Civil Engineering - Surveying - Discussion

Here, it's 60/1080) *360.

@Shubham Vighne

1200-1080 = 120 seconds not 20 seconds.

An angle-measuring instrument reading up to one-sixth of a degree on the main scale is equipped with a vernier having 19 main scale divisions divided into 20 parts.
The correct least count for the instrument is 30 seconds.

The Least Count=(1/6 *)/20
=>1/6*60*60 sec/20 =30" ans.

Least count = S - V.

Where S is the length of one division of main scale which is nothing but least count of main scale and V is the length of one division of vernier scale.

From the above problem we can conclude that (n-1) division of main scale is divided into n division of vernier scale because 60 divisions of vernier coincide exactly with 59 divisions of the main scale.

Therefore, n*V=(n-1)*S ------- (A)

Now, S= L.C of main scale = 360/1080 = 1/3 degrees because in transit main plate there is a circle with 360 degrees.

S= (1/3) degrees = (1/3)* 3600 sec= 1200 seconds.

Now from (A) 60*V=59*1200
V=1080 seconds.
Therefore Least Count = S - V = 1200 - 1080 = 20 seconds.

Total angle 360.
Dividing in 1080 part.
So 1 part in main scale = 1/3 degree or 20'.
1 part of main scale dividing in vernier 60 part
So 1 part in vernier = 20'/60 = 1/3' = 20"

Least Count = S/n.

S = Least count of main scale = 360/1080
n = no of divion on vernier scale = 60

In transit main plate their is circle scale with 360 degree
So S=360/1080 = 1/3

Now least count = 1/3 ÷ 60 = 1/180 degree
Convert in seconds
L.C = 1/180 *60*60 =20 seconds.

(1080/60) - (1080/59)= .3°=20".

Least count = length of one division on the main scale/ no. of divisions of vernier.

Legth of one division on main scale= 360/1080.
= 0.3333333 degrees,
= 0.3333333 x 3600 sec,
= 1200 sec.

No of divisions of vernier = 60.

Therefore, Least count= 1200/60 = 20.

Thank you all for explaining it.

@Ansha.

The total degree of rotation =360°.