 and it is possible that it was not living in association with ants. There is 

 the same doubt with regard to the Greymouth and Auckland specimens. 



Art. XVII. — The Cam-lever Balance. 



By J. Clemext Cuff. 



[Read before the Auckland Institute, 22nd November, 1909.] 



" Cam-lever balance " is the name given by the author to a modification 

 of the bent-lever balance whereby the scale becomes regular throughout 

 its whole length. 



The bent-lever balance is more convenient in use than any other form 

 of gravity balance because it indicates the weight by direct observation 

 without having to slide a counterpoise, or shift the fulcrum, or put counter- 

 balancing weights in a scale-pan. A spring balance also has these advan- 

 tages, but a spring is not so reliable and constant as gxavity. On the score 

 of simplicity of construction and delicacy of action a bent-lever balance 

 is better than a spring balance. The one gxeat defect of the bent-lever 

 balance is the irregularity of its scale ; therefore this paper is written to 

 explain clearly how this solitary defect of this otherwise excellent form 

 of balance can be remedied in a very simple way. 



In the bent-lever balance the counterpoise arm is actually much longer 

 than the scale-pan arm, and these lengths are constant, but the virtual 

 lengths of the two arms change with every change of weight in the scale- 

 pan. The virtual length of the arm is the horizontal distance between 

 the fulcrum and a line drawn vertical to the centre of gravity of the arm 

 and its attached or suspended weight. If the angle of deflection of the 

 long arm from the vertical be called A, then the virtual length of the long 

 arm will vary as the sine of A, and the virtual length of the short arm will 

 vary as the cosine of A, exactly if the efiective directions of the two arms 

 are at right angles, otherwise approximately. This relationship gives a 

 scale increasingly compressed in the direction of the higher readings. 



* Trans. Linn. Sue, 2nd ser., Zool., vol. viii, p. 117. 



