This instrument is a quadrant from north India or Nepal. It was used for telling the time and is quite unusual because it is labelled with Sanskrit numbers and letters.
© Museum of the History of Science, Oxford
Before the invention of clocks and watches, one way to tell the time was to use an horary quadrant. 'Quadrant' means one quarter of a circle. This instrument is called a quadrant because it just looks like a circle cut into four bits. Quadrants that are used to tell the time are called 'horary quadrants' because 'horary' means 'related to hours'. In the Renaissance one type of horary quadrant was even called the 'old quadrant' because it used a way of telling the time that was old even 400 years ago.
In Nepal and northern India the traditional way of telling the time doesn't use the same hours and minutes that we use now. Instead of the day starting at midnight and being split into 24 hours, the Nepali day begins at dawn and is divided into 60 equal parts called 'ghatis'. This means that one ghati equals 24 minutes. Instead of minutes, ghatis are divided into 60 'palas', and instead of seconds, each pala is divided into 60 'bipalas'.
To use a quadrant to tell the time you have to point it to the sun. A quadrant also has a plumb-line (a string with a weight on it) attached to one of its corners. After you have pointed the quadrant towards the sun you then read off the position of the plumb line against one of the scales engraved on the surface of the instrument.
The scales on a quadrant are hour scales. They work by relating the height of the sun in the sky to the time. This is a geometrical principle and requires a lot of mathematics to get it right. One complication is that the height of the sun in the sky at the same time of day changes during the year. For this reason quadrants have to have several different scales on them for the different months of the year. These are the different arcs you can see on the face of the quadrant in the picture.
Unlike many mathematical instruments in museums, this quadrant is not particularly finely made or engraved, although it is quite rare. This shows that it was probably made for someone to use from day to day to tell the time, rather than for a rich collector just to put in a display case and never use. One very nice feature on it is that it is engraved with the words 'This quadrant was made by Buhlo-Varma, having worshipped at the feet of the husband of the mountain goddess, so that the wise may know the time'. The mountain goddess is Parvati, the wife of Siva, the destroyer and one of the three main Hindu Gods.